IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Singularity condition of wrist partitioned 6-r serial manipulator based on gr...eSAT Journals
Abstract
To prevent the singularity of serial robot’s due to the lost of one or more degree of twist freedom, it is necessary to determine the
Jacobian matrix J associated to its instantaneous motion and analyze the vanishing condition of the determinant det (J). Usually,
the large expression of det (J) does not facilitate an efficient geometric analysis. Since Grassmann-Cayley Algebra (GCA) has
powerful tools for geometric interpretation of coordinate free representation and singularity analyzing in real time computing,
this method is implemented in the present work. The goal of this research is to determine the singularity condition of wristpartitioned
6-R serial manipulator (SM) based on GCA. The symbolic approach of Plücker coordinate lines is used to formulate
the twist system (TS) of SM. The twist system is similar to det (J) which rows are Plücker coordinate lines. The vanishing
condition of det (J) based on the linearity condition of TS is determined without algebraic coordinate and provides a single
singularity condition which contains all generals and particulars cases. The keys elements of transition between the rows of J and
singularity condition of a twist-partitioned 6-R SM are the introduction of the symbolic approach of Plücker coordinate lines and
superbracket. The vanishing points of the superbracket are analyzed to describe the singularity condition. The result indicates
that for a wrist-partitioned 6-R SM a single singularity condition contains three generals cases such as the shoulder, elbow and
wrist singularity. Since the three last axis of the wrist are no-coplanar and intersecting at a unique point, it is suggested that for a
wrist-partitioned 6-R serial manipulator, the wrist singularity never occurs physically, except that its design will be modified.
Index Terms: Singularity, 6-R Serial Manipulators, Grassmann-Cayley Algebra, Projective space, Twist graph
This work presents the kinematics model of an RA-
02 (a 4 DOF) robotic arm. The direct kinematic problem is
addressed using both the Denavit-Hartenberg (DH) convention
and the product of exponential formula, which is based on the
screw theory. By comparing the results of both approaches, it
turns out that they provide identical solutions for the
manipulator kinematics. Furthermore, an algebraic solution of
the inverse kinematics problem based on trigonometric
formulas is also provided. Finally, simulation results for the
kinematics model using the Matlab program based on the DH
convention are presented. Since the two approaches are
identical, the product of exponential formula is supposed to
produce same simulation results on the robotic arm studied.
Keywords-Robotics; DH convention; product of exponentials;
kinematics; simulations
The document discusses representing position and orientation of robotic systems using coordinate frames and homogeneous transformations. It introduces coordinate frames and describes how to represent position as a point and orientation as a set of axes. Rotations between frames can be represented by rotation matrices, and transformations between frames are described using homogeneous coordinates. Euler angles provide a method to represent orientation using three angles but require careful consideration of axis sequences due to non-commutativity of rotations.
Position analysis and dimensional synthesisPreetshah1212
This document provides an overview of position analysis and dimensional synthesis for kinematics of machines. It discusses topics such as position and displacement, dimensional synthesis, function generation, path generation, motion generation, limiting conditions like toggle positions and transmission angles, and both graphical and algebraic methods for position analysis including vector loops and the use of complex numbers. The key steps of graphical position analysis and the algebraic algorithm using Freudenstein's equation are described.
This document discusses forward and inverse kinematics examples of different types of robot manipulators including 2R, 3R, and 3P manipulators. It provides examples of solving forward and inverse kinematics for specific manipulator types, including:
1) PUMA robot with both concurrent and non-concurrent wrists. The inverse kinematics is solved to find the joint positions given the end effector position and orientation.
2) SCARA manipulator with RRP pairs as arms. The forward and inverse position calculations are demonstrated.
3) Cylindrical and spherical robots with 3 DOF non-concurrent wrists. The procedures for obtaining the inverse kinematics solutions are described.
4
The Geometric Characteristics of the Linear Features in Close Range Photogram...IJERD Editor
The accuracy of photogrammetry can be increased with better instruments, careful geometric
characteristics of the system, more observations and rigorous adjustment. The main objective of this research is
to develop a new mathematical model of two types of linear features (straight line, spline curve) in addition to
relating linear features in object space to the image space using the Direct Linear Transformation (DLT). The
second main objective of the present paper is to study of some geometric characteristics of the system, when the
linear features are used in close range photogrammetric reduction processes. In this research, the accuracy
improvement has been evaluated by adopting certain assessment criteria, this will be performed by computing
the positional discrepancies between the photogrammetrically calculated object space coordinates of some check
object points, with the original check points of the test field, in terms of their respective RMS errors values. In
addition, the resulting least squares estimated covariance matrices of the check object point's space coordinates.
To perform the above purposes, some experiments are performed with synthetic images. The obtained results
showed significant improvements in the positional accuracy of close range photogrammetry, when starting node,
end nodes, and interior node on straight line and spline curve are increased with certain specifications regarding
the location and magnitude of each type of them.
This document discusses kinematics and mechanisms design. It introduces kinematic pairs, degrees of freedom, and the Chevychev-Grübler-Kutzbach criterion. It describes four-bar linkages and their inversions using Grashof criteria. It discusses coupler curves and adjustable mechanisms for continuous path generation. Equations are provided for determining the driving link angular displacement required to generate a desired coupler curve based on linkage geometry. Conditions for generable coupler curves are defined. Synthesis of cam-follower mechanisms is also briefly mentioned.
The document discusses the kinematic modeling of robot manipulators. It introduces the forward and inverse kinematic problems and describes how the Denavit-Hartenberg convention is used to assign reference frames to each link of a robotic arm. This convention specifies assigning frames using four parameters - link offset (d), joint angle (θ), link length (a), and link twist (α). Together these parameters define the homogeneous transformation between adjacent links via rotation and translation operations, allowing the complete forward kinematic model to be described with minimal parameters.
Singularity condition of wrist partitioned 6-r serial manipulator based on gr...eSAT Journals
Abstract
To prevent the singularity of serial robot’s due to the lost of one or more degree of twist freedom, it is necessary to determine the
Jacobian matrix J associated to its instantaneous motion and analyze the vanishing condition of the determinant det (J). Usually,
the large expression of det (J) does not facilitate an efficient geometric analysis. Since Grassmann-Cayley Algebra (GCA) has
powerful tools for geometric interpretation of coordinate free representation and singularity analyzing in real time computing,
this method is implemented in the present work. The goal of this research is to determine the singularity condition of wristpartitioned
6-R serial manipulator (SM) based on GCA. The symbolic approach of Plücker coordinate lines is used to formulate
the twist system (TS) of SM. The twist system is similar to det (J) which rows are Plücker coordinate lines. The vanishing
condition of det (J) based on the linearity condition of TS is determined without algebraic coordinate and provides a single
singularity condition which contains all generals and particulars cases. The keys elements of transition between the rows of J and
singularity condition of a twist-partitioned 6-R SM are the introduction of the symbolic approach of Plücker coordinate lines and
superbracket. The vanishing points of the superbracket are analyzed to describe the singularity condition. The result indicates
that for a wrist-partitioned 6-R SM a single singularity condition contains three generals cases such as the shoulder, elbow and
wrist singularity. Since the three last axis of the wrist are no-coplanar and intersecting at a unique point, it is suggested that for a
wrist-partitioned 6-R serial manipulator, the wrist singularity never occurs physically, except that its design will be modified.
Index Terms: Singularity, 6-R Serial Manipulators, Grassmann-Cayley Algebra, Projective space, Twist graph
This work presents the kinematics model of an RA-
02 (a 4 DOF) robotic arm. The direct kinematic problem is
addressed using both the Denavit-Hartenberg (DH) convention
and the product of exponential formula, which is based on the
screw theory. By comparing the results of both approaches, it
turns out that they provide identical solutions for the
manipulator kinematics. Furthermore, an algebraic solution of
the inverse kinematics problem based on trigonometric
formulas is also provided. Finally, simulation results for the
kinematics model using the Matlab program based on the DH
convention are presented. Since the two approaches are
identical, the product of exponential formula is supposed to
produce same simulation results on the robotic arm studied.
Keywords-Robotics; DH convention; product of exponentials;
kinematics; simulations
The document discusses representing position and orientation of robotic systems using coordinate frames and homogeneous transformations. It introduces coordinate frames and describes how to represent position as a point and orientation as a set of axes. Rotations between frames can be represented by rotation matrices, and transformations between frames are described using homogeneous coordinates. Euler angles provide a method to represent orientation using three angles but require careful consideration of axis sequences due to non-commutativity of rotations.
Position analysis and dimensional synthesisPreetshah1212
This document provides an overview of position analysis and dimensional synthesis for kinematics of machines. It discusses topics such as position and displacement, dimensional synthesis, function generation, path generation, motion generation, limiting conditions like toggle positions and transmission angles, and both graphical and algebraic methods for position analysis including vector loops and the use of complex numbers. The key steps of graphical position analysis and the algebraic algorithm using Freudenstein's equation are described.
This document discusses forward and inverse kinematics examples of different types of robot manipulators including 2R, 3R, and 3P manipulators. It provides examples of solving forward and inverse kinematics for specific manipulator types, including:
1) PUMA robot with both concurrent and non-concurrent wrists. The inverse kinematics is solved to find the joint positions given the end effector position and orientation.
2) SCARA manipulator with RRP pairs as arms. The forward and inverse position calculations are demonstrated.
3) Cylindrical and spherical robots with 3 DOF non-concurrent wrists. The procedures for obtaining the inverse kinematics solutions are described.
4
The Geometric Characteristics of the Linear Features in Close Range Photogram...IJERD Editor
The accuracy of photogrammetry can be increased with better instruments, careful geometric
characteristics of the system, more observations and rigorous adjustment. The main objective of this research is
to develop a new mathematical model of two types of linear features (straight line, spline curve) in addition to
relating linear features in object space to the image space using the Direct Linear Transformation (DLT). The
second main objective of the present paper is to study of some geometric characteristics of the system, when the
linear features are used in close range photogrammetric reduction processes. In this research, the accuracy
improvement has been evaluated by adopting certain assessment criteria, this will be performed by computing
the positional discrepancies between the photogrammetrically calculated object space coordinates of some check
object points, with the original check points of the test field, in terms of their respective RMS errors values. In
addition, the resulting least squares estimated covariance matrices of the check object point's space coordinates.
To perform the above purposes, some experiments are performed with synthetic images. The obtained results
showed significant improvements in the positional accuracy of close range photogrammetry, when starting node,
end nodes, and interior node on straight line and spline curve are increased with certain specifications regarding
the location and magnitude of each type of them.
This document discusses kinematics and mechanisms design. It introduces kinematic pairs, degrees of freedom, and the Chevychev-Grübler-Kutzbach criterion. It describes four-bar linkages and their inversions using Grashof criteria. It discusses coupler curves and adjustable mechanisms for continuous path generation. Equations are provided for determining the driving link angular displacement required to generate a desired coupler curve based on linkage geometry. Conditions for generable coupler curves are defined. Synthesis of cam-follower mechanisms is also briefly mentioned.
The document discusses the kinematic modeling of robot manipulators. It introduces the forward and inverse kinematic problems and describes how the Denavit-Hartenberg convention is used to assign reference frames to each link of a robotic arm. This convention specifies assigning frames using four parameters - link offset (d), joint angle (θ), link length (a), and link twist (α). Together these parameters define the homogeneous transformation between adjacent links via rotation and translation operations, allowing the complete forward kinematic model to be described with minimal parameters.
Kinematic Model of Anthropomorphic Robotics Finger MechanismsIOSR Journals
Abstract: Research on Kinematic Model of Anthropomorphic robotics Finger mechanisms is being carried out
to accommodate a variety of tasks such as grasping and manipulation of objects in the field of industrial
applications, service robots, and rehabilitation robots. The first step in realizing a fully functional of
anthropomorphic robotics Finger mechanisms is kinematic modeling. In this paper, a Kinematic Model of
Anthropomorphic robotics Finger mechanism is proposed based on the biological equivalent of human hand
where each links interconnect at the metacarpophalangeal (MCP), proximal interphalangeal (PIP) and distal
interphalangeal (DIP) joints respectively. The Kinematic modeling was carried out using Denavit Hartenburg
(DH) algorithm for the proposed of Kinematic Model of Anthropomorphic robotics Finger mechanisms.
Index Terms— Anthropomorphic robot Finger, Modeling, Robotics, Simulation
This document compares kinematic and dynamic models for robotics. The kinematic model studies robot motion without considering forces/torques, and can be used to determine end effector position from joint positions. The dynamic model relates joint torques to motion, and is important for analyzing a robot's dynamic behavior. Key differences include the kinematic model using Denavit-Hartenberg notation while dynamic models employ Lagrange-Euler and Newton-Euler formulations. Both models are essential for robot control and simulation.
This document discusses redundancy in robotics. It defines a kinematically redundant robot as having more degrees of freedom than needed to place an end effector in a desired location. For example, a robot with more than six degrees of freedom can be redundant for tasks in three-dimensional space which only require six degrees. Redundancy allows for multiple feasible inverse kinematics solutions and can be used to achieve additional objectives like avoiding obstacles or singularities. However, redundant robots are also more complex, expensive, and difficult to control.
This document provides an overview of basic joints, kinematics concepts, and coordinate frame transformations using matrices. It defines spherical, revolute, and prismatic joints. It also defines forward and inverse kinematics. The document then reviews dot products, matrix operations, and basic transformations including translation, rotation, and combining them into homogeneous transformations using 4x4 matrices.
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
This document discusses forward and inverse kinematics, including:
1. Forward kinematics determines the position of the robot hand given joint variables, while inverse kinematics calculates joint variables for a desired hand position.
2. Homogeneous transformation matrices are used to represent frames, points, vectors and transformations in space.
3. Standard robot coordinate systems include Cartesian, cylindrical, and spherical coordinates. Forward and inverse kinematics equations are provided for position analysis in each system.
A New Method For Solving Kinematics Model Of An RA-02IJERA Editor
The kinematics miniature are established for a 4 DOF robotic arm. Denavit-Hartenberg (DH) convention and the
product of exponential formula are used for solving kinematic problem based on screw theory. For acquiring
simple matrix for inverse kinematics a new simple method is derived by solving problems like robot base
movement, actuator restoration. Simulations are done by using MATlab programming for the kinematics
exemplary.
This document discusses different types of spline curves used for modeling, including polynomial splines, interpolation splines, and approximation splines. It describes linear spline interpolation which uses linear polynomials to pass through control points. Cubic spline interpolation is discussed next, using cubic polynomials and additional constraints to determine coefficients. Natural cubic splines are described as satisfying C2 continuity across knots. Hermit splines are introduced as allowing local control of tangents at endpoints. Blending functions for Hermit splines are provided.
1. The document discusses differential kinematics and how it can be used to examine the pose velocities of robot frames. It also covers Jacobians and how they map between joint and Cartesian space velocities.
2. Specific topics covered include differential transformations, screw velocity matrices, relating velocities in different frames, determining Jacobians for serial and parallel robots, and examining robot singularities.
3. Singularities occur when the mechanism loses mobility in certain directions and joint rates will increase near these configurations. Workarounds include tooling design, changing to joint space control near singularities, and carefully planning paths.
Java3D is an Application Programming Interface used for writing 3D graphics applications and applets. This paper gives a short introduction of java3D, analyses the mathematics of Hermite, Bezier, FourPoints, B-Splines curve, and describes implementation of curve creation and curve
operations using Java3D API.
This document discusses robot kinematics and various representations used to describe the position and orientation of objects in 3D space. It introduces the homogeneous transformation matrix which uses rotation and translation operators to relate coordinate frames. Different coordinate systems like Cartesian, cylindrical and spherical are covered. It also discusses Euler angles, Denavit-Hartenberg parameters and their rules for assigning coordinates to define the kinematic structure of a robot.
This document provides an introduction to robot kinematics. It discusses the basic joints used in robotics including revolute, spherical, and prismatic joints. It covers forward and inverse kinematics problems. Key concepts explained include homogeneous transformations using 4x4 matrices to represent rotations and translations between coordinate frames, and rotation matrices for transforming between 3D coordinate systems. Examples are provided for finding the homogeneous transformation matrix between different robot link frames.
The document discusses dynamic modeling of robot manipulators using the Euler-Lagrange approach. It introduces dynamic models and the direct and inverse problems. The Euler-Lagrange approach is then explained in detail. It involves computing the kinetic and potential energies of each link based on the link masses, centers of mass, moments of inertia, and joint velocities and positions. This allows deriving the dynamic equations of motion for the manipulator.
The document discusses manipulator kinematics, which refers to the position and orientation of a robot's end effector as a function of time, without regard to forces or mass. It describes different methods for representing an end effector's position, including joint space and world space methods. The key difference between forward and backward transformations is that forward transformation maps from joint space to world space, while backward transformation maps from world space to joint space. Accuracy refers to how well a robot can reach a desired location, while repeatability refers to how well it can return to a previously taught point.
This paper deals with certain configuration spaces
where the underlying geometry is sub-Riemannian because of the
physical constraints arising out of the mechanical systems we are
interested in. A motivated introduction to Sub-Riemannian
structures is included following which we look at the broad
science of mechanics where in the sub-Riemannian geometric
study aids us to talk about applications like robotics and image
analysis.
Kinematics of machines can involve either analyzing an existing mechanism's motion or synthesizing a new mechanism to achieve a desired motion. Kinematic synthesis involves selecting the type of mechanism, determining the number of links needed, and defining the link dimensions. Dimensional synthesis aims to develop link dimensions such that the mechanism's output motion matches the desired motion at select precision points, often spaced using Chebyshev's method to minimize error between points. Slider-crank mechanisms can be synthesized by relating the slider displacement to crank angle at precision points defined using Chebyshev spacing.
The kinematics analysis and trajectory planning of Series robotIJRES Journal
In this paper, a series robot as the research object, using theoretical analysis, numerical simulation method of
combining, to carry out the overall performance analysis and optimization of industrial robots trajectory. For serial
robot, kinematics modeling. The establishment of a first-order influence coefficient method based on
second-order influence coefficient matrix, kinematic and dynamic analysis of performance indicators based on
both Jacobin matrix and Hessian matrix, and the actual size of the work and working space agencies, institutions
initially selected size. Finally, institutional performance indicators for institutional map drawing performance,
combined with the flexibility and maneuverability determine the size of a set of different institutions in the
optimal configuration, and its feasibility through simulation. According to the geometric characteristics of the
surface complex surface fragmentation process, solve the optimal value speed and coating spray width of the
overlapping area on each patch.
This document chapter discusses manipulator kinematics. It covers forward kinematics, which is determining the end effector position from joint angles. Inverse kinematics is determining the joint angles required for a desired end effector position. The manipulator Jacobian relates joint velocities to end effector velocities. Redundant manipulators have more degrees of freedom than required to perform a task. The chapter provides the procedure for determining the forward kinematics, including using the product of exponentials formula. An example of calculating forward kinematics for a SCARA manipulator is also presented.
This document discusses homogeneous coordinate transformations for robot manipulators. It presents two theorems for transforming coordinates between reference frames after rotation. An example problem calculates the position and orientation matrices to transform between the initial and final end effector coordinates for a system picking up an object with three pegs from a table and placing it on an inclined plane. The solution finds the rotation and transformation matrices between the different reference frames attached to the object and end effector to specify its position and orientation in both cases.
This document summarizes a research paper that presents a continuous sliding mode controller (CSMC) for balancing an inverted pendulum system. The CSMC improves upon integral sliding mode control (ISMC) by replacing the discontinuous term, eliminating chattering while maintaining robustness. A super twisting algorithm is used as a disturbance estimator. Simulation results demonstrate the effectiveness of the proposed CSMC at stabilizing the pendulum and depicting its robustness. The document provides mathematical modeling of the inverted pendulum system and formulates the control objective of designing a nonlinear robust controller to balance the pendulum using a continuous sliding mode approach.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Kinematic Model of Anthropomorphic Robotics Finger MechanismsIOSR Journals
Abstract: Research on Kinematic Model of Anthropomorphic robotics Finger mechanisms is being carried out
to accommodate a variety of tasks such as grasping and manipulation of objects in the field of industrial
applications, service robots, and rehabilitation robots. The first step in realizing a fully functional of
anthropomorphic robotics Finger mechanisms is kinematic modeling. In this paper, a Kinematic Model of
Anthropomorphic robotics Finger mechanism is proposed based on the biological equivalent of human hand
where each links interconnect at the metacarpophalangeal (MCP), proximal interphalangeal (PIP) and distal
interphalangeal (DIP) joints respectively. The Kinematic modeling was carried out using Denavit Hartenburg
(DH) algorithm for the proposed of Kinematic Model of Anthropomorphic robotics Finger mechanisms.
Index Terms— Anthropomorphic robot Finger, Modeling, Robotics, Simulation
This document compares kinematic and dynamic models for robotics. The kinematic model studies robot motion without considering forces/torques, and can be used to determine end effector position from joint positions. The dynamic model relates joint torques to motion, and is important for analyzing a robot's dynamic behavior. Key differences include the kinematic model using Denavit-Hartenberg notation while dynamic models employ Lagrange-Euler and Newton-Euler formulations. Both models are essential for robot control and simulation.
This document discusses redundancy in robotics. It defines a kinematically redundant robot as having more degrees of freedom than needed to place an end effector in a desired location. For example, a robot with more than six degrees of freedom can be redundant for tasks in three-dimensional space which only require six degrees. Redundancy allows for multiple feasible inverse kinematics solutions and can be used to achieve additional objectives like avoiding obstacles or singularities. However, redundant robots are also more complex, expensive, and difficult to control.
This document provides an overview of basic joints, kinematics concepts, and coordinate frame transformations using matrices. It defines spherical, revolute, and prismatic joints. It also defines forward and inverse kinematics. The document then reviews dot products, matrix operations, and basic transformations including translation, rotation, and combining them into homogeneous transformations using 4x4 matrices.
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
This document discusses forward and inverse kinematics, including:
1. Forward kinematics determines the position of the robot hand given joint variables, while inverse kinematics calculates joint variables for a desired hand position.
2. Homogeneous transformation matrices are used to represent frames, points, vectors and transformations in space.
3. Standard robot coordinate systems include Cartesian, cylindrical, and spherical coordinates. Forward and inverse kinematics equations are provided for position analysis in each system.
A New Method For Solving Kinematics Model Of An RA-02IJERA Editor
The kinematics miniature are established for a 4 DOF robotic arm. Denavit-Hartenberg (DH) convention and the
product of exponential formula are used for solving kinematic problem based on screw theory. For acquiring
simple matrix for inverse kinematics a new simple method is derived by solving problems like robot base
movement, actuator restoration. Simulations are done by using MATlab programming for the kinematics
exemplary.
This document discusses different types of spline curves used for modeling, including polynomial splines, interpolation splines, and approximation splines. It describes linear spline interpolation which uses linear polynomials to pass through control points. Cubic spline interpolation is discussed next, using cubic polynomials and additional constraints to determine coefficients. Natural cubic splines are described as satisfying C2 continuity across knots. Hermit splines are introduced as allowing local control of tangents at endpoints. Blending functions for Hermit splines are provided.
1. The document discusses differential kinematics and how it can be used to examine the pose velocities of robot frames. It also covers Jacobians and how they map between joint and Cartesian space velocities.
2. Specific topics covered include differential transformations, screw velocity matrices, relating velocities in different frames, determining Jacobians for serial and parallel robots, and examining robot singularities.
3. Singularities occur when the mechanism loses mobility in certain directions and joint rates will increase near these configurations. Workarounds include tooling design, changing to joint space control near singularities, and carefully planning paths.
Java3D is an Application Programming Interface used for writing 3D graphics applications and applets. This paper gives a short introduction of java3D, analyses the mathematics of Hermite, Bezier, FourPoints, B-Splines curve, and describes implementation of curve creation and curve
operations using Java3D API.
This document discusses robot kinematics and various representations used to describe the position and orientation of objects in 3D space. It introduces the homogeneous transformation matrix which uses rotation and translation operators to relate coordinate frames. Different coordinate systems like Cartesian, cylindrical and spherical are covered. It also discusses Euler angles, Denavit-Hartenberg parameters and their rules for assigning coordinates to define the kinematic structure of a robot.
This document provides an introduction to robot kinematics. It discusses the basic joints used in robotics including revolute, spherical, and prismatic joints. It covers forward and inverse kinematics problems. Key concepts explained include homogeneous transformations using 4x4 matrices to represent rotations and translations between coordinate frames, and rotation matrices for transforming between 3D coordinate systems. Examples are provided for finding the homogeneous transformation matrix between different robot link frames.
The document discusses dynamic modeling of robot manipulators using the Euler-Lagrange approach. It introduces dynamic models and the direct and inverse problems. The Euler-Lagrange approach is then explained in detail. It involves computing the kinetic and potential energies of each link based on the link masses, centers of mass, moments of inertia, and joint velocities and positions. This allows deriving the dynamic equations of motion for the manipulator.
The document discusses manipulator kinematics, which refers to the position and orientation of a robot's end effector as a function of time, without regard to forces or mass. It describes different methods for representing an end effector's position, including joint space and world space methods. The key difference between forward and backward transformations is that forward transformation maps from joint space to world space, while backward transformation maps from world space to joint space. Accuracy refers to how well a robot can reach a desired location, while repeatability refers to how well it can return to a previously taught point.
This paper deals with certain configuration spaces
where the underlying geometry is sub-Riemannian because of the
physical constraints arising out of the mechanical systems we are
interested in. A motivated introduction to Sub-Riemannian
structures is included following which we look at the broad
science of mechanics where in the sub-Riemannian geometric
study aids us to talk about applications like robotics and image
analysis.
Kinematics of machines can involve either analyzing an existing mechanism's motion or synthesizing a new mechanism to achieve a desired motion. Kinematic synthesis involves selecting the type of mechanism, determining the number of links needed, and defining the link dimensions. Dimensional synthesis aims to develop link dimensions such that the mechanism's output motion matches the desired motion at select precision points, often spaced using Chebyshev's method to minimize error between points. Slider-crank mechanisms can be synthesized by relating the slider displacement to crank angle at precision points defined using Chebyshev spacing.
The kinematics analysis and trajectory planning of Series robotIJRES Journal
In this paper, a series robot as the research object, using theoretical analysis, numerical simulation method of
combining, to carry out the overall performance analysis and optimization of industrial robots trajectory. For serial
robot, kinematics modeling. The establishment of a first-order influence coefficient method based on
second-order influence coefficient matrix, kinematic and dynamic analysis of performance indicators based on
both Jacobin matrix and Hessian matrix, and the actual size of the work and working space agencies, institutions
initially selected size. Finally, institutional performance indicators for institutional map drawing performance,
combined with the flexibility and maneuverability determine the size of a set of different institutions in the
optimal configuration, and its feasibility through simulation. According to the geometric characteristics of the
surface complex surface fragmentation process, solve the optimal value speed and coating spray width of the
overlapping area on each patch.
This document chapter discusses manipulator kinematics. It covers forward kinematics, which is determining the end effector position from joint angles. Inverse kinematics is determining the joint angles required for a desired end effector position. The manipulator Jacobian relates joint velocities to end effector velocities. Redundant manipulators have more degrees of freedom than required to perform a task. The chapter provides the procedure for determining the forward kinematics, including using the product of exponentials formula. An example of calculating forward kinematics for a SCARA manipulator is also presented.
This document discusses homogeneous coordinate transformations for robot manipulators. It presents two theorems for transforming coordinates between reference frames after rotation. An example problem calculates the position and orientation matrices to transform between the initial and final end effector coordinates for a system picking up an object with three pegs from a table and placing it on an inclined plane. The solution finds the rotation and transformation matrices between the different reference frames attached to the object and end effector to specify its position and orientation in both cases.
This document summarizes a research paper that presents a continuous sliding mode controller (CSMC) for balancing an inverted pendulum system. The CSMC improves upon integral sliding mode control (ISMC) by replacing the discontinuous term, eliminating chattering while maintaining robustness. A super twisting algorithm is used as a disturbance estimator. Simulation results demonstrate the effectiveness of the proposed CSMC at stabilizing the pendulum and depicting its robustness. The document provides mathematical modeling of the inverted pendulum system and formulates the control objective of designing a nonlinear robust controller to balance the pendulum using a continuous sliding mode approach.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Rule based messege filtering and blacklist management for online social networkeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document summarizes a research paper that proposes a parallel k-nearest neighbors (kNN) algorithm using OpenCL on a GPU architecture. The key points are:
1) kNN classification is computationally intensive, especially for large datasets, creating a need for parallelization.
2) The authors designed and implemented a parallel kNN algorithm using OpenCL to distribute distance computations across GPU cores.
3) Experimental results on UCI datasets showed the parallel kNN approach improved performance over a serial kNN implementation.
Self checking approach for reducing soft errors in states of fsmeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
System to convert 2 d x-ray image into 3-d x-ray image in dentistryeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Hyperspectral image mixed noise reduction based on improved k svd algorithmeSAT Publishing House
This document summarizes a proposed algorithm for reducing mixed noise in hyperspectral imagery. Hyperspectral images capture information across the electromagnetic spectrum and can be represented as three-dimensional tensors. The proposed method uses tensor decomposition and an improved K-SVD algorithm to adaptively detect and remove Gaussian noise, impulse noise, and mixtures of these from hyperspectral data. It formulates the noise removal problem using a weighted regularization approach and solves related optimization problems using techniques like singular value decomposition. The goal is to separate noise and noise-free components to reconstruct a cleaned hyperspectral image tensor.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Soft subgrade stabilization with quarry dust an industrial wasteeSAT Publishing House
This document summarizes a study on stabilizing soft subgrade soil using quarry dust, an industrial waste product. Laboratory tests were conducted on soil mixed with various percentages of quarry dust. Tests found that adding up to 40% quarry dust decreased the soil's liquid limit and plasticity index while increasing the maximum dry density and California Bearing Ratio (CBR), indicating increased strength. Specifically, soil mixed with 40% quarry dust saw a 5.88% increase in maximum dry density and a 228% increase in CBR compared to the unmodified soil. The study thus demonstrates the potential of using quarry dust to improve soft subgrade soil for supporting flexible pavements in a more economical way compared to removing and replacing
Factors affecting def and asr in the concrete dam at vrané nad vltavoueSAT Publishing House
1) The document examines factors affecting delayed ettringite formation (DEF) and alkali-silica reaction (ASR) in concrete from a dam in Vrané nad Vltavou, Czech Republic.
2) Samples were taken from 8 locations and tested for residual expansion, then analyzed using microscopy techniques. The sample with the highest residual expansion and microcracking was periodically exposed to water.
3) DEF was found to be the primary degradation mechanism. The sample most affected was located 1 meter above the water line and contained aggregates of acidic volcanic rock that are susceptible to DEF when periodically exposed to water.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Modeling of laminar flow tubular reactor using velocity profileeSAT Publishing House
This document describes a new model for modeling laminar flow tubular reactors (LFTRs) without using residence time distribution (RTD) data. The model divides the reactor into 3D grid cells that each act as continuous stirred tank reactors (CSTRs) in series. The velocity profile within the LFTR is used to calculate flow rates and residence times for each cell. Conversion is then determined for each cell assuming ideal CSTR behavior. The model was tested on LFTRs and showed good agreement with established analytical methods without requiring computationally intensive simulations. The number of grid cells was optimized to balance accuracy and processing time.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
The document discusses a study on the properties of banana fiber reinforced composites. Banana fibers were treated with sodium hydroxide and used to reinforce both epoxy and vinyl ester resin matrices. Coconut shell powder was also used along with the fibers. Various mechanical properties including tensile strength, flexural strength, and impact strength were tested for the untreated and treated fiber composites. The treated fiber composites showed improved mechanical properties compared to the untreated fibers due to better adhesion between the fiber and matrix. A hybrid composite containing both banana fiber and coconut shell powder showed higher strength values than the banana fiber only composite.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Comparative analysis of singularities of 3 prs and 3-prs parallel manipulator...eSAT Journals
Abstract
Grassmann-Cayley Algebra (GCA) is a symbolic approach to Plücker coordinates lines. It is used to write expressions for
geometric incidences in projective geometry.GCA gives a useful way to analyze mechanism singularity without algebraic
coordinate expression. Since it has great powerful tools for coordinate’s free representation, geometric interpretation and
singularity analyzing in real time computing, this method is implemented in the present research. The goal of this study is finding
the singularities conditions of 3-PRS Parallel Manipulators (PMs) based on GCA when the position of the actuators is firstly on
prismatic joints and secondly on revolute joints. Geometric method of reciprocal screw is used to formulate the Global Wrench
System (GWS) of the PMs. GWS represents the determinant of Jacobian matrix which rows are Plücker coordinate lines. The
degeneracy analysis of determinant of this matrix based on the dependency notion of Plücker coordinate lines is performed in
coordinate free expressions and provides double and single singularities conditions, respectively for3-PRS and 3-PRS PMs,
which contains all generals and specials cases. The keys elements of transition between the rows of Jacobian matrix and
singularity condition are the introduction of Plücker lines, superbrackets, join and meet operators. The vanishing points of these
superbrackets decomposition are analyzed to describe the singularity conditions associated with different motions. The results
indicate that for the 3-PRS and 3-PRS PMs, a common singularity occurs when the three constraints forces of the mobile platform
lie on the common plane and intersect at a unique point. It is suggested that both position and orientation of the actuator have to
be integrated in the conceptual design stage in order to optimize the rigidity frame of the mechanism.
Key Words: Singularity, 3-PRS Parallel Manipulators, Grassmann-Cayley Algebra, Projective space, Wrench graph.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document summarizes the kinematics analysis of a 3-UPU (universal-prismatic-universal) parallel robot. Each of the robot's three legs consists of two universal joints connected by a prismatic joint. The document establishes recursive matrix relations for solving the inverse kinematics problem given the position of the mobile platform. Simulation graphs are generated for the input displacements, velocities, and accelerations. The kinematics analysis determines the nine independent variables that define the robot's configuration based on vector-loop equations relating the joint parameters and platform position.
A Detailed Comparative Study between Reduced Order Cumming Observer & Reduced...IJERD Editor
In this article a detailed comparative study between two well known observer design methodologies
namely, reduced order Cumming observer & reduced order Das &Ghoshal observer has been presented. The
necessary equations & conditions corresponding to these two types of observers are discussed in brief.
Thereafter with the help of a structure wise comparison the similarities & dissimilarities between the above
mentioned methods are explained in details. Finally a performance wise comparison between these two is shown
using proper numerical example & illustrations in open loop as well as closed loop.
Design and analysis of x y- positioning stage based on redundant parallel li...eSAT Journals
Abstract This paper presents the concept of a planar positioning stage based on a kinematically redundant parallel linkage. Basic kinematics and workspace analysis of base redundant manipulator is initially explained and the procedure of static analysis to predict the actuated joint torques is described. As there are six actuators in the linkage, the redundancy can be overcome by proper selection of the base joint variables. Also it is assumed that the motion is at a constant speed. A numerical example is shown with a straight line trajectory to illustrate the workspace and joint force calculation aspects of this linkage. The possible arrangement of the stage with electrostatic actuation and sensing are finally highlighted. Keywords: Kinematic redundancy, Parallel mechanism, Static analysis, and Workspace characteristics
This document describes the design and analysis of a planar positioning stage based on a redundantly actuated parallel linkage. The positioning stage has three degrees of freedom (x-y-θ) and uses a 3-PRPR linkage with six actuators. The document analyzes the kinematics and workspace of the linkage. It describes the procedure for static analysis to calculate the actuated joint torques. The positioning stage could enable high-precision motion with a compact design and improved stiffness compared to serial linkages. It is proposed for potential use in micro-scale applications.
This document describes the design and analysis of a planar positioning stage based on a redundantly actuated parallel linkage with six degrees of freedom (three translations and three rotations). The kinematics and workspace analysis of the linkage are presented. A static analysis method to calculate the actuator torques required for a given end-effector force and trajectory is also described. MATLAB programs were developed to analyze the workspace and perform the static analysis. The results show that the redundant actuation can help improve the workspace characteristics and prevent singular configurations compared to non-redundant parallel manipulators. The stage design has potential applications in micro-positioning.
This document discusses the theoretical and experimental study of dynamics and control of a two-link flexible robot arm. It presents the following:
1) A linear dynamic model of the robot arm is constructed using Ritz's approach and validated experimentally.
2) Three active control schemes are designed using pole placement technique for path tracking and vibration suppression, and tested via simulation.
3) A discrete-time state variable feedback control scheme is presented and designed to control the robot arm's motion using three sensors for position and curvature feedback.
A METHODOLOGY FOR ANALYSIS OF TOPOLOGICAL CHARATERISTICS OF PLANETARY GEAR TR...meijjournal
A planetary trains for multi-speed is mainly used for automation in industries of automobile. A planetary
gear train is represented by a graph. It is identified by (i) number of vertices and their connectivity (ii)
number of edges and their types and values (iii) fundamental circuits, their size and adjancy. Connectivity
of individual link is a property characteristic of kinematic chain. It is possible to identify a planetary gear,
therefore of using sets of labele (decimal numbers representing connectivity ) of individual link. The
connectivity of vertices , edges values and circuit values, related to design invariants which in turn
indicates the possible behavior of the gear train ( for example capacity of power transmission, speed ratio
and power carculation). For a specified degree – of – freedom a number of planetary gear kinematic chain
(PGKCs) are selected and hence planetary gear trains (PGTs) can be formed with a given number of links
and joints so that designer must be able to select to select the best train from the view point of say velocity
ratio and capacity of power transmission, space requirements etc. Synthesis of planetary gear kinematic
chain and planetary gear trains has been studied(1-9). Almost all reported work deals with only
identification of distinct chains. Besides providing an atlus of chains, this in itself does not provide any help
to designer in the selection of best possible gear train. In the present paper a simple method based of
circuit property ( based on link-link shortest path distance and degree of links) is presented to determine
the topology values of power transmission efficiency and topology power transmission capacity of five-links
PGKCs and their distinct inversions.
Pick and place task is one among the most important tasks in industrial field handled by “Selective
Compliance Assembly Robot Arm” (SCARA). Repeatability with high-speed movement in horizontal plane is
remarkable feature of this type of manipulator. The challenge of design SCARA is the difficulty of achieving
stability of high-speed movement with long length of links. Shorter links arm can move more stable. This
condition made the links should be considered restrict then followed by restriction of operation area
(workspace). In this research, authors demonstrated on expanding SCARA robot’s workspace in horizontal area
via linear sliding actuator that embedded to base link of the robot arm. With one additional prismatic joint the
previous robot manipulator with 3 degree of freedom (3-DOF), 2 revolute joints and 1 prismatic joint is become
4-DOF PRRP manipulator. This designation increased workspace of robot from 0.5698m2 performed by the
previous arm (without linear actuator) to 1.1281m2 by the propose arm (with linear actuator). The increasing
rate was about 97.97% of workspace with the same links length. The result of experimentation also indicated
that the operation time spent to reach object position was also reduced.
Regularity and complexity in dynamical systemsSpringer
This chapter discusses how variational methods have been used to analyze three classes of snakelike robots: 1) hyper-redundant manipulators guided by backbone curves, 2) flexible steerable needles, and 3) concentric tube continuum robots. Variational methods provide a means to determine optimal backbone curves for manipulators, generate optimal plans for needle steering, and model equilibrium conformations for concentric tube robots based on elastic mechanics principles. The chapter reviews how variational formulations using Euler-Lagrange and Euler-Poincare equations are applied in each case.
Insect inspired hexapod robot for terrain navigationeSAT Journals
Abstract The aim of this paper is to build a sixlegged walking robot that is capable of basicmobility tasks such as walking forward, backward, rotating in place and raising orlowering the body height. The legs will be of a modular design and will have threedegrees of freedom each. This robot will serve as a platform onto which additionalsensory components could be added, or which could be programmed to performincreasingly complex motions. This report discusses the components that make up ourfinal design.In this paper we have selected ahexapod robot; we are focusing &developingmainly on efficient navigation method indifferent terrain using opposite gait of locomotion, which will make it faster and at sametime energy efficient to navigate and negotiate difficult terrain.This paper discuss the Features, development, and implementation of the Hexapod robot Index Terms:Biologically inspired, Gait Generation,Legged hexapod, Navigation.
This document discusses stiffness analysis of flexible parallel manipulators. It presents the forward kinematics analysis of a 3-RRR planar parallel manipulator using genetic algorithms and neural networks to minimize positional errors. The Jacobian and platform stiffness matrices are evaluated within the defined workspace. A pseudo-rigid body model with frame and plate elements is used to analyze the flexible link configuration and compliant joints. Stiffness indices are obtained and validated using commercial finite element software. The methodology is illustrated for a 3-RRR flexible parallel manipulator to study the effects of link flexibility and joint compliance on stiffness.
Dr. Jayanta Kr. Mahato will give a lecture on Miller indices for directions and planes. The lecture will introduce the need for describing directions and planes in crystals, define Miller indices, and explain how to determine the Miller indices for directions and planes. Examples will be provided and important features of Miller indices discussed, such as planes being identical to their negatives and directions having the same indices as perpendicular planes in cubic systems. Homework problems will involve calculating Miller indices for given planes and sketching specific planes in a cubic unit cell. Referred study materials are provided.
Attitude Control of Quadrotor Using PD Plus Feedforward Controller on SO(3)IJECEIAES
This paper proposes a simple scheme of Proportional-Derivative (PD) plus Feedforward controller on SO(3) to control the attitude of a quadrotor. This controller only needs the measurement of angular velocity to calculate the exponential coordinates of the rotation matrix. With rotation matrix as an error variable of the controller, the simulation shows that the controller is able to drive the attitude of the quadrotor from hovering condition to desired attitude and from an attitude condition goes to the hovering condition, despite the system is disturbed. When the system is convergent, the rotation error matrix will be a 3 3 identity matrix.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The document presents a new approach for dynamic analysis of parallel manipulators based on the principle of virtual work. It illustrates the approach using a simple 4-bar linkage example, calculating the inertial forces and moments, virtual displacements, and input torque. It then generalizes the approach for dynamic analysis of a 6 degree-of-freedom parallel manipulator like a Gough-Stewart platform. The approach leads to faster computation than traditional Newton-Euler methods by not requiring calculation of constraint forces between links.
The cubic root unscented kalman filter to estimate the position and orientat...IJECEIAES
In this paper we introduce a cubic root unscented kalman filter (CRUKF) compared to the unscented kalman filter (UKF) for calculating the covariance cubic matrix and covariance matrix within a sensor fusion algorithm to estimate the measurements of an omnidirectional mobile robot trajectory. We study the fusion of the data obtained by the position and orientation with a good precision to localize the robot in an external medium; we apply the techniques of kalman filter (KF) to the estimation of the trajectory. We suppose a movement of mobile robot on a plan in two dimensions. The sensor approach is based on the CRUKF and too on the standard UKF which are modified to handle measurements from the position and orientation. A real-time implementation is done on a three-wheeled omnidirectional mobile robot, using a dynamic model with trajectories. The algorithm is analyzed and validated with simulations.
A two DOF spherical parallel platform posture analysis based on kinematic pri...IJRES Journal
Introducing the principle of kinematic analysis, the mathematical description and analysis
method of the constraints, pose and freedom were briefly outlined. A new 2-PSP & 1-S platform configuration
was presented. To derive attitude mathematical model of the platform, freedom and spinor system of the two
DOF spherical parallel platform were analyzed using kinematics principles. The results show, introducing the
concept of position and pose into the kinematic design, kinematic design method can be more widely used to
deal with the problem of the movement of the mechanism, so as to expand the application range of kinematic
design.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Similar to Singularity condition of wrist partitioned 6-r serial (20)
Hudhud cyclone caused extensive damage in Visakhapatnam, India in October 2014, especially to tree cover. This will likely impact the local environment in several ways: increased air pollution as trees absorb less; higher temperatures without tree canopy; increased erosion and landslides. It also created large amounts of waste from destroyed trees. Proper management of solid waste is needed to prevent disease spread. Suggested measures include restoring damaged plants, building fountains to reduce heat, mandating light-colored buildings, improving waste management, and educating public on health risks. Overall, changes are needed to water, land, and waste practices to rebuild the environment after the cyclone removed green cover.
Impact of flood disaster in a drought prone area – case study of alampur vill...eSAT Publishing House
1) In September-October 2009, unprecedented heavy rainfall and dam releases caused widespread flooding in Alampur village in Mahabub Nagar district, a historically drought-prone area.
2) The flood damaged or destroyed homes, buildings, infrastructure, crops, and documents. It displaced many residents and cut off the village.
3) The socioeconomic conditions and mud-based construction of homes in the village exacerbated the flood's impacts, making damage more severe and recovery more difficult.
The document summarizes the Hudhud cyclone that struck Visakhapatnam, India in October 2014. It describes the cyclone's formation, rapid intensification to winds of 175 km/h, and landfall near Visakhapatnam. The cyclone caused extensive damage estimated at over $1 billion and at least 109 deaths in India and Nepal. Infrastructure like buildings, bridges, and power lines were destroyed. Crops and fishing boats were also damaged. The document then discusses coping strategies and improvements needed to disaster management plans to better prepare for future cyclones.
Groundwater investigation using geophysical methods a case study of pydibhim...eSAT Publishing House
This document summarizes the results of a geophysical investigation using vertical electrical sounding (VES) methods at 13 locations around an industrial area in India. The VES data was interpreted to generate geo-electric sections and pseudo-sections showing subsurface resistivity variations. Three main layers were typically identified - a high resistivity topsoil, a weathered middle layer, and a basement rock. Pseudo-sections revealed relatively more weathered areas in the northwest and southwest. Resistivity sections helped identify zones of possible high groundwater potential based on low resistivity anomalies sandwiched between more resistive layers. The study concluded the electrical resistivity method was useful for understanding subsurface geology and identifying areas prospective for groundwater exploration.
Flood related disasters concerned to urban flooding in bangalore, indiaeSAT Publishing House
1. The document discusses urban flooding in Bangalore, India. It describes how factors like heavy rainfall, population growth, and improper land use have contributed to increased flooding in the city.
2. Flooding events in 2013 are analyzed in detail. A November rainfall caused runoff six times higher than the drainage capacity, inundating low-lying residential areas.
3. Impacts of urban flooding include disrupted daily life, damaged infrastructure, and decreased economic activity in affected areas. The document calls for improved flood management strategies to better mitigate urban flooding risks in Bangalore.
Enhancing post disaster recovery by optimal infrastructure capacity buildingeSAT Publishing House
This document discusses enhancing post-disaster recovery through optimal infrastructure capacity building. It presents a model to minimize the cost of meeting demand using auxiliary capacities when disaster damages infrastructure. The model uses genetic algorithms to select optimal capacity combinations. The document reviews how infrastructure provides vital services supporting recovery activities and discusses classifying infrastructure into six types. When disaster reduces infrastructure services, a gap forms between community demands and available support, hindering recovery. The proposed research aims to identify this gap and optimize capacity selection to fill it cost-effectively.
Effect of lintel and lintel band on the global performance of reinforced conc...eSAT Publishing House
This document analyzes the effect of lintels and lintel bands on the seismic performance of reinforced concrete masonry infilled frames through non-linear static pushover analysis. Four frame models are considered: a frame with a full masonry infill wall; a frame with a central opening but no lintel/band; a frame with a lintel above the opening; and a frame with a lintel band above the opening. The results show that the full infill wall model has 27% higher stiffness and 32% higher strength than the model with just an opening. Models with lintels or lintel bands have slightly higher strength and stiffness than the model with just an opening. The document concludes lintels and lintel
Wind damage to trees in the gitam university campus at visakhapatnam by cyclo...eSAT Publishing House
1) A cyclone with wind speeds of 175-200 kph caused massive damage to the green cover of Gitam University campus in Visakhapatnam, India. Thousands of trees were uprooted or damaged.
2) A study assessed different types of damage to trees from the cyclone, including defoliation, salt spray damage, damage to stems/branches, and uprooting. Certain tree species were more vulnerable than others.
3) The results of the study can help in selecting more wind-resistant tree species for future planting and reducing damage from future storms.
Wind damage to buildings, infrastrucuture and landscape elements along the be...eSAT Publishing House
1) A visual study was conducted to assess wind damage from Cyclone Hudhud along the 27km Visakha-Bheemli Beach road in Visakhapatnam, India.
2) Residential and commercial buildings suffered extensive roof damage, while glass facades on hotels and restaurants were shattered. Infrastructure like electricity poles and bus shelters were destroyed.
3) Landscape elements faced damage, including collapsed trees that damaged pavements, and debris in parks. The cyclone wiped out over half the city's green cover and caused beach erosion around protected areas.
1) The document reviews factors that influence the shear strength of reinforced concrete deep beams, including compressive strength of concrete, percentage of tension reinforcement, vertical and horizontal web reinforcement, aggregate interlock, shear span-to-depth ratio, loading distribution, side cover, and beam depth.
2) It finds that compressive strength of concrete, tension reinforcement percentage, and web reinforcement all increase shear strength, while shear strength decreases as shear span-to-depth ratio increases.
3) The distribution and amount of vertical and horizontal web reinforcement also affects shear strength, but closely spaced stirrups do not necessarily enhance capacity or performance.
Role of voluntary teams of professional engineers in dissater management – ex...eSAT Publishing House
1) A team of 17 professional engineers from various disciplines called the "Griha Seva" team volunteered after the 2001 Gujarat earthquake to provide technical assistance.
2) The team conducted site visits, assessments, testing and recommended retrofitting strategies for damaged structures in Bhuj and Ahmedabad. They were able to fully assess and retrofit 20 buildings in Ahmedabad.
3) Factors observed that exacerbated the earthquake's impacts included unplanned construction, non-engineered buildings, improper prior retrofitting, and defective materials and workmanship. The professional engineers' technical expertise was crucial for effective post-disaster management.
This document discusses risk analysis and environmental hazard management. It begins by defining risk, hazard, and toxicity. It then outlines the steps involved in hazard identification, including HAZID, HAZOP, and HAZAN. The document presents a case study of a hypothetical gas collecting station, identifying potential accidents and hazards. It discusses quantitative and qualitative approaches to risk analysis, including calculating a fire and explosion index. The document concludes by discussing hazard management strategies like preventative measures, control measures, fire protection, relief operations, and the importance of training personnel on safety.
Review study on performance of seismically tested repaired shear wallseSAT Publishing House
This document summarizes research on the performance of reinforced concrete shear walls that have been repaired after damage. It begins with an introduction to shear walls and their failure modes. The literature review then discusses the behavior of original shear walls as well as different repair techniques tested by other researchers, including conventional repair with new concrete, jacketing with steel plates or concrete, and use of fiber reinforced polymers. The document focuses on evaluating the strength retention of shear walls after being repaired with various methods.
Monitoring and assessment of air quality with reference to dust particles (pm...eSAT Publishing House
This document summarizes a study on monitoring and assessing air quality with respect to dust particles (PM10 and PM2.5) in the urban environment of Visakhapatnam, India. Sampling was conducted in residential, commercial, and industrial areas from October 2013 to August 2014. The average PM2.5 and PM10 concentrations were within limits in residential areas but moderate to high in commercial and industrial areas. Exceedance factor levels indicated moderate pollution for residential areas and moderate to high pollution for commercial and industrial areas. There is a need for management measures like improved public transport and green spaces to combat particulate air pollution in the study areas.
Low cost wireless sensor networks and smartphone applications for disaster ma...eSAT Publishing House
This document describes a low-cost wireless sensor network and smartphone application system for disaster management. The system uses an Arduino-based wireless sensor network comprising nodes with various sensors to monitor the environment. The sensor data is transmitted to a central gateway and then to the cloud for analysis. A smartphone app connected to the cloud can detect disasters from the sensor data and send real-time alerts to users to help with early evacuation. The system aims to provide low-cost localized disaster detection and warnings to improve safety.
Coastal zones – seismic vulnerability an analysis from east coast of indiaeSAT Publishing House
This document summarizes an analysis of seismic vulnerability along the east coast of India. It discusses the geotectonic setting of the region as a passive continental margin and reports some moderate seismic activity from offshore in recent decades. While seismic stability cannot be assumed given events like the 2004 tsunami, no major earthquakes have been recorded along this coast historically. The document calls for further study of active faults, neotectonics, and implementation of improved seismic building codes to mitigate vulnerability.
Can fracture mechanics predict damage due disaster of structureseSAT Publishing House
This document discusses how fracture mechanics can be used to better predict damage and failure of structures. It notes that current design codes are based on small-scale laboratory tests and do not account for size effects, which can lead to more brittle failures in larger structures. The document outlines how fracture mechanics considers factors like size effect, ductility, and minimum reinforcement that influence the strength and failure behavior of structures. It provides examples of how fracture mechanics has been applied to problems like evaluating shear strength in deep beams and investigating a failure of an oil platform structure. The document argues that fracture mechanics provides a more scientific basis for structural design compared to existing empirical code provisions.
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Singularity condition of wrist partitioned 6-r serial
1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 12 | Dec-2013, Available @ http://www.ijret.org 700
SINGULARITY CONDITION OF WRIST-PARTITIONED 6-R SERIAL
MANIPULATOR BASED ON GRASSMANN-CAYLEY ALGEBRA
Luc Djimon Clément AKONDE
Ph-D Student, State Key Laboratory of Digital Manufacturing Equipment and Technology, Mechanical school of
Science & Engineering, Huazhong University of Science and Technology, Wuhan, China, goering20@yahoo.fr
Abstract
To prevent the singularity of serial robot’s due to the lost of one or more degree of twist freedom, it is necessary to determine the
Jacobian matrix J associated to its instantaneous motion and analyze the vanishing condition of the determinant det (J). Usually,
the large expression of det (J) does not facilitate an efficient geometric analysis. Since Grassmann-Cayley Algebra (GCA) has
powerful tools for geometric interpretation of coordinate free representation and singularity analyzing in real time computing,
this method is implemented in the present work. The goal of this research is to determine the singularity condition of wrist-
partitioned 6-R serial manipulator (SM) based on GCA. The symbolic approach of Plücker coordinate lines is used to formulate
the twist system (TS) of SM. The twist system is similar to det (J) which rows are Plücker coordinate lines. The vanishing
condition of det (J) based on the linearity condition of TS is determined without algebraic coordinate and provides a single
singularity condition which contains all generals and particulars cases. The keys elements of transition between the rows of J and
singularity condition of a twist-partitioned 6-R SM are the introduction of the symbolic approach of Plücker coordinate lines and
superbracket. The vanishing points of the superbracket are analyzed to describe the singularity condition. The result indicates
that for a wrist-partitioned 6-R SM a single singularity condition contains three generals cases such as the shoulder, elbow and
wrist singularity. Since the three last axis of the wrist are no-coplanar and intersecting at a unique point, it is suggested that for a
wrist-partitioned 6-R serial manipulator, the wrist singularity never occurs physically, except that its design will be modified.
Index Terms: Singularity, 6-R Serial Manipulators, Grassmann-Cayley Algebra, Projective space, Twist graph
--------------------------------------------------------------------***----------------------------------------------------------------------
1. INTRODUCTION
Serial robot’s singularity is commonly defined as
configuration from which certain direction of motion may
be unattainable. This defeat is due to the lost of one or more
degree of twist system ( )TS freedom. One approach to
solve this difficulty is determining where the Jacobian
matrix tJ is non-singular for all values of the joint positions.
Usually the large expressions of the determinant
complicated efficient geometric analysis. To overcome this
problem, several approaches have been proposed over the
past years. Among these approaches Grassmann-Cayley
Algebra ( )GCA is probably one of the most efficient since
it provides sufficient tools to properly analyze geometrically
the singularity condition without coordinate
expression. GCA approach is suitable for analyzing the
rigidity of the framework of the architecture and for scene
analysis [1-8].It has a powerful tools for geometric
interpretation of coordinate free representation and
singularity analyzing in real time computing .The solution
provided in GCA language by vanishing the superbrackets
decomposition is a single condition which contains all
general and particular cases [1-17].To prevent the clash of
serial robot’s actuators which are in singularity
configuration, we firstly determined tJ related to its twist
and secondly calculate the dependency condition of the
det( )tJ which rows are Plücker coordinate lines.
Indeed, R. Paul and C. Stevenson [18] were the pioneers to
observe serial singularity from Jacobian matrix. D. Gottlieb
[19] proved their observation while D. Baker [20] used
topological argument to confirm them. Inter alia method,
analytical approach by dividing the Jacobian matrix in four
distinct square matrix[21],identification method by
developing equation on the sphere [22], algebraic based on
screw theory and it reciprocal [23,25,30],forward and
inverse kinematic equation approach [24,31,32,34,35],
singularity isolation or removing the degenerate part method
[26,36], geometric classification method [27-29], quaternion
based on geometry algebra [38,39],constraint and actuated
force method [33]etc …
Although, singular configuration of serial robot could be
detected by software simulation [37], the large expressions
ofdet( )tJ is still a challenge for researchers. In this scope J.
Merlet [40] confirmed the above-mentioned problem due its
complexity .This research focuses on the singularity
condition which is vanishing condition of det( )tJ using
GCA .This method direct to singularity analysis without
algebraic coordinates and makes a geometric interpretation.
for the vanishing points of the superbracket which is similar
to det( )tJ .
In this paper, the singularity condition for wrist-
partitioned 6 R− serial manipulator based on the
2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 02 Issue: 12 | Dec-2013, Available @ http://www.ijret.org 701
degeneracy of a twist system using the dependency of
Plücker coordinate lines is performed in coordinate free
expression to obtain a single singularity condition including
all general and particular poses. The work is organized as
follow: Sect.2recalls some prerequisites in projective space
used in GCA such as Plücker coordinate lines, twist system
and it associated graph, the concept of join and meet
operators. In Sect.3, describes 6 R− wrist-partitioned
SMs and the adopted representation of the mechanism.
Sect.4 shows the twist system graph while Sect.5 focuses on
the singularity analysis of 6 R− serial manipulator. Finally
conclusion is given at Sect.6.
2. FUNDAMENTALS CONCEPT IN
PROJECTIVE SPACE AND GCA
In this part we will give a brief background of projective
geometry tools used in GCA for serial robot .More details
on Plücker lines and GCA can be found in[4-8;15;41].
2.1 Twist System Projective Space
Projective space
Projective spaceQ is commonly referred as Euclidean space
added with the plane, ∞Π at infinity namely infinite plane,
which is formed by the points and lines at infinity. Any pair
of parallel lines in Q intersects each over at a unique point
at infinity while any pair of parallel planes in Q intersects
each over in the same and unique line at infinity.
Homogeneous coordinates and Plücker coordinates lines
In Cartesian coordinate system
n
R , each point
n
X R∈ is
written as 1 2( , ,..., )T
nX x x x .Adding the ( 1)n th+
coordinate equal to1, we get the homogeneous coordinates
of X .
If 0t ≠ ; the homogeneous form of X is:
1 2 1 2( , ,..., ,1) ( , ,..., , )T T
n nt x x x tx tx tx t= (1)
Then for any vector with ( 1)n + real number where the last
coordinate is a scalar 0t ≠ , we can recover the Cartesian
coordinate of such vector by dividing it to t . Let accept now
the ( 1)thn + coordinate equal to 0if and only if the point
X is at infinity. Toms [42] recalled that all algebraic
representation of projective geometry must be
homogeneous. Lilian [43] and Roy [44] confirmed
respectively that any projective point (line) has four (six)
homogeneous coordinates inQ and each line inQ is called
Plücker line.
n number of independents kinematic chains form
( )n screw space which is a screw subspace who is
composed of ( )n system screw .An instantaneous screw
axis is a Plücker coordinate vector line with its associated
pitch in a given position, then the screw axis of any robot is
described as:
0
ˆ$ [ ,( )]s S s hs= × + (2)
with, s the unit vector along the screw axis, 0S the position
vector of a point on the screw axis with respect to a
reference frame, h the pitch of the screw.
A twist of zero pitch screw , 0 0
ˆ$ [ ,( )]s S s= × ,is a Plücker
coordinate vector of a finite line which is identified as an
instantaneous pure rotation of a rigid body about the axis l .
2.2 Introduction to Grassmann-Cayley Algebra
GCA is a symbolic approach to Plücker coordinates. Points
are represented with their homogeneous coordinates, while
lines and planes are represented with their Plücker
coordinates. Extensors are symbolically denoted by Plücker
coordinates of lines and characterized by their step. For
example in the four-dimensional vector space
4
V
associated with the three dimensional− projective
space
3
Q , extensors of step 1, 2 and 3 represent point,
line l and plane P respectively .(See Fig-1:I,II,III).
'
,l a b P a b c
P l c
= ∨ = ∨ ∨
∧ =
(3)
They are also associated with subspaces of
4
V , of
dimension 1, 2 and 3, respectively. Let
n
V
be ( )n dimensional vector space over the field R , W
be ( )k dimensional subspace of
n
V with 1 2{ , ,..., }kw w w
a basis of W and P a Plücker coordinate vector ofW .
a
b
a
b
c a
cb
d
c f
D=E ¦Ð¡Þ
I II III IV
Fig-1: Illustrations of joint and meet operators and
intersecting parallel lines at infinity
Consider a symbolic level in which P is described without
specific coordinate basis, this symbolic approach represents
also a Plücker coordinate vector P in the
k
nð -dimensional vector space of
k
V and can be written as:
1 2 1 2... ...k kP w w w w w w= ∨ ∨ ∨ = (4)
In coordinate free expression P is called an extensor of
step k . Let be S a finite set of points 1 2{ , ,..., }kw w w
defined now in the ( 1)k − dimensional Projective
3. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 12 | Dec-2013, Available @ http://www.ijret.org 702
space, Q over the field R where 1 2( , ,..., )T
i i i kiw x x x= .
Each iw is represented by it homogeneous coordinate
form k tuple− with 1 i k≤ ≤ .The bracket of these
vectors is defined as the determinant of a matrix having iw
as its columns:
1 1 1 2 1
1 2
1 2
k
k
k k k k
x x x
w w w
x x x
, , ,
, , ,
[ , ,..., ]
L
M M L M
L
==== (5)
In GCA language this determinant formed by the
homogeneous coordinate namely superbracket represents
symbolically the Plücker coordinate lines .The dependency
conditions of these Plücker coordinate lines is related to the
vanishing conditions of the determinant .This approach is
used to analyze the instantaneous kinematics as well as
determining geometrically the singularity configurations in
coordinate free manners. Instantaneously a twist space of
serial combination of motion constraints is the sum of the all
twist spaces of the composing constraints.
In GCA language a twist space of the serial connection of
kinematic chains is the support of the join of all the
extensors which represent the twist spaces of the chains. It
provided that their twists extensors are linearly independent
[41].Consequently Plücker coordinate vectors of all the
system can be denoted symbolically without noting its
coordinates. Eq. (4) is used to find the dependency
condition. Thus, a singularity occurs when these Plücker
coordinate vectors are dependent, which is equivalent to
superbrackets equal to zero.
If the Plücker coordinate lines are linearly independent
1 2 ... 0kP w w w= ∨ ∨ ∨ ≠ (6)
If the Plücker coordinates lines are linearly dependent, the
superbracket which is the determinant formed by the
homogeneous coordinate lines vanish:
1 2
1,1 1,2 1,
1 2
,1 ,2 ,
... 0
[ , ,..., ] 0
k
k
k
k k k k
P w w w
x x x
w w w
x x x
= ∨ ∨ ∨ =
= =
L
M M L M
L
(7)
3. DESCRIPTION AND ADOPTED
REPRESENTATION OF A GENERAL WRIST-
PARTITIONED 6R SERIAL MANIPULATORS
3.1Description of Wrist-Partitioned 6-R SMs
The manipulator under consideration consists of seven links
il ( 1,2,...,7)i = connected in succession by six revolute
joints. The link 1l fixed to the ground in a fixe
frame 1 1 1( )O x y z while the last three non-coplanar axis
intersect at a unique common point h (see Fig-2).
Z1
θ1
Z2
Z3
Z4
Z5
Z6
θ2
θ4
θ5
θ6
θ3
h
Fig-2: A general 6-R wrist-partitioned SMs
3.2 Adopted Representations of 6-R Wrist-
Partitioned SMs
( )a The revolute axis iz are respectively the joint axis of il
and 1il + where 1,2,...,6i =
1( )zb is orthogonal to 2z and orthogonal to 3z .
2( )c z and 3z are parallel.
4 5( ) ,d z z and 6z are three no-coplanar intersecting axis at
a unique point h .
We choose two points on each of these six joint axis centers:
, ,fE,hG,hJaB cD and hL respectively on
1 2 3 4 5, , , ,z z z z z and 6z (see Fig-3)
4. TWIST SYSTEM AND IT'S ASSOCIATED
GRAPH
4.1 Twist System using the Symbolic Approach of
Plücker Coordinate Line in GCA Language
Since 6 R− SM consists of 6 serial joints with six center
of the motion in projective space (see Fig-3.),the symbolic
approach of GCA which represent the Plücker coordinate
vectors in coordinate free manners is the twist spaceT of
serial connection of kinematic links .It is identified as the
join of all the 6-extensors , see Eq.(4) , and describe as :
1 2 3 4 5 6
1 2 3 4 5 6[ ]
T z z z z z
T z z z z z z
= ∨ ∨ ∨ ∨
=
(8)
4. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 12 | Dec-2013, Available @ http://www.ijret.org 703
Z1
Z2
Z3
Z4
Z5
Z6
h
c
f
D=E
Fig-3: Adopted representation of the axis
4.2 Twist Graph of Wrist-Partitioned 6-R SM
The Twist graph is the graphic representation of theTS in
projective space. Each line is represented by one finite point
and one point at infinity. The capital letters represent the
points at infinity. 2z and 3z are parallel and intersect each
over on E D= at infinity. See Fig-1(IV) and Fig-4. Eq. (8)
becomes:
T aB cD fD hG hJ hL= ∨ ∨ ∨ ∨ ∨ (9)
The join of these six vectors axis in projective space
represent det( )tJ which rows are the six Plücker
coordinate lines and similar to the superbracket:
[ , , , , , ]T aB cD fD hG hJ hL= (10)
B
G
D
L
a c f
h
J
¦ С Þ
Fig-4: Twist graph of wrist partitioned 6-R SMs
5. SINGULARITY ANALYSIS OF WRIST-
PARTTIONED 6-R SM USING GCA
The Serial singularity occurs when the robot loses one or
more degree of TS freedom, then the superbracket equal to
zero.
5.1 Singularity Conditions and Associated Motion
of Wrist-Partitioned 6-R SM
Geometrically singularity arises when the joint screws
which are Plücker coordinate lines are linearly dependent.
det( )tJ Vanishes then Eq.(10) becomes :
0
[ , , , , , ] 0
T
aB cD fD hG hJ hL
=
=
(11)
This expression can be developed into 24combination of
linear monomials. Each of them represents the product for
three brackets of four projective points [1, 3].The useful
tool, Graphic User Interface, provided by Stéphane Caro et
al [17] perform this calculus and gives the singularity
condition:
[ , , , , , ]
[ ][ ][ ]
aB cD fD hG hJ hL
aBDh cfDh GjhL
=
−
(12)
And then Eq. (12) vanishes when at least one of the three
monomials vanish.
5.2 Interpretation of Singularity Condition in
Grassmann-Cayley Algebra Language
If [ ] 0aBDh = then: aB hD∧ means h lies either
on aB or aBD .According to the adopted representation h
lies on one of: 1 1 2 1 3{ ,( z ),( z )}z z z with a particular
case 1h z∈ : a shoulder singularity.
If [ ] 0cfDh = then: cD hf∧ or fD hc∧
means h is either collinear to cD or fD since 2z and 3z
are parallel lines and intersect in the projective space at
infinity at point D , h must lies on a plane formed by 2 3z z
: it is a an elbow singularity, the end effector is at the
boundary of the workspace.
And at last if [ ] 0GJhL = then hG LJ∧ or hJ LG∧
or hL GJ∧ , means 4z LJ∧ or 5z LG∧ or 6z GJ∧ , it
is obvious that we are in wrist singularity condition and the
last three axes 4 5 6, ,z z z must be parallel to each over: This
condition is impossible to implement practically: except that
the wrist –partitioned design was modified. Two of the last
three axis must be parallel to each over.
6. CONCLUSIONS
This research presented the singularity configuration of
wrist-partitioned 6-R serial manipulator based on GCA. We
5. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 02 Issue: 12 | Dec-2013, Available @ http://www.ijret.org 704
formulated the twist system by symbolic approach of
Plücker coordinate lines and used an alternative coordinate
free method, GCA, to detect the singularity condition. The
twist graph was obtained by introducing the notion of join
and meet operators. Since GCA provided sufficient tools to
analyze singularity condition without algebraic coordinate,
this method was implemented in this paper and the result
provided a single singularity condition which contained
three classes of singularity such as shoulder, elbow and
wrist singularity. The analysis of these results suggested that
the wrist singularity never occurs physically. Since the
conceptual design of the wrist has last three axes non-
coplanar and intersecting at a unique point, it was deduced
that the wrist singularity could be possible if and only if the
design of two of the last three axes are parallel.
However, we recognize the current work was not entirely
absolute due to the complexity of the topic. The use of GCA
approach to analyze singularity of such robot without
algebraic coordinate was our contribution. These results
may motivate further researchers toward GCA to analysis
singularity condition of any serial robot. Elsewhere the great
powerful tools used in GCA language are also useful in
robotics vision or image modeling.
ACKNOWLEDGEMENT
I wish to thank Doctor ADOKO AMOUSSOU Koffi for his
inspiring advice, support and encouragement during my
research. I’m grateful to the editor and reviewers for their
support.
REFERENCES
[1]. P.Ben-Horin, M.Shoham. Singularity Analysis of a
Class of Parallel Robots based on Grassmann–Cayley
Algebra. Mechanism and Machine Theory, 41, no.8 (2006),
958-970.
[2]. P.Ben-Horin, M.Shoham.Singularity Condition of Six-
Degree-of-Freedom Three-Legged Parallel Robots Based on
Grassmann–Cayley Algebra. IEEE Transactions on
Robotics, 22, no.4 (2006), 577-590.
[3]. P.Ben-Horin,M. Shoham.Application of Grassmann -
Cayley Algebra to Geometrical Interpretation of Parallel
Robot Singularities. The International Journal of Robotics
Research, 28, no.1 (2009), 127-141.
[4]. Laurent Fuchs. Algèbre de Grassmann-Cayley. XLIM-
SIC, Université de Poitiers, France INRIA Sophia-Antipolis
(2009)1-13.
[5]. Neil L . White. A Tutorial on Grassmann-Cayley
Algebra, in:Invariant Methods in Discrete and
Computational Geometry, Proceedings of the Curaçao
Conference. Springer Netherlands (1994) pp 93-106.
[6].Neil L. White. Grassmann–Cayley Algebra and Robotics
Applications, in: Handbook of Geometric Computing.
Applications in Pattern Recognition,Computer Vision,
Neural computing, and Robotics, 8, Springer-Verlag Berlin
Heidelberg (2005), pp 629 -656.
[7]. Neil L. White.Grassmann-Cayley Algebra and Robotics.
Journal of Intelligent and Robotic Systems, 11,(1994)91-
107.
[8]. E. Staffetti, F.Thomas. Kinestatic Analysis of Serial and
Parallel Robot Manipulators Using Grassman-Cayley
Algebra, in: J.Lenarcic and M.M. Stanisic (eds.), Advances
in robot Kinematics, Springer Netherlands (2000), pp17-27.
[9]. S.Caro, G.Moroz , T.Gayral ,D.Chablat, C. Chen.
Singularity Analysis of a Six-Dof Parallel Manipulator
Using Grassmann-Cayley Algebra and Gröbner Bases . J.
Angeles et al. (Eds.) Brain, Body and Machine . Advances in
Intelligent and Soft Computing,83, Springer Berlin
Heidelberg (2010),pp341-352.
[10]. Laurent Fuchs and Laurent Théry. A Formalization of
Grassmann-Cayley Algebra in Coq and its Application to
Theorem Proving in Projective Geometry ,in : Automated
Deduction in Geometry .Lecture Notes in
ComputerScience,6877 ,Springer Berlin Heidelberg (2011),
pp 51-67.
[11].D.Kanaan, P.Wenger ,D.Chablat. Singularity Analysis
of Limited-DOF Parallel Manipulators Using Grassmann-
Cayley Algebra. Advances in Robot Kinematics: Analysis
and Design. Springer Netherlands(2008),pp 59-68.
[12]. D.Kanaan, P. Wenger, S.Caro, D.Chablat. Singularity
Analysis of Lower Mobility Parallel Manipulators Using
Grassmann-Cayley Algebra. IEEE Transactions on
Robotics, 25, no.5 (2009) 995-1004.
[13]. S.Amine, M.T.Masouleh, S.Caro , P.Wenger,
C.Gosselin. Singularity Conditions of 3T1R Parallel
Manipulators with Identical Limb Structures . ASME
,Journal of Mechanisms and Robotics, 4, 1 (2012).
[14]. S. Amine, M.T.Masouleh, S. Caro,P.Wenger,
C.Gosselin. Singularity analysis of 3T2R parallel
mechanisms using Grassmann-Cayley Algebra and
Grassmann geometry. Mechanism and Machine Theory ,52
,(2012) , 326-340.
[15].Hongbo Li. From Past to Future: Graßmann's Work in
Context. Projective Geometric Theorem Proving with
Grassmann-Cayley Algebra. Graßmann Bicentennial
Conference,September 2009 Springer Basel (2011) pp 275-
285.
[16]. Lennart RUBBERT .Conception de Mécanismes
Compliants pour la Robotique Chirurgicale. Ph-D
Dissertation .Université de Strasbourg.(2012),pp96.
[17]. S.Amine ,S.Caro.Singularity Conditions of Lower-
Mobility Parallel Manipulators Based on Grassmann-Cayley
Algebra. L'Agence nationale de la recherche. Retrieved
December 1, 2013, from http ://www.irccyn.ec-
nantes.fr/~caro/SIROPA/GUIGCASiropa.jar
[18]. R.P. Paul, C.N. Stevenson. Kinematics of Robot Wrists
.The International Journal of Robotics Research, 2,
no.1,(1983)31-38.
[19]. D.H. Gottlieb. Robots and Fibre Bundles. Bull. Soc.
Math. Belg. Sér. A, 38, (1987) 219-223.
[20]. D. R. Baker , C.W.Wampler II .The International
Journal of Robotics Research , 7 ,no. 2,(1988 ) 3-21.
[21]. M. J. D. Hayes, M. L. Husty, P. J. Zsombor-Murray.
Singular configurations of wrist-partitioned 6R serial robots:
a geometric perspective for users. Transactions of the
Canadian Society for Mechanical Engineering, 26, no. 1
(2002) 41-55.
[22]. Z.C. Lai, D.C.H. Yang. A New Method for the
Singularity Analysis of Simple Six-link Manipulators. The