This document summarizes a study that performed multi-objective design optimization of a leg mechanism for a piping inspection robot. Three leg mechanism architectures were considered: a slot-follower mechanism, a 4-bar crank and slider mechanism, and a 6-bar crank and slider mechanism. The objectives of the optimization were to minimize the size of the mechanism and maximize the transmission force factor. The optimization determined the optimal geometric parameters for each mechanism under constraints related to the pipe dimensions and forces. Representations of the Pareto fronts and CAD models of optimized mechanism solutions are presented.
A mobile parallel robot used for pipeline inspection is analyzed. The robot consists of single modules resembling a snake. The study determines the robot's singularity-free workspace and derives optimal geometric parameters. When passing through sharp corners in the pipe, the robot encounters singular configurations that disrupt mobility. To overcome this, prismatic joints are added to the arms, allowing continuous singularity-free motion across corners through optimal control strategies like path following control and gradient ascent to maximize arm length. Simulation results demonstrate the robot can navigate corners without getting stuck, leading to a continuous singularity-free workspace.
This document presents a pipe inspection robot designed to traverse inside pipes with forward and backward motion. The robot is meant to move through pipes of various diameters. It uses a mechanical design with angled passive wheels that remain parallel to the pipe surface to prevent engaging with walls. The robot has applications in pipe inspection, locating holes, painting pipes from the inside, and material dosing through pipes. Future developments include coupling the robot's hands to prevent wobbling and adding a wireless controller and battery for longer inspections.
This document summarizes the design, assembly, working, and testing of a pipe inspection robot. Key points include:
1) The robot's mechanical linkage mechanism converts rotary motion to linear motion, allowing it to expand and contract between diameters of 13 and 8 inches to move through pipes.
2) The electrical components including sensors, microcontroller, and motors are assembled and allow the robot to be controlled remotely by a computer. Temperature, gas, and camera sensors provide data to the computer.
3) Testing showed the robot could successfully travel forward and backward through an 8-inch pipe, with no visual defects detected. Temperature and gas readings were also taken successfully during testing.
This document describes the design of a pipe inspection robot. The robot is designed to crawl inside pipes and use a camera to identify defects. It uses a four-bar linkage mechanism with wheels connected by links to move inside pipes of varying diameters. The objectives are to fabricate the robot using CAD, determine the required motor torque and voltage, and test its ability to move inside pipes. Experiments are conducted to validate the design in pipes of different orientations. The robot is able to successfully inspect pipes and transmit video to identify cracks and corrosion.
This document discusses the design and fabrication of a pipe inspection robot. It describes how robots can perform dangerous and labor-intensive inspection tasks. The document then discusses different pipe inspection methods and focuses on visual inspection. It provides details on the design of a pipe inspection robot prototype, including its parameters, links, motion calculation and applications. The robot is intended to inspect the interior of pipes ranging from 140-180mm in diameter to detect corrosion, cracks or other defects. Limitations and suitable applications are also covered.
This document describes the design of a pipe inspection robot capable of inspecting pipes with diameters between 48-60 cm. The robot has a foreleg system, rear leg system, and central body, with each leg containing three wheels arranged 120 degrees from each other to navigate pipes of varying diameters. The robot's range of motion allows it to move forward and backward inside pipes for inspection. Static analysis was performed on the robot's four-link mechanism to determine it has one degree of freedom, making it suitable for practical inspection tasks. The robot wirelessly transmits inspection photos and video to an external monitor. The design aims to allow non-destructive pipe inspection to detect issues early and reduce costs from failure.
A mobile parallel robot used for pipeline inspection is analyzed. The robot consists of single modules resembling a snake. The study determines the robot's singularity-free workspace and derives optimal geometric parameters. When passing through sharp corners in the pipe, the robot encounters singular configurations that disrupt mobility. To overcome this, prismatic joints are added to the arms, allowing continuous singularity-free motion across corners through optimal control strategies like path following control and gradient ascent to maximize arm length. Simulation results demonstrate the robot can navigate corners without getting stuck, leading to a continuous singularity-free workspace.
This document presents a pipe inspection robot designed to traverse inside pipes with forward and backward motion. The robot is meant to move through pipes of various diameters. It uses a mechanical design with angled passive wheels that remain parallel to the pipe surface to prevent engaging with walls. The robot has applications in pipe inspection, locating holes, painting pipes from the inside, and material dosing through pipes. Future developments include coupling the robot's hands to prevent wobbling and adding a wireless controller and battery for longer inspections.
This document summarizes the design, assembly, working, and testing of a pipe inspection robot. Key points include:
1) The robot's mechanical linkage mechanism converts rotary motion to linear motion, allowing it to expand and contract between diameters of 13 and 8 inches to move through pipes.
2) The electrical components including sensors, microcontroller, and motors are assembled and allow the robot to be controlled remotely by a computer. Temperature, gas, and camera sensors provide data to the computer.
3) Testing showed the robot could successfully travel forward and backward through an 8-inch pipe, with no visual defects detected. Temperature and gas readings were also taken successfully during testing.
This document describes the design of a pipe inspection robot. The robot is designed to crawl inside pipes and use a camera to identify defects. It uses a four-bar linkage mechanism with wheels connected by links to move inside pipes of varying diameters. The objectives are to fabricate the robot using CAD, determine the required motor torque and voltage, and test its ability to move inside pipes. Experiments are conducted to validate the design in pipes of different orientations. The robot is able to successfully inspect pipes and transmit video to identify cracks and corrosion.
This document discusses the design and fabrication of a pipe inspection robot. It describes how robots can perform dangerous and labor-intensive inspection tasks. The document then discusses different pipe inspection methods and focuses on visual inspection. It provides details on the design of a pipe inspection robot prototype, including its parameters, links, motion calculation and applications. The robot is intended to inspect the interior of pipes ranging from 140-180mm in diameter to detect corrosion, cracks or other defects. Limitations and suitable applications are also covered.
This document describes the design of a pipe inspection robot capable of inspecting pipes with diameters between 48-60 cm. The robot has a foreleg system, rear leg system, and central body, with each leg containing three wheels arranged 120 degrees from each other to navigate pipes of varying diameters. The robot's range of motion allows it to move forward and backward inside pipes for inspection. Static analysis was performed on the robot's four-link mechanism to determine it has one degree of freedom, making it suitable for practical inspection tasks. The robot wirelessly transmits inspection photos and video to an external monitor. The design aims to allow non-destructive pipe inspection to detect issues early and reduce costs from failure.
Design and Analysis of Articulated Inspection Arm of RobotIJTET Journal
Nowadays Robot play a vital role in all the activities in human life including industrial needs. There is a definite trend in the manufacture of robotic arms toward more dexterous devices, more degrees of-Freedom, and capabilities beyond the human arm. The ultimate objective is to save human lives in addition to increasing productivity and quality of high technology work environments. The objective of this project is to design, analysis of a Generic articulated robot Arm. This project deals with the modeling of a special class of single-link articulated inspection arms of robot. These arms consist of flexible massless structures having some masses concentrated at certain points of hollow sections at the beam. Some aspects of the articulated Robot that are anticipated as useful are its small cross section and its projected ability to change elevation and maneuver over obstacle require large joint torque to weight ratios for joint actuation. A knuckle joint actions actuation scheme is described and its implementation is detailed in this project. The parts of the (AIA) arm are analyzed for deflection and stress concentration under loading conditions in different angles.
This document describes a constructive solution for a rotating machine with profiled rotors that can function as either a force machine or work machine. Key points:
- The machine has two counter-rotating profiled rotors inside casings that transport fluid from a suction to discharge connection.
- A mathematical relationship is derived showing that the height of the rotating pistons should equal the rotor radius to maximize efficiency.
- Details are provided on the gear mechanism used to synchronize rotation of the rotors without penetrating shafts.
- Equations are given to calculate the coordinates that define the contour profile of the rotors based on design parameters like rotor radius.
- Tables show example coordinate points used to
1. The project involves the design and fabrication of a laser operated robot for pipe inspection. It will have a three finger mechanism and use LDR sensors to detect cracks in pipes using laser light reflection.
2. The robot will be controlled using a microcontroller and transmit video footage and sensor data to a laptop or mobile device for monitoring. It aims to inspect pipes in a fast, cost effective and safer manner compared to manual inspection.
3. Expected outcomes include a functional prototype robot that can accurately inspect pipes for defects and conditions while remaining compliant with inspection regulations to reduce environmental impacts during operations.
This document presents a design for an in-pipe inspection robot with an Adaptable Quad Arm Mechanism (AQAM) and Swivel Hand Mechanism (SHM) to enable it to navigate various pipe configurations, including branches and elbows. The AQAM allows the arms to rotate independently, allowing the robot to traverse reduced branch pipes and zero-radius curves. The SHM enables the robot to change its orientation by rotating the "hands" to bypass obstacles. A prototype was built and tested, demonstrating it could successfully navigate branch pipes and elbows of different diameters and orientations. The mechanisms aim to address issues faced by previous in-pipe robots in inspecting complex pipe networks.
Research on The Control of Joint Robot TrajectoryIJRESJOURNAL
ABSTRACT: This paper relates to a Robot that belongs to the category of Joint Robot.In the article,we analyze the path planning and control system of the robot,specifically speaking,it involves the interpolation of the robot trajectory, the analysis of the inverse kinematics, the introduction of the method to reduce the trajectory error, the optimization of the trajectory and in the end, the corresponding control system is designed according to the relevant parameters. This research project first introduces the importance of the robot, and then analyzes the whole process of the robot from the grasping pin, the screw to they are delivered to the designated position,finally, the process is introduced in detail, and the simulation result is displayed.
Robust Control of a Spherical Mobile RobotIRJET Journal
This document summarizes a research paper about controlling a spherical mobile robot using sliding mode control. It begins with an abstract that describes the challenges of controlling spherical robots due to their underactuated systems. It then provides background on previous control methods for spherical robots. The document presents the kinematic model of a 2-DOF spherical robot and describes how sliding mode control can be used to provide robust control and path following for the robot. It provides the equations for the sliding mode controller design. Finally, it presents simulation results showing the robot following a desired trajectory with minimal tracking error using the sliding mode controller.
This document provides an introduction to robots and robotics. It defines a robot as a programmable mechanical device that uses sensors and actuators to manipulate objects. Robotics is the study of designing, manufacturing, and using robots. Robots are useful for performing dangerous, repetitive, or precision tasks that humans prefer to avoid. The document discusses robot components like manipulators, joints, end-effectors, and workspaces. It also categorizes robots based on functions, sizes, applications, tasks, controllers, and configurations. The goal is to understand how to classify and select robots based on their specifications and intended applications.
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 presents a method for designing a variable coupler curve four-bar mechanism that can generate different desired coupler curves through continuous adjustment of link lengths. The method involves replacing one link with an adjustable screw-nut link driven by a servomotor. Different coupler curves can be generated by controlling the angular displacement of the driving link and adjusting the length of the adjustable link. Equations are derived to calculate the required driving link angles and adjustable link lengths corresponding to desired coupler curves. Examples applying this mechanism to deburring pipes with non-circular cross-sections are provided.
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.
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
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
Design and Fabrication of In-Pipe Inspection Robot for Crack Analysis and Det...IRJET Journal
The document describes the design and fabrication of an in-pipe inspection robot for crack analysis and detection using computer vision techniques. The robot is intended to autonomously navigate through pipes and use OpenCV and visual odometry to detect cracks from video feedback, measuring absolute distance traveled. It discusses the constraints considered in the design, including size, maneuverability, durability, and power efficiency. The key components of the robot include an Arduino Uno microcontroller, ESP32 cameras, an ESP8266 WiFi module, and DC motors. It has a symmetrical six-legged structure for maneuvering inside pipes and transmitting real-time video and data to operators outside via wireless communication.
The document discusses kinematics of machines and mechanisms. It covers topics such as kinematics, types of links, kinematic pairs, classification of kinematic pairs based on contact and motion, degrees of freedom, kinematic chains, joints, inversion of mechanisms, and straight line generators. Examples of mechanisms are provided to illustrate concepts like the 4-bar linkage, Scott-Russell straight line mechanism, Peaucellier straight line mechanism, and mechanical advantage.
The document provides an overview of theory of machines and machine elements design. It discusses kinematics, which is the study of motion without considering forces. Kinematics of machines deals with the relative motion between machine parts through displacement, velocity and acceleration. A mechanism is defined as part of a machine that transmits motion and power from input to output. Key concepts discussed include links, kinematic pairs, degrees of freedom, and inversions of mechanisms. Common mechanisms like slider crank chains and their inversions are presented. The document also discusses straight line motion generators, intermittent motion mechanisms, and mechanical advantage in mechanisms.
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.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
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
089 CC2011 Crete (2011) Rail Straightness Control in ServiceAndrea Bracciali
This document discusses rail straightness and quality control. It begins by describing how rails are produced and straightened, but still have residual deviations from being perfectly straight due to cooling differences. These deviations can cause issues like ground vibrations and noise if they have long wavelengths over 1m. The paper then presents a methodology to measure rail straightness in service using a portable trolley. It compares results from different measurement campaigns and shows that residual deviations depend on the specific rail production plant.
Or: Beyond linear.
Abstract: Equivariant neural networks are neural networks that incorporate symmetries. The nonlinear activation functions in these networks result in interesting nonlinear equivariant maps between simple representations, and motivate the key player of this talk: piecewise linear representation theory.
Disclaimer: No one is perfect, so please mind that there might be mistakes and typos.
dtubbenhauer@gmail.com
Corrected slides: dtubbenhauer.com/talks.html
Design and Analysis of Articulated Inspection Arm of RobotIJTET Journal
Nowadays Robot play a vital role in all the activities in human life including industrial needs. There is a definite trend in the manufacture of robotic arms toward more dexterous devices, more degrees of-Freedom, and capabilities beyond the human arm. The ultimate objective is to save human lives in addition to increasing productivity and quality of high technology work environments. The objective of this project is to design, analysis of a Generic articulated robot Arm. This project deals with the modeling of a special class of single-link articulated inspection arms of robot. These arms consist of flexible massless structures having some masses concentrated at certain points of hollow sections at the beam. Some aspects of the articulated Robot that are anticipated as useful are its small cross section and its projected ability to change elevation and maneuver over obstacle require large joint torque to weight ratios for joint actuation. A knuckle joint actions actuation scheme is described and its implementation is detailed in this project. The parts of the (AIA) arm are analyzed for deflection and stress concentration under loading conditions in different angles.
This document describes a constructive solution for a rotating machine with profiled rotors that can function as either a force machine or work machine. Key points:
- The machine has two counter-rotating profiled rotors inside casings that transport fluid from a suction to discharge connection.
- A mathematical relationship is derived showing that the height of the rotating pistons should equal the rotor radius to maximize efficiency.
- Details are provided on the gear mechanism used to synchronize rotation of the rotors without penetrating shafts.
- Equations are given to calculate the coordinates that define the contour profile of the rotors based on design parameters like rotor radius.
- Tables show example coordinate points used to
1. The project involves the design and fabrication of a laser operated robot for pipe inspection. It will have a three finger mechanism and use LDR sensors to detect cracks in pipes using laser light reflection.
2. The robot will be controlled using a microcontroller and transmit video footage and sensor data to a laptop or mobile device for monitoring. It aims to inspect pipes in a fast, cost effective and safer manner compared to manual inspection.
3. Expected outcomes include a functional prototype robot that can accurately inspect pipes for defects and conditions while remaining compliant with inspection regulations to reduce environmental impacts during operations.
This document presents a design for an in-pipe inspection robot with an Adaptable Quad Arm Mechanism (AQAM) and Swivel Hand Mechanism (SHM) to enable it to navigate various pipe configurations, including branches and elbows. The AQAM allows the arms to rotate independently, allowing the robot to traverse reduced branch pipes and zero-radius curves. The SHM enables the robot to change its orientation by rotating the "hands" to bypass obstacles. A prototype was built and tested, demonstrating it could successfully navigate branch pipes and elbows of different diameters and orientations. The mechanisms aim to address issues faced by previous in-pipe robots in inspecting complex pipe networks.
Research on The Control of Joint Robot TrajectoryIJRESJOURNAL
ABSTRACT: This paper relates to a Robot that belongs to the category of Joint Robot.In the article,we analyze the path planning and control system of the robot,specifically speaking,it involves the interpolation of the robot trajectory, the analysis of the inverse kinematics, the introduction of the method to reduce the trajectory error, the optimization of the trajectory and in the end, the corresponding control system is designed according to the relevant parameters. This research project first introduces the importance of the robot, and then analyzes the whole process of the robot from the grasping pin, the screw to they are delivered to the designated position,finally, the process is introduced in detail, and the simulation result is displayed.
Robust Control of a Spherical Mobile RobotIRJET Journal
This document summarizes a research paper about controlling a spherical mobile robot using sliding mode control. It begins with an abstract that describes the challenges of controlling spherical robots due to their underactuated systems. It then provides background on previous control methods for spherical robots. The document presents the kinematic model of a 2-DOF spherical robot and describes how sliding mode control can be used to provide robust control and path following for the robot. It provides the equations for the sliding mode controller design. Finally, it presents simulation results showing the robot following a desired trajectory with minimal tracking error using the sliding mode controller.
This document provides an introduction to robots and robotics. It defines a robot as a programmable mechanical device that uses sensors and actuators to manipulate objects. Robotics is the study of designing, manufacturing, and using robots. Robots are useful for performing dangerous, repetitive, or precision tasks that humans prefer to avoid. The document discusses robot components like manipulators, joints, end-effectors, and workspaces. It also categorizes robots based on functions, sizes, applications, tasks, controllers, and configurations. The goal is to understand how to classify and select robots based on their specifications and intended applications.
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 presents a method for designing a variable coupler curve four-bar mechanism that can generate different desired coupler curves through continuous adjustment of link lengths. The method involves replacing one link with an adjustable screw-nut link driven by a servomotor. Different coupler curves can be generated by controlling the angular displacement of the driving link and adjusting the length of the adjustable link. Equations are derived to calculate the required driving link angles and adjustable link lengths corresponding to desired coupler curves. Examples applying this mechanism to deburring pipes with non-circular cross-sections are provided.
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.
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
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
Design and Fabrication of In-Pipe Inspection Robot for Crack Analysis and Det...IRJET Journal
The document describes the design and fabrication of an in-pipe inspection robot for crack analysis and detection using computer vision techniques. The robot is intended to autonomously navigate through pipes and use OpenCV and visual odometry to detect cracks from video feedback, measuring absolute distance traveled. It discusses the constraints considered in the design, including size, maneuverability, durability, and power efficiency. The key components of the robot include an Arduino Uno microcontroller, ESP32 cameras, an ESP8266 WiFi module, and DC motors. It has a symmetrical six-legged structure for maneuvering inside pipes and transmitting real-time video and data to operators outside via wireless communication.
The document discusses kinematics of machines and mechanisms. It covers topics such as kinematics, types of links, kinematic pairs, classification of kinematic pairs based on contact and motion, degrees of freedom, kinematic chains, joints, inversion of mechanisms, and straight line generators. Examples of mechanisms are provided to illustrate concepts like the 4-bar linkage, Scott-Russell straight line mechanism, Peaucellier straight line mechanism, and mechanical advantage.
The document provides an overview of theory of machines and machine elements design. It discusses kinematics, which is the study of motion without considering forces. Kinematics of machines deals with the relative motion between machine parts through displacement, velocity and acceleration. A mechanism is defined as part of a machine that transmits motion and power from input to output. Key concepts discussed include links, kinematic pairs, degrees of freedom, and inversions of mechanisms. Common mechanisms like slider crank chains and their inversions are presented. The document also discusses straight line motion generators, intermittent motion mechanisms, and mechanical advantage in mechanisms.
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.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
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
089 CC2011 Crete (2011) Rail Straightness Control in ServiceAndrea Bracciali
This document discusses rail straightness and quality control. It begins by describing how rails are produced and straightened, but still have residual deviations from being perfectly straight due to cooling differences. These deviations can cause issues like ground vibrations and noise if they have long wavelengths over 1m. The paper then presents a methodology to measure rail straightness in service using a portable trolley. It compares results from different measurement campaigns and shows that residual deviations depend on the specific rail production plant.
Or: Beyond linear.
Abstract: Equivariant neural networks are neural networks that incorporate symmetries. The nonlinear activation functions in these networks result in interesting nonlinear equivariant maps between simple representations, and motivate the key player of this talk: piecewise linear representation theory.
Disclaimer: No one is perfect, so please mind that there might be mistakes and typos.
dtubbenhauer@gmail.com
Corrected slides: dtubbenhauer.com/talks.html
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1. Proceedings of the ASME 2014 International Design Engineering Technical Conferences &
Computers and Information in Engineering Conference
IDETC/CIE 2014
August 17-20, 2014, Buffalo, USA
DETC2014/MR-34593
MULTI-OBJECTIVE DESIGN OPTIMIZATION OF THE LEG MECHANISM FOR A
PIPING INSPECTION ROBOT
Renaud HENRY, Damien CHABLAT,
Mathieu POREZ, Fr´ed´eric BOYER
Institut de Recherche en Communications et
Cybern´etique de Nantes (IRCCyN)
UMR CNRS n◦ 6597
1, rue de la No¨e, 44321 Nantes Cedex 03, France
Email addresses:
{renaud.henry, damien.chablat}@irccyn.ec-nantes.fr
{mathieu.porez, frederic.boyer}@irccyn.ec-nantes.fr
Daniel KANAAN
AREVA NC, Bagnols sur C`eze, France
Email addresses: daniel.kanaan@areva.com
ABSTRACT
This paper addresses the dimensional synthesis of an adap-
tive mechanism of contact points ie a leg mechanism of a piping
inspection robot operating in an irradiated area as a nuclear
power plant. This studied mechanism is the leading part of the
robot sub-system responsible of the locomotion. Firstly, three ar-
chitectures are chosen from the literature and their properties are
described. Then, a method using a multi-objective optimization
is proposed to determine the best architecture and the optimal
geometric parameters of a leg taking into account environmen-
tal and design constraints. In this context, the objective functions
are the minimization of the mechanism size and the maximization
of the transmission force factor. Representations of the Pareto
front versus the objective functions and the design parameters
are given. Finally, the CAD model of several solutions located
on the Pareto front are presented and discussed.
INTRODUCTION
In a nuclear power plant, there are many places that the hu-
man workers cannot reach due to the high level of irradiation
(which can be deadly). However, for safety reasons inherent
to a nuclear power plant, the pipe-line equipments (which are
large in such a plant) require periodic and rigorous inspections.
In this context, the development of robotic system suitable to
finding and to repaire a failure in such an environment is essen-
tial. It is for this reason, since many years, numerous articles
appeared on this subject. In [1], the key issues raised by the de-
sign and the control of a piping inspection robot are presented.
More generally, in the field of pipe inspections, four following
major issues have to be faced: 1) how to move in a pipe; 2)
how to locate in a pipe; 3) how to inspect a pipe area; 4) how
to repair a default. Let us note that the work presented in our
paper only deals with the first issue which falls within the loco-
motion issue. To achieve locomotion in such highly constrained
pipe environment, we can classify the robot designs in two cat-
egories depending whether one takes inspiration from animals
living in narrow spaces or from engineering knowledge and nine
associated subcategories [2]. In the first category, we can imag-
ine designs inspired from the earthworms [3], the snakes [4], the
millipedes [5], the Lizards [6] and even from soft animals as the
octopus [7]. For the second one, we find designs based on the us-
ing of wheels and pulleys [8], the telescopic [9], the impact [10]
and the natural peristalsis [11]. The main problem of all these
solutions is that each designed robot has a specific architecture
for a given specification which is different in each case. Thus it
is difficult to find the best architecture that responds to an user
request. Despite this fact, the common denominators of all these
2. systems are the mechanisms to adapt the contact points of the
robot on the pipe surface and those to generate the expected con-
tact forces required by the desired motion in the pipe. It is in this
context that this paper takes place. Thus, the aim of the paper
is to design a mechanism able to adapt the contacts on the inner
surface of a pipe under constraints inherent to the environment.
More precisely, before defining the complete architecture of our
piping robot, we want to find by an optimization into a mecha-
nism selection, the best design minimizing the bulk volume of
the robot and maximizing the transmission factor between the
embedded motor and the contact points. To simplify, in this arti-
cle, we call now such a system : the legs such as they are depicted
in figure 1. In the context of our study, the considered pipe has a
variable diameter between 28 mm and 58 mm with bends.
a)
b)
2 rmax
2 rmin
FIGURE 1. Piping robot with a generic adaptive mechanism of the
contact points when the inner diameter: a) increases or b) decreases.
The outline of the paper is as follows. The mechanisms that
we use to make the legs of our piping inspection robot are pre-
sented in first section. Then, the objective functions and the con-
straints on the design parameters are introduced. In section three,
the optimization results under the form of Pareto fronts are pre-
sented. Moreover, CAD models of candidate mechanisms are
shown. Finally, the article ends with a discussion and conclud-
ing remarks.
Locomotion and environment
The locomotion can be obtained either by putting actuated
wheels or by varying the body length while the front and the
rear part are alternately fixed to the pipe, the way worms do.
These examples come from the classification made in [12] where
seven categories of locomotion types as (i) the pig [13], (ii),
the wheel [14], (iii) the crawler [15], (iv) the wall press [16],
(v) the walking [17], (vi) the inchworm [18] and (vii) the screw
type [19]. However, it is a well-known that the locomotion can
be achieved in different ways according to the type of pipe:
the wheels for the straight lines and the earthworms for the bends.
Before presenting the retained mechanisms, let us introduce
some notations. Its inner radius of the pipe r varies between rmin
and rmax with rmin = 14 mm and rmax = 29 mm.The minimum
value is fixed in such a way that the robot can embedded a mo-
tor, electric and energy. Moreover, we define a reference frame
whose the axis of motion, denoted by x, is along the main pipe
axis and the motion of the mechanism under study is along the
radius axis (Figure 1).
Geometric variations of piping
Park [20] lists a five principal geometric variations of pip-
ing. There are variations of (a) diameter, (b) curvature, and (c)
inclination, (d) branched pipe, and (e) uneven inner surface. A
pipe section can combine several geometric variations. For ex-
ample we can have an inclined branched pipe with uneven inner
surface. The variations of curvature limit the size of the robot
when it negotiates the elbow [14]. There are four parameters to
determine the size of the robot (1). The pipe have two parame-
ters with the radius of piping rp and the curvature rc. The robot
is defined in a cylinder with a diameter dr and length lr.
lr = 2 (2rp −dr)(2rc +dr) . (1)
So we choice a cylinder with a diameter of dr = 30mm and
a length of lr = 60mm because the minus radius of curvature is
rc = 45 mm and radius of piping rp = 20 mm.
Selection architectures of mechanism
We have selected two locomotion types, the inchworms
. Then we have selected compatible mechanisms of locomo-
tion types and geometric variations of piping. The three ar-
chitectures of mechanism selected is a slot-follower mechanism
[21–23], a crank and slider mechanism with 4 bars [12] and 6
bars [24]. Several mechanism have been removed. the solutions
of Kawaguchi [25] have proposed magnetic wheels but the envi-
ronment is nonmagnetic. Dertien [26] have built the Pirate robot
for diameter range between 63 mm to 125 mm but the robot can-
not be miniaturized and climb vertical pipe. Suzumori [27] have
designed a micro inspection robot for recover an object in a 25
mm pipe, but drive system [28] is limited a small pipe diameter
variation. Anthierens’s thesis [29, 30] focuses on an inchworms
locomotion in steam generator but variations and curvatures of
diameter are not possible.
3. A slot-follower mechanism, a crank and slider mecha-
nism with 4 bars and 6 bars
From the literature review, we have selected three architec-
tures of mechanism suitable to be used according to the size of
the pipe. For the three mechanisms, O is the origin of the refer-
ence frame, P(x,y) is the coordinate of the end-effector and ρ is
the length of the prismatic joint OA.
A
B
l2
l1
P(x,y)
O(0,0)x
y
FIGURE 2. A slot-follower mechanism.
Figure 2 is a slot-follower mechanism [21–23] where the
fixed prismatic joint is actuated and the other joints are idle.
Lengths l1 and l2 denoting the lengths of AP and OB respectively
define the geometry of mechanism entirely. The serial singulari-
ties (working mode changing) occur when the points A and O are
coincided. The mechanical limits occur when the points P and B
are coincided.
x
y
A
B
P(x,y)
O(0,0)
l1l2
l3
FIGURE 3. Crank and slider mechanism with 4 bars.
Figure 3 is a crank and slider mechanism with 4 bars [12]
where the fixed prismatic joint is actuated and the other joints
are idle. Lengths l1, l2 and l3 denoting the lengths of AB, OB and
BP respectively define the geometry of mechanism entirely. The
parallel singularities occur when O, B and A are aligned.
x
y
A
B
CD
l1
l2
l3l3
l2
l1
P(x,y)
O(0,0)
FIGURE 4. Crank and slider mechanism with 6 bars.
Figure 4 is a crank and slider mechanism with 6 bars [24]
where one fixed prismatic joint is actuated and the other joints
are idle. To reduce the design parameter space, we have added
some equalities. Lengths l1 denotes the lengths of AB and OB,
lengths l2 denotes the lengths of BD and BC and lengths l3 de-
notes the lengths of DP and CP. These simplifications will be
justified by the conclusion of the optimization of the crank and
slider mechanism with 4 bars (See Section V). The parallel sin-
gularities occur when O, B and A are aligned or C, D and P are
aligned.
Kinematic modeling of three mechanisms
The geometric parameters of the mechanism, l1, l2 , l3 (only
4 bars and 6 bars mechanism) and the actuator displacements ρ
permit us to define the Direct Kinematics Model (DKM) to have
the relation between the geometric parameters of the mechanism,
the actuator displacements and the moving platform pose y. The
assembly mode is chosen such that y > 0 and y > yB, where yB
is the ordinate coordinate of the point B. We also add constraints
to avoid the singular configurations. The limits of y is defined by
ymax and ymin. Figures 5–7 depict the three mechanisms in their
lower, upper and intermediate configurations for the assembly
mode chosen in the paper. The size of the mechanism is defined
by ∆x.
For a slot-follower mechanism (Figure 5), a single assembly
mode exists and we have:
y =
l2 l1
l2
2
+ρ2
. (2)
The limits ymax and ymin are:
ymin = l2 and ymax = l1 . (3)
4. −5
0
5
10
15
20
25
30
∆ x
O A
P
B
FIGURE 5. The black lines represent a slot-follower mechanism at an
intermediate configuration. The gray lines correspond to the lower and
upper configurations of the mechanism. The dotted line is the trajectory
of P and ∆x is the size of the mechanism.
ymin is constrained by the mechanical limits, when the points P
and B are coincide and ymax is constrained by the length of l1 in
vertical, when the points A and O are coincide (Figure 5). As
∆ x
A
B
P
O
FIGURE 6. The black lines represent a Crank and slider mechanism
with 4 bars at an intermediate configuration. The gray lines correspond
to the lower and upper configurations of the mechanism. The dotted line
is the trajectory of P and ∆x is the size of the mechanism.
for a crank and slider mechanism with 4 bars (Figure 6), two
assembly modes exist and we set
y =
2l2
1l2
2 −l4
1 +2l2
1ρ2 −l4
2 +2ρ2l2
2 −ρ4 (l2 +l3)
2ρl2
. (4)
The limits ymax and ymin are:
ymin = 0 and ymax = min l2
l3
l1
+1 ,l1 +l3 . (5)
ymin is zero when the mechanism is in parallel singularities be-
cause the points O, B and A are aligned.
∆ x
B
C
P
AO
D
FIGURE 7. The black lines represent a Crank and slider mechanism
with 6 bars at an intermediate configuration. The gray lines correspond
to the lower and upper configurations of the mechanism. The dotted line
is the trajectory of P and ∆x is the size of the mechanism.
As for a crank and slider mechanism with 6 bars (Figure 7),
four assembly modes exist and we set
y =
a1 +2
√
a2
2l1
, (6)
with:
a1 =4l1
4
+8l1
3
l2 +4l1
2
l2
2
+4l1
2
l3
2
−l1
2
ρ2
−2l1 l2 ρ2
−2l2
2
ρ2
,
a2 =(2l1 −ρ)(2l1 +ρ)(l1 +l2)2
(2l1 l3 −l2 ρ)(2l1 l3 +l2 ρ) .
The limits ymax an ymin are:
ymax = l1 +l2 +l3 , (7)
if l3 ≥ l2 then ymin = (l3)2 −(l2)2 , (8)
else ymin = (l2)2 −(l3)2
l1
l2
+1 . (9)
5. ymax is equal l1 + l2 + l3 because the mechanism is in serial sin-
gularities when the all points are aligned in vertical. ymin is con-
strain by parallel singularities.
MULTI-OBJECTIVE DESIGN OPTIMIZATION
Objective functions
The multi-objective optimization problem aims to determine
the optimum geometric parameters of the leg mechanism in or-
der to minimize the size of the mechanism and to maximize the
transmission factor.
Size of the mechanism There are numerous ways to
define the compactness of a mechanism. The first objection func-
tion is
f1 = ∆x . (10)
where ∆x is the size of the mechanism on the x axis which is
directly connected with the swept volume of the mechanism. ∆x
is obtained by the projection onto the x-axis of any points of the
mechanism during its motion. We set:
ρ ≥ 0.5 mm and ∆x ≤ 35 mm. (11)
The first limit avoids the serial singularities [31] and the second
one restricts the mechanism size.
Transmission force efficiency The second objective
function is the transmission force efficiency which is defined as
the ratio between output and input forces. We note
f2 = ηf =
Fw
Fa
. (12)
where Fa is the actuator force along the x axis, Fw is the contact
force in P along the y axis and ηf is the transmission efficiency
between the two forces. Moreover, for convenience, we set the
transmission efficiency as follows:
ηf ≥ 0.3 . (13)
In accordance with the definition of the transmission efficiency,
for a slot-follower mechanism, we have:
ηf =
l2
2
+ρ2 3/2
l2 l1 ρ
. (14)
As regarding the crank and slider mechanism with 4 bars, we
have:
ηf = 2
−l1
4
+2l1
2
l2
2
+2l1
2
ρ2 −l2
4
+2l2
2
ρ2 −ρ4ρ2l2
(l2 +l3) l1
2
−l2
2
+ρ2 L12
−l2
2
−ρ2
.
(15)
Finally, for a crank and slider mechanism with 6 bars, we have:
ηf = 2
l1
√
B
√
A
ρC
, (16)
with
A = (2l1 −ρ)(2l1 +ρ)(l1 +l2)2
(2l3 l1 −l2 ρ)
(2l3 l1 +l2 ρ) , (17)
B = 4l1
4
+8l1
3
l2 +4l1
2
l2
2
−2l2
2
ρ2
+4l3
2
l1
2
−l1
2
ρ2
−2l1 ρ2
l2 +2
√
A , (18)
C = 2l2
2
√
A+l1
2
√
A+2l1 l2
√
A+4l2
4
l1
2
+8l2
3
l1
3
−2l2
4
ρ2
−2l1
2
l2
2
ρ2
−
4l2
3
ρ2
l1 +4l2
2
l1
4
+4l3
2
l1
4
+8l2 l3
2
l1
3
+4l1
2
l2
2
l3
2
.
Design constraints
Due to assembly constraints, we have a set of inequalities.
For a slot-follower mechanism, we have:
l1 ≥ rmax and l2 ≤ rmin . (19)
For a crank and slider mechanism with 4 bars, we have:
min l2
l3
l1
+1 ,l1 +l3 ≥ rmax and rmin = 0. (20)
For a crank and slider mechanism with 6 bars, we have:
l1 +l2 +l3 ≥ rmax , (21)
if l2 ≥ l3 then
l2
2
−l3
2
l2
(l1 +l2) ≤ rmin , (22)
else l3
2
−l2
2
≤ rmin . (23)
Design Variables
Along with the above mentioned geometric parameters l1,
l2 and l3 are considered as design variables, also called decision
6. variables. As there are three leg mechanisms under study, the leg
type is another design variable that has to be taken into account.
Let d denote the leg type: d = 1 stands for the slot-follower
mechanism; d = 2 stands for crank and slider mechanism with
4 bars and d = 3 stands for the crank and slider mechanism with
6 bars. As a result, the optimization problem contains one dis-
crete variable, i.e., d, and three continuous design variables, i.e.,
l1, l2, l3. Hence, the design variables vector x is given by:
x = [d,l1,l2,l3]T
(24)
Multi-objective optimization problem statement
The Multi-objective Optimization Problem (MOO) for a leg
mechanism can be stated as: Find the optimum design variables
x of leg mechanism in order to minimize the size of the mecha-
nism and maximize the transmission factor subject to geometric
constraints. Mathematically, the problem can be written as:
minimize f1(x) = ∆x ;
maximize f2(x) = ηf .
over x = [d,l1,l2,l3]T
subject to :
g1 : l1 ≥ rmax for d = 1 ;
g2 : l2 ≤ rmin for d = 1 ;
g3 : min l2
l3
l1
+1 ,l1 +l3 ≥ rmax for d = 2 ;
g4 : rmin ≥ 0 for d = 2 ;
g5 : l1 +l2 +l3 ≥ rmax for d = 3 ;
g6 : if l2 ≥ l3 then
l2
2
−l3
2
l2
(l1 +l2) ≤ rmin
else l3
2
−l2
2
≤ rmin for d = 3 ;
g7 : ηf ≥ 0.3 ;
g8 : ρ ≥ 0.5 mm ;
g9 : ∆x ≤ 35 mm ;
g10 : 1 mm ≤ l1,l2,l3 ≤ 50 mm .
Optimization implementation
The classic approach to optimization is to calculate all pos-
sible combinations in the solution space. With five settings
(l1,l2,l3,d,ρ), the computation time becomes excessive. For ex-
ample, we have 12 billion combinations with 250 values for
l1,l2,l3,ρ and 3 values of d.
To solve the optimization problem, we use the genetic algo-
rithm of Matlab [32]. A genetic algorithm is a search heuristic
that mimics the process of natural selection. The computation
time per mechanism is 2 hours with the settings:
• population size: 6000;
• pareto fraction: 50%;
• tolerance function: 10−4;
• number of sessions per problem: 5.
To scan the solution space, the algorithm uses a population of
6000 individuals with 50% of individuals on the Pareto front.
This allows the other half of the population to reach other opti-
mal solutions. For the same reason, we execute five sessions per
mechanism in order to have redundancy. To reduce the computa-
tion time, tolerance precision of the objectives functions is 10−4.
The computer use an Intel Core i5-560 at 2.67GHz with 8 Go
RAM.
RESULTS AND DISCUSSIONS
Based on the kinematic models introduced in section III, the
multi-objective optimization problem, expressed in section IV, is
solved by means MAPLE and MATLAB. MAPLE codes given
the expression of the objective functions and MATLAB code pro-
vides functions for the optimization and to make filter to obtain
the Pareto front. Figure 8 depicts the Pareto front obtained after
the optimization.
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
25
26
27
28
29
30
31
32
33
ηf
∆x(mm)
Front 2 Pareto 2D − bellette AE
Suboptimal
solutions
Pareto
Front
Utopian
solutions
Optimum
efficiency
Optimum size
Intermediate
solution
FIGURE 8. Example of the Pareto front with a mechanism versus
the two objective functions ∆x and ηf . The Pareto front includes opti-
mal solutions. The suboptimal solutions are feasible but inferior to the
Pareto front. Utopian solutions are to better than optimal solutions but
infeasible.
To allow a better understanding of the Pareto front, we made
7. three optimizations by setting d = 1, 2, 3, i.e. the type of mecha-
nism, as is depicted in Figure 9.
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
15
20
25
30
35
ηf
∆x(mm)
Pareto All 2 − Avec Encombrent
A slot−follower mechanism.
Crank and slider mechanism with 4 bars
Crank and slider mechanism with 6 bars
S1a
S3c
S2a
S3a
S2b
S3b
S2c
S1b
S1c
FIGURE 9. Pareto front associated with the three mechanisms with
the two objective functions ∆x and ηf .
Slot-follower mechanism
From the Pareto front, we can extract three values:
• optimum value of ∆x = 25.7 mm with ηf = 0.35:
l1 = 29.2 mm and l2 = 3.9 mm ; (25)
• optimum value of ηf = 1.25 with ∆x = 32.3:
l1 = 29.0 mm and l2 = 14.0 mm ; (26)
• intermediate solution ∆x = 29.1 and ηf = 0.94:
l1 = 29.0 mm and l2 = 10.5 mm . (27)
Figure 10 depicts the evolution of the design variables and Fig-
ure 11 the CAD model associated with the optimal value of ∆x
and ηf and an intermediate solution. We note that l2 = rmin. Fig-
ure 12 depicts the evolution of the transmission force efficiency
between the lower and upper configurations of the slot-follower
mechanism. The constraint g8 prevents a serial singularity. So
the lever arm between points P, B and C intervenes. The value of
transmission force efficiency is high for the optimum efficiency
and Intermediate solutions because the length between P and B
is small with l2 ≈ rmin. In contrast to the optimum size with a l2
small.
29 29.05 29.1 29.15 29.2 29.25
2
4
6
8
10
12
14
l
1
(mm)
l
2
(mm)
Graphique 2D − Front Pareto dans l espace articulaire − bellette AE
S1c
S
1b
S
1a
FIGURE 10. Pareto front for the slot-follower mechanism in the de-
sign parameter space. S1a is an optimum efficiency solution, S1b is an
intermediate solution and S1c is an optimum size solution.
a) b) c)
FIGURE 11. CAD model of the three solutions from the Pareto front
for the slot-follower mechanism with a) the optimum size solution, b)
the intermediate solution, c) the optimum efficiency solution.
0 5 10 15 20 25 30
0
2
4
6
8
10
12
14
ρ (mm)
ηf
Trace Optimum biellette
Optimum value of η
f
Intermediate solution
Optimum value of ∆ x
FIGURE 12. Evolution of the transmission force efficiency between
the high and low position of the slot-follower mechanism.
Crank and slider mechanism with 4 bars
From the Pareto front, we can extract three values:
8. • optimum value of ∆x = 25.4mm with ηf = 0.52:
l1 = 13.8 mm,l2 = 13.8 mm and l3 = 15.2 mm ; (28)
• optimum value of ηf = 0.75 with ∆x = 35.0mm:
l1 = 20.0 mm,l2 = 20.0 mm and l3 = 9.0 mm ; (29)
• intermediate solution ∆x = 30.3mm and ηf = 0.65:
l1 = 17.3 mm,l2 = 17.3 mm and l3 = 11.7 mm . (30)
Figure 13 depicts the evolution of the design variables and Fig-
ure 14 the CAD model associated with the optimal value of ∆x
and ηf and an intermediate solution. We note that l1 = l2 and the
Pareto front is defined by:
l1 −2l2 −l3 +28.99 = 0 (31)
The Pareto front is a straight line in the design parameter space
of mechanism. The size of the mechanism is proportional in the
length of l1 and l2. The transmission force efficiency is propor-
tional in the length of l3 because there is a lever arm between
l1 and l3. If l1 is smaller than l3, the size of the mechanism is
favoured. If l3 is smaller than l1, the transmission force efficiency
is favored.
Crank and slider mechanism with 6 bars
From the Pareto front, we can extract three values:
• optimum value of ∆x = 16.4mm with ηf = 0.30:
l1 = 8.8 mm,l2 = 8.8 mm and l3 = 11.6 mm ; (32)
• optimum value of ηf = 0.75 with ∆x = 34.9:
l1 = 19.8 mm,l2 = 4.6 mm and l3 = 4.6 mm ; (33)
• intermediate solution ∆x = 25.7mm and ηf = 0.56:
l1 = 14.7 mm,l2 = 7.2 mm and l3 = 7.2 mm . (34)
Figure 15 depicts the evolution of the design variables and Fig-
ure 16 the CAD model associated with the optimal value of ∆x
12
14
16
18
20
12 13 14 15 16 17 18 19 20
8
9
10
11
12
13
14
15
16
l
1
(mm)
Graphique 2D − Front Pareto dans l espace articulaire − barres3 AE
l3
(mm)
S2b
S2a
l2
(mm)
S
2c
FIGURE 13. Pareto front for the crank and slider mechanism with 4
bars in the design parameter space. S2a is an optimum efficiency solu-
tion , S2b is an intermediate solution and S2c is an optimum size solution
.
a) b) c)
FIGURE 14. CAD model of the three solutions from the Pareto front
for the Crank and slider mechanism with 4 bars a) the optimum size so-
lution, b) the intermediate solution, c) the optimum efficiency solution.
and ηf and an intermediate solution.The Pareto front is defined
by:
−l1 −l2 −l3 +29.04 = 0 (35)
The first line of the Pareto front is without constraint g9 and l2 =
l3. The second line of the Pareto front with constraint g9 and
l1 = l2. The two lines are orthogonal. If we want to maximize the
transmission force efficiency, we are in the case l2 = l3 (S3a), so
the ratio of the lever arm depends l1/l2. If we want to minimize
the size of the mechanism, it is in the case l1 = l2 (S3c), so the
ratio of the lever arm depends l2/l3.
CONCLUSIONS
In this article, we have presented a multi-objective optimiza-
tion problem to design the leg mechanisms of a pipe inspection
robot. Three closed loop mechanisms are candidate to be used
for the locomotion of this robot. We have defined two objective
functions and a set of constraint equations related to the kine-
9. 5
10
15
20
4 5 6 7 8 9 10
4
5
6
7
8
9
10
11
12
l
1
(mm)
Graphique 2D − Front Pareto dans l espace articulaire − barres6 AE
l
2
(mm)
l3
(mm)
S3c
S
3b
S
3a
FIGURE 15. Pareto front for the crank and slider mechanism with 6
bars in the design parameter space. S3a is an optimum efficiency solu-
tion , S3b is an intermediate solution and S3c is an optimum size solution
.
a) b) c)
FIGURE 16. CAD model of the three solutions from the Pareto front
for the Crank and slider mechanism with 6 bars a) the optimum size so-
lution, b) the intermediate solution, c) the optimum efficiency solution.
matic behavior. A genetic algorithm is used to solve this prob-
lem with discrete and continuous variables. The optimization is
made for each mechanism as three separate problems to explain
the Pareto front obtained by the multi-objective problem resolu-
tion. We find out that the slot-follower mechanism is the best
solution for a transmission force efficiency greater than 60% and
the Crank and slider mechanism with 6 bars is the best for the
other cases. We note that, for our constraint equations, the crank
and slider mechanisms have similar performances. We select a
S1a solution of slot-follower mechanism. The size of the mech-
anisms changes little between different solutions. The transmis-
sion force efficiency significantly changes between 60 % and 125
%. In a practical case, there will be at least 3 legs by groups.
But The contact forces of legs is influenced by the cantilever be-
tween points 0, P and between two groups of legs. Similarly, dy-
namic phenomena are not taken into account in this paper. The
transmission force efficiency is lower than for the slot-follower
mechanism. Conversely, the slot-follower mechanism may be
more difficult to build because of the passive prismatic and fric-
tion can reduce its efficiency. The mechanical strength of axes
mechanisms may limit the transmitted power. In future works,
the dynamic model with friction parameters will be used in lo-
comotion phases to compare the efficiency of these mechanisms.
Several locomotion pattern will be tested in our simulator to en-
sure contact between the robot and the inside surface of the pipe.
ACKNOWLEDGMENT
The work presented in this paper was partially funded by
the AREVA company by and a grant of the Ecole des Mines de
Nantes, France.
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