The Pivot algorithm is a very efficient ‘dynamic’ algorithm for generating d-dimensional canonical ensemble.
It drastically modifies the chain dimension.
The document discusses mechanical advantage and velocity analysis of mechanisms. It defines mechanical advantage as the ratio of output to input force or torque. Mechanical advantage is infinite when the input link is in line with the coupler link. Velocity analysis involves studying the linear velocities of points on links and angular velocities of links. Velocity analysis can be done analytically or graphically, with the graphical method using the instantaneous center method or relative velocity method.
This document analyzes the problem of balancing an inverted pendulum, where a steel ball rolls on arched tracks attached to a movable cart. It describes the control objective of keeping the ball balanced on top of the arc while positioning the cart. The key points are:
1) The problem is modeled using basic physical equations accounting for the vertical and horizontal reaction forces on the ball and cart.
2) The equations are nonlinear and coupled, but can be linearized around the origin for control purposes.
3) State feedback control is implemented using linearized model parameters to feed back the four states to the controller.
4) Cascade control divides the problem into inner-loop ball control and outer-loop cart
the presentation consists of various important terms that are generally linked with the analysis of a common four bar mechanism which are as follows - coupler curves, toggle positions, transmission angles, mechanical advantage, acc analysis and coriolis component.
Intermittent predictive control of an inverted pendulumIvan Tim Oloya
The Rotary Inverted Pendulum (RIP) represents a broad class of under actuated sys-tems making its control a classic problem. The dynamic equations used to represent the RIP are complex and nonlinear, which makes design and control of the system challenging.
This paper presents swing up and stabilization of the RIP system. The controller used to achieve swing up is energy based and acts by adding energy to the system until the pendulum reaches the linear region in the vertical upright position. A high gain ob-server has been implemented to estimate the unmeasurable system states during swing up.
Once in the linear region, a stabilizing control is switched on. The switch on is made possible by designing a mode-switching strategy to determine the point at which tran-sition occurs. A linearized model of the RIP is used to determine the feedback gains needed for stabilization by applying the Linear-Quadratic Regulator (LQR) method.
Two different stabilizing controllers are compared. An intermittent controller, which can be either time-triggered or event-triggered and a continuous predictive controller. A linear Luenberger observer has been designed to estimate the unmeasurable system states when the pendulum has switched to stabilization control.
Effectiveness of this system has been verified through simulation using MATLAB and Simulink.
This document summarizes a student project on stabilizing and balancing linear and rotary inverted pendulum systems. It discusses the design and implementation of PID controllers to balance an inverted pendulum mounted on a cart (linear system) and a rotary inverted pendulum prototype. Key steps included mathematical modeling, simulation in MATLAB, PID controller tuning, and applying the controller to experimental setups. Results showed the systems could be stabilized using optimized PID and LQR controllers designed via pole placement and minimizing cost functions.
- Today's lecture covers transmission angle, instantaneous center method, and locating instantaneous centers in mechanisms.
- The transmission angle between the output link and coupler is maximum at 90 degrees for maximum torque transmission.
- The instantaneous center method and relative velocity method can be used for velocity or acceleration analysis of mechanisms.
- The instantaneous center method uses the centers of rotation between two links to determine velocities. The number of instantaneous centers equals the number of possible link combinations.
This document provides an overview of an upcoming lecture on mechanisms and kinematics. It will include a numerical problem to calculate the velocity and acceleration of parts in an engine mechanism using velocity and acceleration diagrams. Specifically, students will analyze the motion of slider D and link CD, calculating their acceleration and angular acceleration given the crank rotates uniformly at 180 rpm and geometric dimensions of the mechanism are provided. The document provides the problem statement and notes it is Example 8.7 from the reference book Theory of Machines. Details on setting up the problem using specific scales are also given, as well as the topics to be covered in the next lecture.
This document summarizes a project to stabilize an inverted pendulum using a lead-lag compensator. It includes the mathematical modeling of the inverted pendulum system and motor cart dynamics. The transfer functions of the individual systems and overall plant are derived. Root locus analysis is used to design the compensator. An analog to digital converter and parallel port are used to interface the hardware and send sensor readings to the computer for processing. References on control systems and inverted pendulum simulations are also provided.
The document discusses mechanical advantage and velocity analysis of mechanisms. It defines mechanical advantage as the ratio of output to input force or torque. Mechanical advantage is infinite when the input link is in line with the coupler link. Velocity analysis involves studying the linear velocities of points on links and angular velocities of links. Velocity analysis can be done analytically or graphically, with the graphical method using the instantaneous center method or relative velocity method.
This document analyzes the problem of balancing an inverted pendulum, where a steel ball rolls on arched tracks attached to a movable cart. It describes the control objective of keeping the ball balanced on top of the arc while positioning the cart. The key points are:
1) The problem is modeled using basic physical equations accounting for the vertical and horizontal reaction forces on the ball and cart.
2) The equations are nonlinear and coupled, but can be linearized around the origin for control purposes.
3) State feedback control is implemented using linearized model parameters to feed back the four states to the controller.
4) Cascade control divides the problem into inner-loop ball control and outer-loop cart
the presentation consists of various important terms that are generally linked with the analysis of a common four bar mechanism which are as follows - coupler curves, toggle positions, transmission angles, mechanical advantage, acc analysis and coriolis component.
Intermittent predictive control of an inverted pendulumIvan Tim Oloya
The Rotary Inverted Pendulum (RIP) represents a broad class of under actuated sys-tems making its control a classic problem. The dynamic equations used to represent the RIP are complex and nonlinear, which makes design and control of the system challenging.
This paper presents swing up and stabilization of the RIP system. The controller used to achieve swing up is energy based and acts by adding energy to the system until the pendulum reaches the linear region in the vertical upright position. A high gain ob-server has been implemented to estimate the unmeasurable system states during swing up.
Once in the linear region, a stabilizing control is switched on. The switch on is made possible by designing a mode-switching strategy to determine the point at which tran-sition occurs. A linearized model of the RIP is used to determine the feedback gains needed for stabilization by applying the Linear-Quadratic Regulator (LQR) method.
Two different stabilizing controllers are compared. An intermittent controller, which can be either time-triggered or event-triggered and a continuous predictive controller. A linear Luenberger observer has been designed to estimate the unmeasurable system states when the pendulum has switched to stabilization control.
Effectiveness of this system has been verified through simulation using MATLAB and Simulink.
This document summarizes a student project on stabilizing and balancing linear and rotary inverted pendulum systems. It discusses the design and implementation of PID controllers to balance an inverted pendulum mounted on a cart (linear system) and a rotary inverted pendulum prototype. Key steps included mathematical modeling, simulation in MATLAB, PID controller tuning, and applying the controller to experimental setups. Results showed the systems could be stabilized using optimized PID and LQR controllers designed via pole placement and minimizing cost functions.
- Today's lecture covers transmission angle, instantaneous center method, and locating instantaneous centers in mechanisms.
- The transmission angle between the output link and coupler is maximum at 90 degrees for maximum torque transmission.
- The instantaneous center method and relative velocity method can be used for velocity or acceleration analysis of mechanisms.
- The instantaneous center method uses the centers of rotation between two links to determine velocities. The number of instantaneous centers equals the number of possible link combinations.
This document provides an overview of an upcoming lecture on mechanisms and kinematics. It will include a numerical problem to calculate the velocity and acceleration of parts in an engine mechanism using velocity and acceleration diagrams. Specifically, students will analyze the motion of slider D and link CD, calculating their acceleration and angular acceleration given the crank rotates uniformly at 180 rpm and geometric dimensions of the mechanism are provided. The document provides the problem statement and notes it is Example 8.7 from the reference book Theory of Machines. Details on setting up the problem using specific scales are also given, as well as the topics to be covered in the next lecture.
This document summarizes a project to stabilize an inverted pendulum using a lead-lag compensator. It includes the mathematical modeling of the inverted pendulum system and motor cart dynamics. The transfer functions of the individual systems and overall plant are derived. Root locus analysis is used to design the compensator. An analog to digital converter and parallel port are used to interface the hardware and send sensor readings to the computer for processing. References on control systems and inverted pendulum simulations are also provided.
This document discusses simple machines and their uses. It defines six types of simple machines: lever, pulley, wheel and axle, inclined plane, screw, and wedge. For each machine it explains how it works and provides examples. It also covers concepts like work, energy, power, mechanical advantage, efficiency, and how machines conserve energy. Simple machines allow us to do work more easily by reducing the amount of force needed.
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.
• Optimization of shaking force and shaking moment using mathematical modeling in MATLAB and ADAMS simulation.
• Studied the effect of projectile mass, counterweight and pivot height on the range of the projectile.
• Modelled and simulated the trebuchet using ADAMS.
• Mathematical analysis and plotting of resulting graphs using MATLAB
• Analysis of structure and material in ANSYS.
• Optimization of the projectile mass to be launched with respect to the counter weight used.
• Calculation of shaking force and shaking moment using mathematical modeling and ADAMS simulation
• The effect of counterweight, projectile mass and height of pivot on the range of projectile through graphical plots
• Analysis of the hinge forces and the hinge torques and the projectile velocity’s X-component and Y-component were studied through graphical plots.
• The shaking torque comes out to be negligible and the shaking force is a considerable amount so we have to attach a counterweight to minimise the shaking force.
This document is the final project report for controlling an inverted pendulum system. It includes modeling the nonlinear dynamics of the pendulum cart system and deriving the state space equations. The goal is to balance the pendulum in the vertically upward unstable equilibrium position using feedback control. The report outlines modeling the system, linearizing about the unstable point, designing a feedback controller using linear quadratic regulation, and simulating the closed-loop response. Parameter perturbations are also analyzed through simulation to study the transient behavior and stability margins of the controlled system.
This document provides an excerpt from the textbook "Vector Mechanics for Engineers: Dynamics" which discusses plane motion of rigid bodies. It includes sections on equations of motion for rigid bodies, angular momentum of rigid bodies in plane motion, and D'Alembert's principle applied to plane motion. It also provides sample problems demonstrating how to set up and solve equations of motion for rigid bodies undergoing plane motion, including problems involving translation, rotation, and combinations of the two.
The document discusses manipulator Jacobians in robotics. A manipulator Jacobian is a matrix that is used to transform the velocity of robot joints into the velocity of the end effector. It has an upper half that describes the linear velocity of the end effector and a lower half that describes the angular velocity. The Jacobian allows the relationship between joint velocities and end effector velocities to be expressed mathematically. Examples are given to demonstrate how to calculate the Jacobian for specific robot manipulators.
1. Two tests were conducted on a vertical axis wind turbine: one with just the rotor, and one with a conveyor placed in front of the rotor.
2. Power production increased by 50% over 13 m/s wind speed and 30% below 13 m/s when the conveyor was added.
3. Calculations show that with a larger, optimized conveyor and increased rotor diameter and length, power production could reach the goal of 2360 watts at a wind speed of 10 m/s.
This document contains chapter materials from the textbook "Vector Mechanics for Engineers: Dynamics, Ninth Edition" regarding the kinematics of rigid bodies. It discusses various types of rigid body motion including translation, rotation about a fixed axis, general plane motion, and general motion. It provides definitions and equations for the velocity and acceleration of particles in a rigid body undergoing different types of motion, including examples calculating velocity, acceleration, and angular displacement over time. Key concepts covered include absolute and relative velocity and acceleration in plane motion, instantaneous centers of rotation, and the effects of rotating reference frames.
1. Trajectories for robotic arms can include via points that the arm passes close to but not necessarily through. Both position and orientation of the arm need to be interpolated along the trajectory.
2. Transitions between straight line segments of a trajectory involve constant acceleration curves like parabolas. The trajectory is planned to satisfy constraints like initial and final positions, velocities, and times.
3. Rotational transitions between orientations are found similarly by defining equivalent axes of rotation and making the rotation a linear function of time along the transition.
A manipulator is a series of linked segments connected by actuated joints that can manipulate objects without direct contact. The Jacobian inverse allows computation of the joint velocities required to achieve a desired end effector velocity as long as the Jacobian matrix is square and non-singular. The Jacobian inverse has applications in robotics such as handling materials, surgery, space and underwater exploration, and entertainment.
The inverse kinematics problem - Aiman Al-AllaqAimanAlAllaq
The document discusses inverse kinematics and how to solve the inverse kinematics problem for a robotic manipulator. It uses a 5-axis Rhino XR-3 robot as an example. It explains that inverse kinematics determines the joint variables given a desired position and orientation of the tool, which is important for tasks planned using external sensors. It then outlines the step-by-step process used to solve the inverse kinematics problem, which involves using the tool configuration vector obtained from the arm matrix and performing trigonometric operations to isolate each joint variable.
The document describes a project to program an Adept iCobra 600 robot to pick up wooden bricks from a conveyor belt and place them in an 'S' shaped pattern. The robot is programmed using Adept ACE software. Coordinates for pick up and placement locations are determined using jog control in LabVIEW. The program was successfully tested and helped students learn basics of industrial robot programming.
This document provides an overview of the topics that will be covered in Chapter 1 of the textbook "Vector Mechanics for Engineers: Statics". It defines mechanics and its categories, discusses fundamental concepts like space, time, mass and force. It also outlines fundamental principles including Newton's Laws, reviews common systems of units, and describes the typical method of solving mechanics problems including drawing free-body diagrams and checking solutions. Finally, it discusses numerical accuracy in engineering problems and solutions.
The document discusses different methods for representing 3D rotations and orientations, including rotation matrices, Euler angles, and quaternions. It explains that quaternions represent a rotation as a combination of a scalar and vector, and describe how to perform operations like rotation, composition, and normalization using quaternions. Quaternions use fewer parameters than rotation matrices but more easily represent arbitrary rotations and can be interpolated for smooth animation.
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.
This chapter discusses statics of particles, including:
- Representing multiple forces on a particle with a single resultant force
- Conditions for a particle to be in equilibrium
- Using free-body diagrams to analyze forces on a particle
- Adding vector forces using graphical and trigonometric methods
- Resolving forces into rectangular components and adding the components
- Solving example problems by drawing free-body diagrams, applying equilibrium conditions, and using vector math to determine unknown forces
Kinematics is the study of motion without considering forces. Robot kinematics specifically refers to the analytical study of robot motion and how robotic systems move. There are two main types of kinematics: forward kinematics and inverse kinematics. Forward kinematics uses the robotic equations to determine the position of the end effector given the joint parameters. Inverse kinematics determines the necessary joint parameters to achieve a desired end effector position and orientation. Inverse kinematics is important for robot trajectory planning but is generally more difficult than forward kinematics.
The document discusses optimization of tool path for robots in an assembly environment. It aims to develop new algorithms and techniques to optimize the tool path for increased productivity and efficiency with lower energy costs. This includes formulating the tool path optimization problem as a traveling salesman problem (TSP) and developing insertion and reordering algorithms to find optimal non-intersecting paths between target points visited by the robot tool. The document also covers inverse kinematics techniques to determine robot joint parameters required to reach specified target points.
There are three main types of stepper motors: variable reluctance, permanent magnet, and hybrid. Variable reluctance stepper motors use changes in magnetic reluctance to rotate and can be single or multi-stack. They provide high torque but have torque ripple issues. Permanent magnet stepper motors use permanent magnets on the rotor and have bipolar drive circuits. They can achieve a 45 degree step angle through alternate single and two phase excitation. Hybrid stepper motors combine features of variable reluctance and permanent magnet motors, with a 4 pole stator and 5 pole rotor construction. Each motor type has advantages and disadvantages related to torque, torque ripple, and drive circuit complexity.
1) A 4-bar linkage mechanism is used to design a recumbent elliptical trainer to rehabilitate people with lower extremity mobility restrictions. The linkage converts rotational motion to an elliptical trajectory.
2) The 4-bar linkage mechanism has one degree of freedom according to Grubler's equation. An elliptical trajectory is achieved by connecting the legs to the point that traces an ellipse during the linkage's back-and-forth motion.
3) Velocity and acceleration are derived using velocity and acceleration diagrams from the 4-bar linkage mechanism. The slider's velocity is calculated as 1.6756 m/s and acceleration is -3.5975 m/s2 using D'Alembert's principle
This document discusses simple machines and their uses. It defines six types of simple machines: lever, pulley, wheel and axle, inclined plane, screw, and wedge. For each machine it explains how it works and provides examples. It also covers concepts like work, energy, power, mechanical advantage, efficiency, and how machines conserve energy. Simple machines allow us to do work more easily by reducing the amount of force needed.
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.
• Optimization of shaking force and shaking moment using mathematical modeling in MATLAB and ADAMS simulation.
• Studied the effect of projectile mass, counterweight and pivot height on the range of the projectile.
• Modelled and simulated the trebuchet using ADAMS.
• Mathematical analysis and plotting of resulting graphs using MATLAB
• Analysis of structure and material in ANSYS.
• Optimization of the projectile mass to be launched with respect to the counter weight used.
• Calculation of shaking force and shaking moment using mathematical modeling and ADAMS simulation
• The effect of counterweight, projectile mass and height of pivot on the range of projectile through graphical plots
• Analysis of the hinge forces and the hinge torques and the projectile velocity’s X-component and Y-component were studied through graphical plots.
• The shaking torque comes out to be negligible and the shaking force is a considerable amount so we have to attach a counterweight to minimise the shaking force.
This document is the final project report for controlling an inverted pendulum system. It includes modeling the nonlinear dynamics of the pendulum cart system and deriving the state space equations. The goal is to balance the pendulum in the vertically upward unstable equilibrium position using feedback control. The report outlines modeling the system, linearizing about the unstable point, designing a feedback controller using linear quadratic regulation, and simulating the closed-loop response. Parameter perturbations are also analyzed through simulation to study the transient behavior and stability margins of the controlled system.
This document provides an excerpt from the textbook "Vector Mechanics for Engineers: Dynamics" which discusses plane motion of rigid bodies. It includes sections on equations of motion for rigid bodies, angular momentum of rigid bodies in plane motion, and D'Alembert's principle applied to plane motion. It also provides sample problems demonstrating how to set up and solve equations of motion for rigid bodies undergoing plane motion, including problems involving translation, rotation, and combinations of the two.
The document discusses manipulator Jacobians in robotics. A manipulator Jacobian is a matrix that is used to transform the velocity of robot joints into the velocity of the end effector. It has an upper half that describes the linear velocity of the end effector and a lower half that describes the angular velocity. The Jacobian allows the relationship between joint velocities and end effector velocities to be expressed mathematically. Examples are given to demonstrate how to calculate the Jacobian for specific robot manipulators.
1. Two tests were conducted on a vertical axis wind turbine: one with just the rotor, and one with a conveyor placed in front of the rotor.
2. Power production increased by 50% over 13 m/s wind speed and 30% below 13 m/s when the conveyor was added.
3. Calculations show that with a larger, optimized conveyor and increased rotor diameter and length, power production could reach the goal of 2360 watts at a wind speed of 10 m/s.
This document contains chapter materials from the textbook "Vector Mechanics for Engineers: Dynamics, Ninth Edition" regarding the kinematics of rigid bodies. It discusses various types of rigid body motion including translation, rotation about a fixed axis, general plane motion, and general motion. It provides definitions and equations for the velocity and acceleration of particles in a rigid body undergoing different types of motion, including examples calculating velocity, acceleration, and angular displacement over time. Key concepts covered include absolute and relative velocity and acceleration in plane motion, instantaneous centers of rotation, and the effects of rotating reference frames.
1. Trajectories for robotic arms can include via points that the arm passes close to but not necessarily through. Both position and orientation of the arm need to be interpolated along the trajectory.
2. Transitions between straight line segments of a trajectory involve constant acceleration curves like parabolas. The trajectory is planned to satisfy constraints like initial and final positions, velocities, and times.
3. Rotational transitions between orientations are found similarly by defining equivalent axes of rotation and making the rotation a linear function of time along the transition.
A manipulator is a series of linked segments connected by actuated joints that can manipulate objects without direct contact. The Jacobian inverse allows computation of the joint velocities required to achieve a desired end effector velocity as long as the Jacobian matrix is square and non-singular. The Jacobian inverse has applications in robotics such as handling materials, surgery, space and underwater exploration, and entertainment.
The inverse kinematics problem - Aiman Al-AllaqAimanAlAllaq
The document discusses inverse kinematics and how to solve the inverse kinematics problem for a robotic manipulator. It uses a 5-axis Rhino XR-3 robot as an example. It explains that inverse kinematics determines the joint variables given a desired position and orientation of the tool, which is important for tasks planned using external sensors. It then outlines the step-by-step process used to solve the inverse kinematics problem, which involves using the tool configuration vector obtained from the arm matrix and performing trigonometric operations to isolate each joint variable.
The document describes a project to program an Adept iCobra 600 robot to pick up wooden bricks from a conveyor belt and place them in an 'S' shaped pattern. The robot is programmed using Adept ACE software. Coordinates for pick up and placement locations are determined using jog control in LabVIEW. The program was successfully tested and helped students learn basics of industrial robot programming.
This document provides an overview of the topics that will be covered in Chapter 1 of the textbook "Vector Mechanics for Engineers: Statics". It defines mechanics and its categories, discusses fundamental concepts like space, time, mass and force. It also outlines fundamental principles including Newton's Laws, reviews common systems of units, and describes the typical method of solving mechanics problems including drawing free-body diagrams and checking solutions. Finally, it discusses numerical accuracy in engineering problems and solutions.
The document discusses different methods for representing 3D rotations and orientations, including rotation matrices, Euler angles, and quaternions. It explains that quaternions represent a rotation as a combination of a scalar and vector, and describe how to perform operations like rotation, composition, and normalization using quaternions. Quaternions use fewer parameters than rotation matrices but more easily represent arbitrary rotations and can be interpolated for smooth animation.
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.
This chapter discusses statics of particles, including:
- Representing multiple forces on a particle with a single resultant force
- Conditions for a particle to be in equilibrium
- Using free-body diagrams to analyze forces on a particle
- Adding vector forces using graphical and trigonometric methods
- Resolving forces into rectangular components and adding the components
- Solving example problems by drawing free-body diagrams, applying equilibrium conditions, and using vector math to determine unknown forces
Kinematics is the study of motion without considering forces. Robot kinematics specifically refers to the analytical study of robot motion and how robotic systems move. There are two main types of kinematics: forward kinematics and inverse kinematics. Forward kinematics uses the robotic equations to determine the position of the end effector given the joint parameters. Inverse kinematics determines the necessary joint parameters to achieve a desired end effector position and orientation. Inverse kinematics is important for robot trajectory planning but is generally more difficult than forward kinematics.
The document discusses optimization of tool path for robots in an assembly environment. It aims to develop new algorithms and techniques to optimize the tool path for increased productivity and efficiency with lower energy costs. This includes formulating the tool path optimization problem as a traveling salesman problem (TSP) and developing insertion and reordering algorithms to find optimal non-intersecting paths between target points visited by the robot tool. The document also covers inverse kinematics techniques to determine robot joint parameters required to reach specified target points.
There are three main types of stepper motors: variable reluctance, permanent magnet, and hybrid. Variable reluctance stepper motors use changes in magnetic reluctance to rotate and can be single or multi-stack. They provide high torque but have torque ripple issues. Permanent magnet stepper motors use permanent magnets on the rotor and have bipolar drive circuits. They can achieve a 45 degree step angle through alternate single and two phase excitation. Hybrid stepper motors combine features of variable reluctance and permanent magnet motors, with a 4 pole stator and 5 pole rotor construction. Each motor type has advantages and disadvantages related to torque, torque ripple, and drive circuit complexity.
1) A 4-bar linkage mechanism is used to design a recumbent elliptical trainer to rehabilitate people with lower extremity mobility restrictions. The linkage converts rotational motion to an elliptical trajectory.
2) The 4-bar linkage mechanism has one degree of freedom according to Grubler's equation. An elliptical trajectory is achieved by connecting the legs to the point that traces an ellipse during the linkage's back-and-forth motion.
3) Velocity and acceleration are derived using velocity and acceleration diagrams from the 4-bar linkage mechanism. The slider's velocity is calculated as 1.6756 m/s and acceleration is -3.5975 m/s2 using D'Alembert's principle
This document provides an overview of key concepts in rotational kinematics covered in Chapter 8, including angular displacement, velocity, and acceleration. It defines these rotational variables and their relationships to linear motion. Examples are given to illustrate calculating angular variables and transforming between rotational and tangential linear motion for objects like rolling wheels or helicopter blades. Formulas for rotational kinematics with constant angular acceleration are also presented.
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.
A cam is a mechanical device used to convert rotational motion into linear or oscillating motion. It works through direct contact with a follower. Cams can be classified based on the follower's surface, type of motion, and position relative to the cam's center. Common follower surfaces include knife-edge, roller, and flat or spherical faces. Follower motion may be translatory, oscillatory, or a combination. The document provides examples of displacement diagrams and motions including uniform, modified uniform, parabolic, simple harmonic, and cycloidal. It also defines cam nomenclature and describes the process for designing a cam profile based on a given follower motion specification.
The document summarizes key concepts about robot motion. It discusses robot locomotion systems and common configurations like differential drive and tricycle drive. These configurations are non-holonomic and have constraints on instantaneous motion. The document also covers integrating motion in 2D using odometry equations to estimate new positions from motor rotations and control of DC motors using feedback from encoders. Path planning is discussed where a robot follows waypoints by turning to face the next point and driving straight towards it.
This document discusses stepper motors and their types. It begins by defining stepper motors as electromagnetic devices that rotate a specific number of degrees in response to each electric pulse. The main types are then described as variable reluctance, permanent magnet, and hybrid motors. Variable reluctance motors are further broken down into single stack, multi-stack, and those with different pole configurations to achieve smaller step sizes. Permanent magnet stepper motors are similar to single stack variable reluctance motors but use permanent magnets in the rotor. Hybrid stepper motors combine characteristics of variable reluctance and permanent magnet motors. Circuit diagrams and switching sequences are provided to illustrate the operating principles of several example motors.
Robust control theory based performance investigation of an inverted pendulum...Mustefa Jibril
This document describes a study investigating the performance of an inverted pendulum system using robust control theory. Two controllers - H∞ mixed sensitivity and H∞ loop shaping using Glover McFarlane method - are designed and their performance compared in simulations. The inverted pendulum with the mixed sensitivity controller showed smaller rise time, settling time and overshoot for step responses, as well as better impulse responses. Overall the mixed sensitivity controller provided the best performance in simulations.
External geneva mechanism mini project reportHamza Nawaz
In the mechanics of machines lab, an external geneva mechanism was designed in CAD software creo parametric 7.0.0.0 and then a mechanism analysis was run at constant speed to see the behaviour of the mechanism during motion. Several graphs were obtained to confirm its motion pattern.
The analytical design was also studied and presented in the mini-project.
Troubleshooting and Enhancement of Inverted Pendulum System Controlled by DSP...Thomas Templin
An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart-and-pole system. A normal pendulum is always stable since the pendulum hangs downward, whereas the inverted pendulum is inherently unstable and trivially underactuated (because the number of actuators is less than the degrees of freedom). For these reasons, the inverted pendulum has become one of the most important classical problems of control engineering. Since the 1950s, the inverted-pendulum benchmark, especially the cart version, has been used for the teaching and understanding of the use of linear-feedback control theory to stabilize an open-loop unstable system.
The objectives of this project are to:
• Focus on hardware and software troubleshooting and enhancement of an inverted-pendulum system controlled by a DSP28355 microprocessor and CCSv7.1 software.
• Use the swing-up strategy to move the pendulum into the unstable upward position (‘saddle’). The cart/pole system employs linear bearings for back-and-forward motion. The motor shaft has a pinion gear that rides on a track permitting the cart to move in a linear fashion. Both rack and pinion are made of hardened steel and mesh with a tight tolerance. The rack-and-pinion mechanism eliminates undesirable effects found in belt-driven and free-wheel systems, such as slippage or belt stretching, ensuring consistent and continuous traction.
• The motor shaft is coupled to a high-resolution optical encoder that accurately measures the position of the cart. The angle of the pendulum is also measured by an optical encoder, and the system employs an LQR controller to stabilize the pendulum rod at the unstable-equilibrium position.
• Addition of real-time status reporting and visualization of the system.
For the project, the Quanser High Frequency Linear Cart (HFLC) was used. The HFLC system consists of a precisely machined solid aluminum cart driven by a high-power 3-phase brushless DC motor. The cart slides along two high-precision, ground-hardened stainless steel guide rails, allowing for multiple turns and continuous measurement over the entire range of motion.
Our team implemented a control strategy that consists of a linear stabilizing LQR controller, proportional-integral swing-up control, and a supervisory coordinator that determines the control strategy (LQR or swing-up) to be used at any given time. The function of the linear stabilizer is to stabilize the system when it is in the vicinity of the unstable equilibrium. When the pendulum is in its natural state (straight-down stable-equilibrium node), the swing-up controller provides the cart/pendulum system with adequate energy to move the pendulum to the unstable equilibrium inside the “region of attraction” in which the linearized LQR controller is functional.
This document discusses circular interpolation in CNC machining. It describes how circular interpolation directs CNC machines to cut circular paths by moving the tool simultaneously in the X and Y directions in short linear segments that approximate an arc. It discusses cutting direction, the G02 and G03 commands used to specify clockwise or counterclockwise motion, and programming arcs using radius or center point vectors. Examples are provided of programming arcs using absolute and incremental coordinates.
The document discusses different types of swinging mechanisms. It explains that a pantograph uses a system of parallelograms to produce identical or scaled copies of an image traced by one pen using a second pen. It then discusses various swinging mechanisms like the toothed-rack system, crank and slotted lever, crank and rocker, and cam and follower mechanisms. The Geneva mechanism is described as a timing device that translates continuous rotation into intermittent rotary motion using a pin and slot system. Applications mentioned include movie projectors and automated devices.
study of yaw and pitch control in quad copter PranaliPatil76
This document describes an experimental study of yaw and pitch control in quadcopters. It discusses how quadcopters use independent variation of rotor speeds to control pitch, roll, and yaw. Yaw control is achieved by varying the net torque on the quadcopter by increasing the thrust of rotors spinning in one direction compared to the other. Pitch control is achieved by varying the net center of thrust. The document provides equations for calculating torque and describes how adjusting rotor thrusts can cause the quadcopter to yaw or rotate in different directions.
Power transmission systems are used to transmit motion from a prime mover to end equipment. They include gears, belts, chains, and shafts. Gears transmit motion through meshing teeth and can be used to increase or decrease speed. Belts and chains are used over long distances. Motion is converted between rotary and linear using various mechanisms like lead screws, rack and pinion, and cams. Bearings support shafts and provide low friction rotation. Couplings connect transmission components.
This document provides an overview of mathematical modeling of mechanical systems including translational, rotational, and linkage systems. It begins with an outline describing translational systems, rotational systems, and mechanical linkages. It then discusses the basic elements of translational systems including springs, masses, and dampers. Several examples are provided of modeling simple translational spring-mass systems and deriving the equations of motion. The document also covers rotational systems and provides examples of modeling rotational spring-mass systems. Mechanical linkages such as gears are briefly discussed.
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.
Attitude Control of Satellite Test Setup Using Reaction WheelsA. Bilal Özcan
This document summarizes a presentation about attitude control of a satellite test setup using reaction wheels. It describes the mathematical models of DC motors, reaction wheels, and the satellite test setup. It also discusses the implementation of a PID controller to control the satellite's orientation by generating angular velocity references for the reaction wheels. Simulation results show that the settling time of the system was decreased from 21.5 seconds to 6.1 seconds by optimizing the PID gains. Future work is planned to consider effects like vibrations and actuator saturations when testing the system.
This document provides an introduction to kinematics and the analysis of mechanisms using velocity and acceleration diagrams. It discusses:
1. Key concepts in mechanisms including different types of motion transformations and common mechanism components like four-bar linkages.
2. How to determine the displacement, velocity, and acceleration of points within a mechanism using either mathematical equations or graphical methods using velocity and acceleration diagrams.
3. How to construct velocity diagrams by determining the absolute and relative velocities of points and drawing them as vectors. This allows solving for unknown velocities.
4. How to extend the method to acceleration diagrams to determine centripetal and other accelerations which are important for calculating inertia forces.
The document provides examples
Impartiality as per ISO /IEC 17025:2017 StandardMuhammadJazib15
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Supermarket Management System Project Report.pdfKamal Acharya
Supermarket management is a stand-alone J2EE using Eclipse Juno program.
This project contains all the necessary required information about maintaining
the supermarket billing system.
The core idea of this project to minimize the paper work and centralize the
data. Here all the communication is taken in secure manner. That is, in this
application the information will be stored in client itself. For further security the
data base is stored in the back-end oracle and so no intruders can access it.
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...PriyankaKilaniya
Energy efficiency has been important since the latter part of the last century. The main object of this survey is to determine the energy efficiency knowledge among consumers. Two separate districts in Bangladesh are selected to conduct the survey on households and showrooms about the energy and seller also. The survey uses the data to find some regression equations from which it is easy to predict energy efficiency knowledge. The data is analyzed and calculated based on five important criteria. The initial target was to find some factors that help predict a person's energy efficiency knowledge. From the survey, it is found that the energy efficiency awareness among the people of our country is very low. Relationships between household energy use behaviors are estimated using a unique dataset of about 40 households and 20 showrooms in Bangladesh's Chapainawabganj and Bagerhat districts. Knowledge of energy consumption and energy efficiency technology options is found to be associated with household use of energy conservation practices. Household characteristics also influence household energy use behavior. Younger household cohorts are more likely to adopt energy-efficient technologies and energy conservation practices and place primary importance on energy saving for environmental reasons. Education also influences attitudes toward energy conservation in Bangladesh. Low-education households indicate they primarily save electricity for the environment while high-education households indicate they are motivated by environmental concerns.
Sri Guru Hargobind Ji - Bandi Chor Guru.pdfBalvir Singh
Sri Guru Hargobind Ji (19 June 1595 - 3 March 1644) is revered as the Sixth Nanak.
• On 25 May 1606 Guru Arjan nominated his son Sri Hargobind Ji as his successor. Shortly
afterwards, Guru Arjan was arrested, tortured and killed by order of the Mogul Emperor
Jahangir.
• Guru Hargobind's succession ceremony took place on 24 June 1606. He was barely
eleven years old when he became 6th Guru.
• As ordered by Guru Arjan Dev Ji, he put on two swords, one indicated his spiritual
authority (PIRI) and the other, his temporal authority (MIRI). He thus for the first time
initiated military tradition in the Sikh faith to resist religious persecution, protect
people’s freedom and independence to practice religion by choice. He transformed
Sikhs to be Saints and Soldier.
• He had a long tenure as Guru, lasting 37 years, 9 months and 3 days
Accident detection system project report.pdfKamal Acharya
The Rapid growth of technology and infrastructure has made our lives easier. The
advent of technology has also increased the traffic hazards and the road accidents take place
frequently which causes huge loss of life and property because of the poor emergency facilities.
Many lives could have been saved if emergency service could get accident information and
reach in time. Our project will provide an optimum solution to this draw back. A piezo electric
sensor can be used as a crash or rollover detector of the vehicle during and after a crash. With
signals from a piezo electric sensor, a severe accident can be recognized. According to this
project when a vehicle meets with an accident immediately piezo electric sensor will detect the
signal or if a car rolls over. Then with the help of GSM module and GPS module, the location
will be sent to the emergency contact. Then after conforming the location necessary action will
be taken. If the person meets with a small accident or if there is no serious threat to anyone’s
life, then the alert message can be terminated by the driver by a switch provided in order to
avoid wasting the valuable time of the medical rescue team.
AI in customer support Use cases solutions development and implementation.pdfmahaffeycheryld
AI in customer support will integrate with emerging technologies such as augmented reality (AR) and virtual reality (VR) to enhance service delivery. AR-enabled smart glasses or VR environments will provide immersive support experiences, allowing customers to visualize solutions, receive step-by-step guidance, and interact with virtual support agents in real-time. These technologies will bridge the gap between physical and digital experiences, offering innovative ways to resolve issues, demonstrate products, and deliver personalized training and support.
https://www.leewayhertz.com/ai-in-customer-support/#How-does-AI-work-in-customer-support
Blood finder application project report (1).pdfKamal Acharya
Blood Finder is an emergency time app where a user can search for the blood banks as
well as the registered blood donors around Mumbai. This application also provide an
opportunity for the user of this application to become a registered donor for this user have
to enroll for the donor request from the application itself. If the admin wish to make user
a registered donor, with some of the formalities with the organization it can be done.
Specialization of this application is that the user will not have to register on sign-in for
searching the blood banks and blood donors it can be just done by installing the
application to the mobile.
The purpose of making this application is to save the user’s time for searching blood of
needed blood group during the time of the emergency.
This is an android application developed in Java and XML with the connectivity of
SQLite database. This application will provide most of basic functionality required for an
emergency time application. All the details of Blood banks and Blood donors are stored
in the database i.e. SQLite.
This application allowed the user to get all the information regarding blood banks and
blood donors such as Name, Number, Address, Blood Group, rather than searching it on
the different websites and wasting the precious time. This application is effective and
user friendly.
2. What Is Pivot Algorithm?
• The Pivot algorithm is a very efficient ‘dynamic’ algorithm for
generating d-dimensional canonical ensemble.[1][2][3]
• It drastically modifies the chain dimension.
3. How It Works?
The pivot algorithm uses pivot moves as the transitions in
Markov chain which proceeds as follows.
• Choose the pivot point.
• Transform the coordinates of either side by rotating about the
pivot point.
• If the resulting walk is self-avoiding the move is accepted,
otherwise the move is rejected and the original walk is
retained.
4. How To Rotate About Pivot?
For rotating the chain about its pivot one must have
knowledge about coordinate transformation.
Following are the common rotation matrices for 2D system:
5. Example
A*(1,2)
Pivot P(1,1) O
A(2,1)
If we have a line segment joining P (1, 1) and A (2, 1), and we want the line segment to rotate
90° counterclockwise about point P (P is pivot).
So the x and y coordinate of the new point A:
1.
2.
3.
4.
Hence, the new coordinates after 90° counterclockwise rotation is (1, 2).
7. Analysis – Scaling Exponent
Scaling exponent can be computed for the system using
Square Average Radius of Gyration.
8. Analysis – Scaling Exponent (contd.)
< Rg2
> ∝ (N) 2ν
For 2D system: ν = 0.75
For 3D system: ν = 0.588
9. References
• [1] M. Kroger, Introduction to Computational Physics,
Lecture Notes; ETH Zurich (2008).
• [2] Joachim P. Wittmer et. al., Monte Carlo Simulation of
Polymers, NIC Series 23, 83-140 (2001).
• [3] Nathan Clisby, Efficient Implementation of pivot
algorithm for self-avoiding walks, ARC, (2010).