scholarly journals Kinematics of Serial Manipulators

2020 ◽  
Author(s):  
Ivan Virgala ◽  
Michal Kelemen ◽  
Erik Prada
Keyword(s):  
Rigid Body ◽  
Numerical Solutions ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Body Motion ◽  
Robot Kinematics ◽  
Kinematic Modeling ◽  
Open Chain ◽  
Serial Manipulators ◽  
Serial Robot

This book chapter deals with kinematic modeling of serial robot manipulators (open-chain multibody systems) with focus on forward as well as inverse kinematic model. At first, the chapter describes basic important definitions in the area of manipulators kinematics. Subsequently, the rigid body motion is presented and basic mathematical apparatus is introduced. Based on rigid body conventions, the forward kinematic model is established including one of the most used approaches in robot kinematics, namely the Denavit-Hartenberg convention. The last section of the chapter analyzes inverse kinematic modeling including analytical, geometrical, and numerical solutions. The chapter offers several examples of serial manipulators with its mathematical solution.

Kinematic Modeling and Internal Motion Analysis of Proteins From a Robot Kinematics Viewpoint

2011 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Jacobian Matrix ◽  
Robot Manipulator ◽  
Kinematic Model ◽  
Internal Motion ◽  
Robot Kinematics ◽  
Kinematic Modeling ◽  
Serial Link ◽  
Internal Motions ◽  
Basic Equations ◽  
External Forces

This paper discusses the kinematic modeling of proteins and the analysis of their internal motion from the viewpoint of robot kinematics. First, a kinematic model of a protein is introduced. This model consists of multiple serial link mechanisms and interaction lines (lines between alpha carbons). The protein model is regarded as a type of a robot manipulator that uses joint angles to control the lengths of the interaction lines, and the Jacobian matrix of the manipulator is derived. On the basis of this Jacobian matrix, the basic equations for calculating the deformation caused by external forces and evaluating the structural compliance of specified parts are derived. Finally, by combining the derived basic equations, we analyze the internal motions of lactoferrin and hemoglobin and compare the results with the reported measured characteristics of their internal motions. Despite the approximations by the model, the results obtained by the proposed method agree with the measured internal motion.

Grasshopper Knee Joint – Inverse Kinematic Modeling and Simulation of Ionic Polymer Metal Composites (IPMC) Actuators

2014 ◽  
Vol 19 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Farid ◽  
Zhao Gang ◽  
Tran Linh Khuong ◽  
Zhuang Zhi Sun ◽  
Naveed Ur Rehman
Keyword(s):  
Knee Joint ◽  
Low Voltage ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Kinematic Modeling ◽  
Ionic Polymer ◽  
Wolfram Mathematica ◽  
Polymer Metal ◽  
Transcendental Functions ◽  
Simulation Results

Biomimetic is the field of engineering in which biological structures and functions are analyzed and are used as the basis for the design and manufacturing of machines. Insects are the most populated creature and present everywhere in the world and can survive the most hostile environmental situations. IPMC is a smart material which has exhibited a significant bending and tip force after the application of a low voltage. It is light-weighted, flexible, easily actuated, multi-directional applicable and requires simple manufacturing.In this paper,five different contributions are made. Firstly, a two link grasshopper knee joint physical model is presented in which the actuation force required for moving the knee is provided by the IPMC material. This material constitutes one link of the linkage. Secondly,inverse kinematic modelhas been developed for the linkage. Thirdly, the system of equations is solved by proposing solutions to the known transcendental functions with unknown coefficients. Fourthly, wolfram mathematica is employed for thesimulationof the model. Finally,angles, velocity and accelerationof the links are analyzed based on the simulation results. The simulation results show that the tibia is displaying a lag in time from the femur verifying that it is operated by the force provided by the femur (IPMC). Also, it verified the flexible nature of the IPMC material through multiple peaks and troughs in the graphs. The angles range of the tibia is found quite admirable and it is believed that the IPMC material can add a new horizon to the manufacturing of small biomimetic equipment and low force actuated manipulators.

Kinematic Modeling and Error Analysis for a 3DOF Parallel-Link Coordinate Measuring Machine

2006 ◽  
Vol 532-533 ◽  
pp. 313-316 ◽  
Author(s):  
De Jun Liu ◽  
Hua Qing Liang ◽  
Hong Dong Yin ◽  
Bu Ren Qian
Keyword(s):  
Kinematic Model ◽  
Coordinate Measuring Machine ◽  
Inverse Kinematic ◽  
Differential Method ◽  
Error Model ◽  
Structural Parameter ◽  
Kinematic Modeling ◽  
Position Errors ◽  
Measuring Machine ◽  
Parallel Link

First, the forward kinematic model, the inverse kinematic model and the error model of a kind of coordinate measuring machine (CMM) using 3-DOF parallel-link mechanism are established based on the spatial mechanics theory and the total differential method, and the error model is verified by computer simulation. Then, the influence of structural parameter errors on probe position errors is systematically considered. This research provides an essential theoretical basis for increasing the measuring accuracy of the parallel-link coordinate measuring machine. It is of particular importance to develop the prototype of the new measuring equipment.

Nine Degree-of-Freedom Kinematic Modeling of the Upper-Limb Complex for Constrained Workspace Evaluation

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Brayden DeBoon ◽  
Ryan C. A. Foley ◽  
Scott Nokleby ◽  
Nicholas J. La Delfa ◽  
Carlos Rossa
Keyword(s):  
Upper Limb ◽  
Evaluation Method ◽  
Kinematic Model ◽  
Joint Space ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Kinematic Modeling ◽  
Joint Angles ◽  
Rehabilitative Treatment ◽  
Rehabilitation Devices

Abstract The design of rehabilitation devices for patients experiencing musculoskeletal disorders (MSDs) requires a great deal of attention. This article aims to develop a comprehensive model of the upper-limb complex to guide the design of robotic rehabilitation devices that prioritize patient safety, while targeting effective rehabilitative treatment. A 9 degree-of-freedom kinematic model of the upper-limb complex is derived to assess the workspace of a constrained arm as an evaluation method of such devices. Through a novel differential inverse kinematic method accounting for constraints on all joints1820, the model determines the workspaces in which a patient is able to perform rehabilitative tasks and those regions where the patient needs assistance due to joint range limitations resulting from an MSD. Constraints are imposed on each joint by mapping the joint angles to saturation functions, whose joint-space derivative near the physical limitation angles approaches zero. The model Jacobian is reevaluated based on the nonlinearly mapped joint angles, providing a means of compensating for redundancy while guaranteeing feasible inverse kinematic solutions. The method is validated in three scenarios with different constraints on the elbow and palm orientations. By measuring the lengths of arm segments and the range of motion for each joint, the total workspace of a patient experiencing an upper-limb MSD can be compared to a preinjured state. This method determines the locations in which a rehabilitation device must provide assistance to facilitate movement within reachable space that is limited by any joint restrictions resulting from MSDs.

6-Axis Serial Robot Simulation Based on SimulationX

2012 ◽  
Vol 152-154 ◽  
pp. 1010-1017
Author(s):  
Si Jun Zhao ◽  
Jia Yua Shan ◽  
Lu Yan Bi
Keyword(s):  
Trajectory Planning ◽  
Simulation Analysis ◽  
Inverse Kinematic ◽  
Robot Kinematics ◽  
Robot System ◽  
Planning And Control ◽  
Simulation Based ◽  
Serial Robot ◽  
And Control ◽  
Trajectory Planning And Control

This paper presents research and simulation analysis on kinematics and dynamics problem based on the 6-axis serial robot. By means of Denavit-Hartenberg method, the robot kinematics model is established as well as and the derivation process of kinematic and inverse kinematic resolution is described in detail. Furthermore, in software simulationX, robot system model including mechanical sub-system and control sub-system are founded. Additionally, through simulation, different performances of robot are illustrated based on different trajectory planning and control. In this way a theoretical reference is provided for the further study on trajectory planning and controls of 6-axis serial robot.

scholarly journals Rigid Body Motions and Local Compliance Response during Impact of Two Deformable Spheres

2017 ◽  
Vol 8 (1) ◽  
pp. 1 ◽  
Author(s):  
Akuro Big-Alabo
Keyword(s):  
Rigid Body ◽  
Dynamic Models ◽  
Numerical Solutions ◽  
Simple Procedure ◽  
Body Motion ◽  
Impact System ◽  
Rigid Body Motions ◽  
Local Compliance ◽  
Nonlinear Dynamic Models ◽  
The Impact

The impact of two hard deformable spheres is revisited with the aim of investigating the constituent rigid body motions and indentation response of each sphere during collision. The latter are determined theoretically and the theoretical solutions are validated by comparing with numerical solutions of the coupled nonlinear dynamic models for impact of two hard deformable spheres. For elastic impact events, normalized tabulated solutions are derived using the Force Indentation Linearisation Method (FILM) and the tabulated solutions can be used to generate actual rigid body motions and indentation histories for each of the colliding spheres without need for numerical or finite element solutions. The analysis shows that the rigid body motion and local compliance response of each sphere depend on: (a) ratio of mass of sphere to effective mass of impact system, and (b) ratio of initial velocity of sphere to initial relative velocity of impact system. Finally, the 2-D collision problem is discussed and a simple procedure to determine the unique solution of all four unknowns is presented.

Kinematic Model of Dynamic Drilling Process

2004 ◽  
Author(s):  
Jochem C. Roukema ◽  
Yusuf Altintas
Keyword(s):  
Mathematical Model ◽  
Rigid Body ◽  
Kinematic Model ◽  
Chip Thickness ◽  
Body Motion ◽  
Depth Of Cut ◽  
Force Model ◽  
Drilling Process ◽  
Structural Vibrations ◽  
Radial Depth

A mathematical model of the torsional-axial chatter vibrations in drilling is presented. The model considers the exact kinematics of both rigid body, and coupled torsional and axial vibrations of the drill. The drill is modeled as a pretwisted beam that exhibits axial deflections due to torque and thrust loading. A mechanistic cutting force model is used to model the cutting torque and thrust as a function of feedrate, speed, radial depth of cut, and drill geometry. The drill rotates and feeds axially into the workpiece while the structural vibrations are excited by the cutting torque and thrust force. The exact location of the drill edge is predicted using the model, and the generated surface is digitized at discrete time intervals. The distribution of chip thickness, which is affected by both rigid body motion and structural vibrations, is evaluated by subtracting the presently generated surface from the previous one. The model considers nonlinearities in cutting coefficients, tool jumping out of cut and overlapping of multiple regeneration waves. The dynamic chip thickness obtained from the true kinematics model allows simultaneous prediction of force, torque, power and dimensional form errors left on the surface. The time domain simulation model allows prediction of stability lobes. The paper provides details of the mathematical model, supported by experimental results of both stable and unstable cuts.

scholarly journals Inverse Kinematic Control of a Delta Robot Using Neural Networks in Real-Time

Robotics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 115
Author(s):  
Akram Gholami ◽  
Taymaz Homayouni ◽  
Reza Ehsani ◽  
Jian-Qiao Sun
Keyword(s):  
Neural Networks ◽  
Real Time ◽  
Trajectory Tracking ◽  
Tracking Error ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Robot Kinematics ◽  
Kinematic Control ◽  
Modeling Uncertainties ◽  
Delta Robot

This paper presents an inverse kinematic controller using neural networks for trajectory controlling of a delta robot in real-time. The developed control scheme is purely data-driven and does not require prior knowledge of the delta robot kinematics. Moreover, it can adapt to the changes in the kinematics of the robot. For developing the controller, the kinematic model of the delta robot is estimated by using neural networks. Then, the trained neural networks are configured as a controller in the system. The parameters of the neural networks are updated while the robot follows a path to adaptively compensate for modeling uncertainties and external disturbances of the control system. One of the main contributions of this paper is to show that updating the parameters of neural networks offers a smaller tracking error in inverse kinematic control of a delta robot with consideration of joint backlash. Different simulations and experiments are conducted to verify the proposed controller. The results show that in the presence of external disturbance, the error in trajectory tracking is bounded, and the negative effect of joint backlash in trajectory tracking is reduced. The developed method provides a new approach to the inverse kinematic control of a delta robot.

scholarly journals Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory

2020 ◽  
Vol 10 (8) ◽  
pp. 2781
Author(s):  
José Guzmán-Giménez ◽  
Ángel Valera Fernández ◽  
Vicente Mata Amela ◽  
Miguel Ángel Díaz-Rodríguez
Keyword(s):  
Control System ◽  
Kinematic Model ◽  
Lexicographic Order ◽  
Inverse Kinematic ◽  
Robotic Systems ◽  
Walking Robots ◽  
Groebner Basis ◽  
Open Chain ◽  
Monomial Order ◽  
Kinematic Models

One of the most important elements of a robot’s control system is its Inverse Kinematic Model (IKM), which calculates the position and velocity references required by the robot’s actuators to follow a trajectory. The methods that are commonly used to synthesize the IKM of open-chain robotic systems strongly depend on the geometry of the analyzed robot. Those methods are not systematic procedures that could be applied equally in all possible cases. This project presents the development of a systematic procedure to synthesize the IKM of non-redundant open-chain robotic systems using Groebner Basis theory, which does not depend on the geometry of the robot’s structure. The inputs to the developed procedure are the robot’s Denavit–Hartenberg parameters, while the output is the IKM, ready to be used in the robot’s control system or in a simulation of its behavior. The Groebner Basis calculation is done in a two-step process, first computing a basis with Faugère’s F4 algorithm and a grevlex monomial order, and later changing the basis with the FGLM algorithm to the desired lexicographic order. This procedure’s performance was proved calculating the IKM of a PUMA manipulator and a walking hexapod robot. The errors in the computed references of both IKMs were absolutely negligible in their corresponding workspaces, and their computation times were comparable to those required by the kinematic models calculated by traditional methods. The developed procedure can be applied to all Cartesian robotic systems, SCARA robots, all the non-redundant robotic manipulators that satisfy the in-line wrist condition, and any non-redundant open-chain robot whose IKM should only solve the positioning problem, such as multi-legged walking robots.

scholarly journals Kinematic Modeling of a Combined System of Multiple Mecanum-Wheeled Robots with Velocity Compensation

Sensors ◽  
2019 ◽  
Vol 20 (1) ◽  
pp. 75
Author(s):  
Yunwang Li ◽  
Shirong Ge ◽  
Sumei Dai ◽  
Lala Zhao ◽  
Xucong Yan ◽  
...  
Keyword(s):  
Large Scale ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Kinematic Modeling ◽  
Combined System ◽  
Wheeled Mobile Robots ◽  
Physical Prototype ◽  
Kinematic Models ◽  
Simulated Motion ◽  
Multiple Robot

In industry, combination configurations composed of multiple Mecanum-wheeled mobile robots are adopted to transport large-scale objects. In this paper, a kinematic model with velocity compensation of the combined mobile system is created, aimed to provide a theoretical kinematic basis for accurate motion control. Motion simulations of a single four-Mecanum-wheeled virtual robot prototype on RecurDyn and motion tests of a robot physical prototype are carried out, and the motions of a variety of combined mobile configurations are also simulated. Motion simulation and test results prove that the kinematic models of single- and multiple-robot combination systems are correct, and the inverse kinematic correction model with velocity compensation matrix is feasible. Through simulations or experiments, the velocity compensation coefficients of the robots can be measured and the velocity compensation matrix can be created. This modified inverse kinematic model can effectively reduce the errors of robot motion caused by wheel slippage and improve the motion accuracy of the mobile robot system.

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