An iterative method for the inverse kinematics of lower-mobility parallel mechanism with three RS or SR chains based on kinematically equivalent mechanism

2019 ◽  
Vol 141 ◽  
pp. 40-51 ◽  
Author(s):  
Xinghai Liang ◽  
Yukio Takeda
Keyword(s):  
Iterative Method ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Lower Mobility ◽  
Equivalent Mechanism

scholarly journals Sensitivity Analysis of Reliability of Low-Mobility Parallel Mechanisms Based on a Response Surface Method

2021 ◽  
Vol 11 (19) ◽  
pp. 9002
Author(s):  
Qiang Yang ◽  
Hongkun Ma ◽  
Jiaocheng Ma ◽  
Zhili Sun ◽  
Cuiling Li
Keyword(s):  
Sensitivity Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Error Component ◽  
Parallel Mechanisms ◽  
Kinematic Accuracy ◽  
Surface Method ◽  
Input Error

Kinematic accuracy is a crucial indicator for evaluating the performance of mechanisms. Low-mobility parallel mechanisms are examples of parallel robots that have been successfully employed in many industrial fields. Previous studies analyzing the kinematic accuracy analysis of parallel mechanisms typically ignore the randomness of each component of input error, leading to imprecise conclusions. In this paper, we use homogeneous transforms to develop the inverse kinematics models of an improved Delta parallel mechanism. Based on the inverse kinematics and the first-order Taylor approximation, a model is presented considering errors from the kinematic parameters describing the mechanism’s geometry, clearance errors associated with revolute joints and driving errors associated with actuators. The response surface method is employed to build an explicit limit state function for describing position errors of the end-effector in the combined direction. As a result, a mathematical model of kinematic reliability of the improved Delta mechanism is derived considering the randomness of every input error component. And then, reliability sensitivity of the improved Delta parallel mechanism is analyzed, and the influences of the randomness of each input error component on the kinematic reliability of the mechanism are quantitatively calculated. The kinematic reliability and proposed sensitivity analysis provide a theoretical reference for the synthesis and optimum design of parallel mechanisms for kinematic accuracy.

scholarly journals Stability and Gait Planning of 3-UPU Hexapod Walking Robot

Robotics ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 48 ◽  
Author(s):  
Ruiqin Li ◽  
Hongwei Meng ◽  
Shaoping Bai ◽  
Yinyin Yao ◽  
Jianwei Zhang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Step Length ◽  
Parallel Robot ◽  
Search Method ◽  
Walking Robot ◽  
Gait Control ◽  
Gait Planning ◽  
Forward And Inverse Kinematics ◽  
Passing Ability

The paper presents an innovative hexapod walking robot built with 3-UPU parallel mechanism. In the robot, the parallel mechanism is used as both an actuator to generate walking and also a connecting body to connect two groups of three legs, thus enabling the robot to walk with simple gait by very few motors. In this paper, forward and inverse kinematics solutions are obtained. The workspace of the parallel mechanism is analyzed using limit boundary search method. The walking stability of the robot is analyzed, which yields the robot’s maximum step length. The gait planning of the hexapod walking robot is studied for walking on both flat and uneven terrains. The new robot, combining the advantages of parallel robot and walking robot, has a large carrying capacity, strong passing ability, flexible turning ability, and simple gait control for its deployment for uneven terrains.

scholarly journals Design and Analysis of a Flexible, Elastic, and Rope-Driven Parallel Mechanism for Wrist Rehabilitation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zaixiang Pang ◽  
Tongyu Wang ◽  
Junzhi Yu ◽  
Shuai Liu ◽  
Xiyu Zhang ◽  
...  
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Parallel Structure ◽  
Flexible Joints ◽  
Rehabilitation Robots ◽  
Hybrid Mechanism ◽  
Compression Spring ◽  
Moving Platform

This paper proposes a bionic flexible wrist parallel mechanism to simulate human wrist joints, which is characterized by a rope-driven, compression spring-supported hybrid mechanism. Specifically, to realize the movement of the wrist mechanism, a parallel structure is adopted to support the mobile platform and is controlled by a cable, which plays the role of wrist muscles. Because the compression spring is elastic, it is difficult to directly solve inverse kinematics. To address this problem, the external force acting on the moving platform is firstly equivalent to the vector force and torque at the center of the moving platform. Then, based on inverse kinematic and static analyses, the inverse motion of the robot model can be solved according to the force and torque balance conditions and the lateral spring bending equation of the compression spring. In order to verify the proposed method, kinematics, statics, and parallel mechanism workspace are further analyzed by the software MATLAB. The obtained results demonstrate the effectiveness and feasibility of the designed parallel mechanism. This work offers new insights into the parallel mechanism with flexible joints in replicating the movements of the human wrist, thus promoting the development of rehabilitation robots and rope-driven technology to some extent.

Acceleration and Dexterity Performance Indices for 6-DOF and Lower-Mobility Parallel Mechanism

2004 ◽  
Author(s):  
X. J. Guo ◽  
F. Q. Chang ◽  
S. J. Zhu
Keyword(s):  
Parallel Mechanism ◽  
Robot Manipulator ◽  
Coefficient Matrix ◽  
Second Order ◽  
Influence Coefficient ◽  
Global Index ◽  
Performance Indices ◽  
First Order ◽  
Lower Mobility

On the basis of first-order and second-order kinematic influence coefficient matrices, dynamics characteristics indices for robot manipulator are presented in the paper. Different from indices before, these indices include not only the first-order kinematics influence coefficient matrix G, but also the second-order kinematic influence coefficient matrix H. Then with the global index, these indices can be used to guide the dynamics design.

Kinematics of a n–bay triangle–triangle variable geometry truss manipulator

Robotica ◽  
1992 ◽  
Vol 10 (3) ◽  
pp. 263-267
Author(s):  
L. Beiner
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Variable Length ◽  
Variable Geometry ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Forward And Inverse Kinematics ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

SUMMARYVariable geometry truss manipulators (VGTM) are static trusses where the lengths of some members can be varied, allowing one to control the position of the free end relative to the fixed one. This paper deals with a planar VGTM consisting of a n–bay triangle-triangle truss with one variable length link (i.e. one DOF) per bay. Closed-form solutions to the forward, inverse, and velocity kinematics of a 3-DOF version of this VGTM are presented, while the forward and inverse kinematics of an n–DOF (redundant) one are solved by a recursive and an iterative method, respectively. A numerical example is presented.

scholarly journals Research on multidimensional loading device of material mechanical test

2018 ◽  
Vol 207 ◽  
pp. 03012
Author(s):  
Guohua Zhao ◽  
Dan Wang ◽  
Liangbao Liu ◽  
Rui Fanand ◽  
Rukun Mi
Keyword(s):  
Tensile Testing ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Mechanical Test ◽  
Testing Machine ◽  
Tensile Tests ◽  
Determination Method ◽  
Average Yield ◽  
Tensile Testing Machine ◽  
Loading Device

A multidimensional loading device for the material mechanical test based on Stewart Platform was proposed and manufactured in this paper. A determination method of mechanism parameters toward specific engineering requirements was analysed via inverse kinematics and contact interference boundary condition of mechanism components. A set of optimized mechanism parameters was achieved and then the pose space was obtained. Meanwhile, five repeated quasi-static standard tensile tests were performed on the multidimensional loading device and the standard tensile testing machine, respectively. The average yield strength and ultimate strength of the specimen achieved from the different testers were both merely 1.13%. Results indicated that material mechanical multidimensional loading could be conducted by the parallel mechanism.

Analysis of a mechanism with redundant drive for antenna pointing

2016 ◽  
Vol 231 (2) ◽  
pp. 229-239 ◽  
Author(s):  
Xin Li ◽  
Xilun Ding ◽  
Gregory S Chirikjian
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Numerical Examples ◽  
Pointing Device ◽  
Key Factor ◽  
Rotary Motors ◽  
Redundantly Actuated ◽  
Pointing Accuracy ◽  
Forward And Inverse Kinematics ◽  
Redundant Drive

Orientation accuracy is a key factor in the design of mechanisms for antenna pointing. Our design uses a redundantly actuated parallel mechanism which may provide an effective way to solve this problem, and even can increase its payload capability and reliability. The presented mechanism can be driven by rotary motors fixed on the base to reduce the inertia of the moving parts and to lower the power consumption. The mechanism is redundantly actuated by three arms, and is used as a two-dimensional antenna tracking and pointing device. Both the forward and inverse kinematics are investigated to find all the possible solutions. Detailed characters of the platform are analyzed to demonstrate the advantages in eliminating singularities and improving pointing accuracy. A method of calculating the overconstrained orientational error is also proposed based on the differential kinematics. All the methods are verified by numerical examples.

Real-Time Interpolator and Contour Tracking in Link-Space for a 3 DOF Parallel Mechanism

2008 ◽  
Vol 594 ◽  
pp. 415-436
Author(s):  
Yuan Ming Cheng ◽  
Chien Hsun Kuo ◽  
Jih Hua Chin
Keyword(s):  
Real Time ◽  
Trajectory Tracking ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Contour Tracking ◽  
Control Points ◽  
Parallel Mechanisms ◽  
Time Efficiency ◽  
Compensation Control ◽  
Space Approach

Parallel mechanisms could be hardly used in contour tracking because of their mechanism features. This study proposed a link-space real time contour tracking for a 3 DOF (Z、α and β) hydraulic parallel mechanism. The essence of this approach is to convert control points of command trajectory to link space by inverse kinematics. A real-time interpolator was created and the multi-axis cross-coupled pre-compensation control (MCCPM) was constructed for link-space contour tracking. It was shown that a contour-accurate trajectory tracking could be performed which was impossible in the original Z-α-β space. Other advantages of this link-space approach were time efficiency and the uniform tracking velocity.

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