Wrench Capabilities of a Kinematically Redundant Planar Parallel Manipulator

Robotica ◽  
2021 ◽  
pp. 1-16
Author(s):  
Roger Boudreau ◽  
Scott Nokleby ◽  
Marise Gallant
Keyword(s):  
Explicit Solution ◽  
Parallel Manipulator ◽  
Maximum Force ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Force Analysis ◽  
Maximum Moment ◽  
Planar Parallel Manipulator

SUMMARY This paper presents a methodology to obtain the wrench capabilities of a kinematically redundant planar parallel manipulator using a wrench polytope approach. A methodology proposed by others for non-redundant and actuation-redundant manipulators is adapted to a kinematically redundant manipulator. Four wrench capabilities are examined: a pure force analysis, the maximum force for a prescribed moment, the maximum reachable force, and the maximum moment with a prescribed force. The proposed methodology, which finds the exact explicit solution for three of the four wrench capabilities, does not use optimization and is very efficient.

scholarly journals SINGULARITY ANALYSIS OF A 3-PRRR KINEMATICALLY REDUNDANT PLANAR PARALLEL MANIPULATOR

1970 ◽  
Vol 41 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Soheil Zarkandi
Keyword(s):  
Motion Control ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Redundant Manipulators ◽  
Static Behavior ◽  
Singular Configurations ◽  
Planar Parallel Manipulator ◽  
And Control ◽  
Planar Parallel Manipulators

Finding Singular configurations (singularities) is one of the mandatory steps during the design and control of mechanisms. Because, in these configurations, the instantaneous kinematics is locally undetermined that causes serious problems both to static behavior and to motion control of the mechanism. This paper addresses the problem of determining singularities of a 3-PRRR kinematically redundant planar parallel manipulator by use of an analytic technique. The technique leads to an input –output relationship that can be used to find all types of singularities occurring in this type of manipulators.Key Words: Planar parallel manipulators; Redundant manipulators; Singularity analysis; Jacobian matrices.DOI: 10.3329/jme.v41i1.5356Journal of Mechanical Engineering, Vol. ME 41, No. 1, June 2010 1-6

Optimum force balancing of a planar parallel manipulator

2003 ◽  
Vol 217 (5) ◽  
pp. 515-524 ◽  
Author(s):  
G Alici ◽  
B Shirinzadeh
Keyword(s):  
Parallel Manipulator ◽  
Optimization Problem ◽  
Optimization Approach ◽  
Static Force ◽  
Force Analysis ◽  
Kinematic Chains ◽  
Revolute Joints ◽  
Planar Parallel Manipulator ◽  
Motion Optimization ◽  
Balancing Conditions

This paper focuses on optimum force balancing of a planar parallel manipulator, articulated with revolute joints, with a combination of a proper distribution of link masses and two springs connected to the driving links. After conducting the static force analysis of the mechanism, the force balancing is formulated as an optimization problem such that a mean-square root of the sum-squared values of bearing and spring forces is minimized throughout an operation range of the manipulator, provided that a set of balancing constraints consisting of balancing conditions and the sizes of some inertial and geometric parameters are satisfied. The minimization of bearing forces and spring forces adds to the life of bearings and springs, transmits less shaking force and moment to the ground, decreases wear in the mechanism components and consequently reduces the actuation burden on the actuators when the manipulator is in motion. Optimization results indicate that the proposed optimization approach is systematic, versatile and easy to implement for the optimal balancing of the parallel manipulator and other kinematic chains.

scholarly journals Performance Analysis and Optimum Design of a Redundant Planar Parallel Manipulator

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 908 ◽  
Author(s):  
Xiaoyong Wu
Keyword(s):  
Optimum Design ◽  
Parallel Manipulator ◽  
Optical Design ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Performance Comparison ◽  
Design Parameters ◽  
Redundant Manipulator ◽  
Symmetrical Structure ◽  
Planar Parallel Manipulator

This work presents a comprehensive performance evaluation and optimum design of a novel symmetrical 4-PPR (P indicates the prismatic joint, R denotes the revolute joint, and the letter with underline represents an active joint) redundant planar parallel manipulator. The kinematic model is established, upon which the inverse position and singularity are analyzed. Based on the evaluation of dexterity, velocity, and stiffness performance, the optimum region is achieved. With the optical design parameters, a case study for the analysis of dynamic behavior is conducted. Performance comparison between the redundant manipulator and another two non-redundant 3-PPR planar parallel manipulators, one with a Δ-shape symmetrical structure and the other with U-shape symmetrical structure, is presented. Simulation results reveal that the U-shape manipulator has the greatest velocity performance. Moreover, the redundant manipulator possesses the best dexterity, stiffness, and dynamic performance.

A Kind of Kinematically Redundant Planar Parallel Manipulator for Optimal Output Accuracy

2009 ◽  
Author(s):  
Genliang Chen ◽  
Hao Wang ◽  
Yong Zhao ◽  
Zhongqin Lin
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Redundant Manipulators ◽  
Kinematic Redundancy ◽  
End Effector ◽  
Optimal Output ◽  
Parallel Structures ◽  
Planar Parallel Manipulator ◽  
Redundant Structure ◽  
Active Joints

Theoretically, parallel manipulators perform higher precision than their serial counterparts. However, the output accuracy is sensitive to their configurations and dimensions. This paper presents a kind of parallel manipulator with kinematically redundant structure, which can improve the output accuracy by optimizing the error transmission from the active joints to the end-effector. With the kinematic redundancy, free redundant variables can be defined as second task variables, which provide the possibility to select a proper configuration for least error transmission at any pose (the position and orientation) of the end-effector for a given task. Contrast to non-redundant manipulators, the output errors of the proposed manipulator, caused by the active joints input errors, can be optimized rather than determined. By this goal, new limbs with redundant parallel structures are introduced to non-redundant planar parallel manipulators. Numerical example shows that the new architecture has the potential to enhance the output accuracy for a given pose or prescribed trajectory of the end-effector.

Stiffness analysis of a planar parallel manipulator with variable platforms

2021 ◽  
pp. 1-18
Author(s):  
Xiaoyong Wu ◽  
Yujin Wang ◽  
Zhaowei Xiang ◽  
Ran Yan ◽  
Rulong Tan ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Stiffness Analysis ◽  
Planar Parallel Manipulator

Dual arm-angle parameterisation and its applications for analytical inverse kinematics of redundant manipulators

Robotica ◽  
2015 ◽  
Vol 34 (12) ◽  
pp. 2669-2688 ◽  
Author(s):  
Wenfu Xu ◽  
Lei Yan ◽  
Zonggao Mu ◽  
Zhiying Wang
Keyword(s):  
Inverse Kinematics ◽  
Reference Plane ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Singularity Problem ◽  
Human Arm ◽  
Angle Method ◽  
Self Motion ◽  
Dual Arm ◽  
Configuration Control

SUMMARYAn S-R-S (Spherical-Revolute-Spherical) redundant manipulator is similar to a human arm and is often used to perform dexterous tasks. To solve the inverse kinematics analytically, the arm-angle was usually used to parameterise the self-motion. However, the previous studies have had shortcomings; some methods cannot avoid algorithm singularity and some are unsuitable for configuration control because they use a temporary reference plane. In this paper, we propose a method of analytical inverse kinematics resolution based on dual arm-angle parameterisation. By making use of two orthogonal vectors to define two absolute reference planes, we obtain two arm angles that satisfy a specific condition. The algorithm singularity problem is avoided because there is always at least one arm angle to represent the redundancy. The dual arm angle method overcomes the shortcomings of traditional methods and retains the advantages of the arm angle. Another contribution of this paper is the derivation of the absolute reference attitude matrix, which is the key to the resolution of analytical inverse kinematics but has not been previously addressed. The simulation results for typical cases that include the algorithm singularity condition verified our method.

Integrated optimal design of a high-speed planar parallel manipulator

2018 ◽  
Vol 233 (9) ◽  
pp. 2976-2990 ◽  
Author(s):  
Zhengsheng Chen ◽  
Minxiu Kong
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
High Speed ◽  
Design Method ◽  
Tracking Error ◽  
Dimensional Synthesis ◽  
Tracking Accuracy ◽  
Nsga Ii ◽  
Parameters Tuning ◽  
Planar Parallel Manipulator

To obtain excellent comprehensive performances of the planar parallel manipulator for the high-speed application, an integrated optimal design method, which integrated dimensional synthesis, motors/reducers selection, and control parameters tuning, is proposed, and the 3RRR parallel manipulator was taken as the example. The kinematic and dynamic performances of condition number, velocity index, acceleration capability, and low-order frequency are taken into accounts for the dimensional synthesis. Then, to match motors/reducers parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic forward plus proportional–derivative control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including dimensional synthesis, motors/reducers selection and controller parameters tuning is established, which is solved by the genetic algorithm II (NSGA-II). The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design, and the prototype was constructed according to the Pareto-optimal front.

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