Inverse Kinematics and Dynamics of a 3RRR Planar Parallel Manipulator in the Presence of Singularities

2021 ◽  
pp. 228-237
Author(s):  
Nguyen Quang Hoang ◽  
Vu Duc Vuong
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Kinematics And Dynamics ◽  
Planar Parallel Manipulator

Kinematics and Dynamics of a Parallel Manipulator With Woven Joints

1993 ◽  
Author(s):  
Hyunsok Pang
Keyword(s):  
Lagrange Multipliers ◽  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Numerical Technique ◽  
Vector Analysis ◽  
Kinematics And Dynamics ◽  
Governing Equations ◽  
Numerical Examples

Abstract Presented is an analysis of the kinematics and the inverse dynamics of a proposed three DOF parallel manipulator resembling the Stewart platform in a general form. In the kinematic analysis, the inverse kinematics, velocity and acceleration analyses are performed, respectively, using vector analysis and general homogeneous transformations. An algorithm to solve the inverse dynamics of the proposed parallel manipulator is then presented using a Lagrangin technique. In this case, it is found that one should introduce and subsequently eliminate Lagrange multipliers in order to arrive at the governing equations. Numerical examples are finally carried out to examine the validity of the approach and the accuracy of the numerical technique employed. The trajectory of motion of the manipulator is also performed using a cubic spline.

Optimal Kinematic Design of a 2-DOF Planar Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1843-1847
Author(s):  
Xiao Rong Zhu ◽  
Hui Ping Shen ◽  
Wei Zhu
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Operating Mode ◽  
Performance Indices ◽  
Operating Modes ◽  
Geometry Design ◽  
Planar Parallel Manipulator ◽  
Inverse Solutions ◽  
Linear Actuators ◽  
Global And Local

This paper addresses geometry design and operating mode optimum design of a new kind of 2-DOF parallel manipulator actuated horizontally by linear actuators. The forward and inverse kinematics of this manipulator are derived. The four groups of inverse solution correspond to four different operating modes which cannot transit to each other smoothly. The workspace and the singularity trajectory of each mode are discussed. Based on the desired workspace, the geometry of the mechanism is determined. The operating mode of the mechanism is optimized according to distributing of all global and local performance indices on the workspace. The results are very useful for the design and application of the new manipulator with multiple forward and inverse solutions.

Differential kinematics of parallel manipulators using Assur virtual chains

2009 ◽  
Vol 223 (7) ◽  
pp. 1697-1711 ◽  
Author(s):  
A Campos ◽  
R Guenther ◽  
D Martins
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Kinematic Constraints ◽  
Passive Joint ◽  
Planar Parallel Manipulator ◽  
Stewart Gough Platform ◽  
Homogeneous Linear

This article introduces the concept of Assur virtual chains and its applications in differential kinematics of parallel manipulators. Using Assur virtual chains, the differential kinematics has a simple matricial formulation and the choice between direct and inverse kinematics is reduced to select primary variables in a homogeneous linear system. Assur virtual chains are also useful for obtaining information about the relative movements or to imposing particular kinematic constraints between two links of a kinematic chain. Additionally, a new systematic algorithm is established to analytically eliminate passive joint velocities and calculate the Jacobian matrices. This elimination approach is based on screw theory concepts such as twist, wrench, and reciprocity; also, graph theory is used for kinematic chain representation. At the end of the article, the method is applied to a 3RRR planar parallel manipulator and a general universal-prismatic-spheric Stewart—Gough platform.

Inverse Kinematic and Dynamic Analyses of the 6-UCU Parallel Manipulator

2011 ◽  
Vol 127 ◽  
pp. 172-180 ◽  
Author(s):  
Guo Jun Liu ◽  
Shu Tao Zheng ◽  
Peter O. Ogbobe ◽  
Jun Wei Han
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Driving Forces ◽  
Stewart Platform ◽  
Inverse Kinematic ◽  
Euler Method ◽  
Kinematics And Dynamics ◽  
Precise Analysis ◽  
Dynamic Analyses ◽  
Reaction Forces

From the practical viewpoint, the inverse kinematics and dynamics of a practical Stewart platform, the 6-UCU parallel manipulator, are established in this paper. The velocities and accelerations of the manipulator are derived with the consideration of the attachments of the joints, and then the driving forces actuated by the actuators and the reaction forces applied to the joints are derived based on the Newton Euler method. In the last, the correctness of the equations established in this paper is confirmed by the study of a case. These equations can be used as the base for the precise analysis of the 6-UCU parallel manipulator.

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

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

A Novel Spherical Parallel Manipulator with Circular Guide

2013 ◽  
Vol 325-326 ◽  
pp. 1014-1018
Author(s):  
Hai Rong Fang ◽  
Zhi Hong Chen ◽  
Yue Fa Fang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
High Rigidity ◽  
Geometric Conditions ◽  
Spherical Parallel Manipulator

In this paper, a novel 3-degree-of-freedom (DOF) parallel manipulator that can perform three rotations around the remote centre is presented. The theory of screws and reciprocal screws is employed for the analysis of the geometric conditions. In particular, using circular guide to instead of R joints, so that has the advantage of enabling continuous 360° revolute around Z-axis. The inverse kinematics of mechanism is given and the workspace has a good performance. To compare with the machine constructed with traditional joints, it has the advantage of high rigidity and precision.

Kinematics of a Fully-Decoupled Remote Center-of-Motion Parallel Manipulator for Minimally Invasive Surgery

2012 ◽  
Vol 6 (2) ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Surgical Instruments ◽  
End Effector ◽  
Minimally Invasive Surgical ◽  
Inverse Kinematics Problem

A crucial design challenge in minimally invasive surgical (MIS) robots is the provision of a fully decoupled four degrees-of-freedom (4-DOF) remote center-of-motion (RCM) for surgical instruments. In this paper, we present a new parallel manipulator that can generate a 4-DOF RCM over its end-effector and these four DOFs are fully decoupled, i.e., each of them can be independently controlled by one corresponding actuated joint. First, we revisit the remote center-of-motion for MIS robots and introduce a projective displacement representation for coping with this special kinematics. Next, we present the proposed new parallel manipulator structure and study its geometry and motion decouplebility. Accordingly, we solve the inverse kinematics problem by taking the advantage of motion decouplebility. Then, via the screw system approach, we carry out the Jacobian analysis for the manipulator, by which the singular configurations are identified. Finally, we analyze the reachable and collision-free workspaces of the proposed manipulator and conclude the feasibility of this manipulator for the application in minimally invasive surgery.

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