An efficient method for the dynamic modeling and analysis of Stewart parallel manipulator based on the screw theory

2019 ◽  
Vol 234 (3) ◽  
pp. 808-821
Author(s):  
Yulei Hou ◽  
Guoxing Zhang ◽  
Daxing Zeng
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Force Balance ◽  
Constraint Matrix ◽  
Scheme Design ◽  
Control Scheme

Dynamic modeling serves as the fundamental basis for dynamic performance analysis and is an essential aspect of the control scheme design of parallel manipulators. This report presents a concise and efficient solution to the dynamics of Stewart parallel manipulators based on the screw theory. The initial pose of these manipulators is described. Then the pose matrix of each link of the Stewart parallel mechanism is obtained using an inverse kinematics solution and an exponential product formula. Considering the constraint relationship between joints, the constraint matrix of the Stewart parallel manipulator is deduced. In addition, the Jacobian matrix and the twist of each link are obtained. Moreover, by deriving the differential form of the constraint matrix, the spatial acceleration of each link is obtained. Based on the force balance relationship of each link, the inverse dynamics and the general form of the dynamic model of the Stewart parallel manipulator is established and the process of inverse dynamics is summarized. The dynamic model is then verified via dynamic simulation using the ADAMS software. A numerical example is considered to demonstrate the feasibility and effectiveness of this model. The proposed dynamic modeling approach serves as a fundamental basis for structural optimization and control scheme design of the Stewart parallel manipulators.

Structure Synthesis of 3-RRS Type Spatial Compliant Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1375-1379
Author(s):  
Da Chang Zhu ◽  
Li Meng ◽  
Tao Jiang
Keyword(s):  
Parallel Manipulator ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Weight Ratio ◽  
Parallel Manipulators ◽  
Robot System ◽  
New Approach ◽  
Structure Synthesis ◽  
Rigid Joints ◽  
Type 3

Parallel manipulators has been extensively studied by virtues or its high force-to-weight ratio and widely spread applications such as vehicle or flight simulator, a machine tool and the end effector of robot system. However, as each limb includes several rigid joints, assembling error is demanded strictly, especially in precision measurement and micro-electronics. On the other hand, compliant mechanisms take advantage of recoverable deformation to transfer or transform motion, force, or energy and the benefits of compliant mechanisms mainly come from the elimination of traditional rigid joints, but the traditional displacement method reduce the stiffness of spatial compliant parallel manipulators. In this paper, a new approach of structure synthesis of 3-DoF rotational compliant parallel manipulators is proposed. Based on screw theory, the structures of RRS type 3-DoF rotational spatial compliant parallel manipulator are developed. Experiments via ANSYS are conducted to give some validation of the theoretical analysis.

Singularity robust inverse dynamics of planar 2-RPR parallel manipulators

2004 ◽  
Vol 218 (7) ◽  
pp. 721-730 ◽  
Author(s):  
S Kemal Ider
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Full Rank ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dynamic Equations ◽  
Revolute Joints ◽  
Planar Parallel Manipulator ◽  
Pass Through ◽  
Full Utilization

In planar parallel robots, limitations occur in the functional workspace because of interference of the legs with each other and because of drive singularities where the actuators lose control of the moving platform and the actuator forces grow without bounds. A 2-RPR (revolute, prismatic, revolute joints) planar parallel manipulator with two legs that minimizes the interference of the mechanical components is considered. Avoidance of the drive singularities is in general not desirable since it reduces the functional workspace. An inverse dynamics algorithm with singularity robustness is formulated allowing full utilization of the workspace. It is shown that if the trajectory is planned to satisfy certain conditions related to the consistency of the dynamic equations, the manipulator can pass through the drive singularities while the actuator forces remain stable. Furthermore, for finding the actuator forces in the vicinity of the singular positions a full rank modification of the dynamic equations is developed. A deployment motion is analysed to illustrate the proposed approach.

Kinematics and Dynamics Modeling of a New 4-DOF Cable-Driven Parallel Manipulator

2013 ◽  
pp. 249-265
Author(s):  
Hamoon Hadian ◽  
Yasser Amooshahi ◽  
Abbas Fattah
Keyword(s):  
Dynamic Model ◽  
Parallel Manipulator ◽  
Joint Space ◽  
Kinematics And Dynamics ◽  
Dynamics Modeling ◽  
Kinematic Constraint ◽  
Control Scheme ◽  
Minimum Number ◽  
Dynamical Properties ◽  
Computed Torque

This paper addresses the kinematics and dynamics modeling of a 4-DOF cable-driven parallel manipulator with new architecture and a typical Computed Torque Method (CTM) controller is developed for dynamic model in SimMechanics. The novelty of kinematic architecture and the closed loop formulation is presented. The workspace model of mechanism’s dynamic is obtained in an efficient and compact form by means of natural orthogonal complement (NOC) method which leads to the elimination of the nonworking kinematic-constraint wrenches and also to the derivation of the minimum number of equations. To verify the dynamic model and analyze the dynamical properties of novel 4-DOF cable-driven parallel manipulator, a typical CTM control scheme in joint-space is designed for dynamic model in SimMechanics.

Path Tracking of Parallel Manipulators in the Presence of Force Singularity

2005 ◽  
Vol 127 (4) ◽  
pp. 550-563 ◽  
Author(s):  
C. K. Kevin Jui ◽  
Qiao Sun
Keyword(s):  
Motion Planning ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Manipulators ◽  
Path Tracking ◽  
Singularity Avoidance ◽  
Design Complexity ◽  
Actuation Redundancy ◽  
Planar Parallel Manipulator ◽  
Simulation Results

Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach.

Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory1

2004 ◽  
Vol 126 (1) ◽  
pp. 101-108 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
General Procedure ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Validity Condition ◽  
First Time ◽  
Spherical Parallel Manipulator ◽  
Selection Of

A spherical parallel manipulator (SPM) refers to a 3-DOF (degree-of-freedom) parallel manipulator generating 3-DOF spherical motion. A method is proposed for the type synthesis of SPMs based on screw theory. The wrench systems of a spherical parallel kinematic chain (SPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of SPMs. The type synthesis of legs for SPKCs, the type synthesis of SPKCs, as well as the selection of inputs of SPMs are dealt with in sequence. An input validity condition of SPMs is proposed. SPKCs with and without inactive joints are synthesized. The number of overconstraints of each SPKC is also given. The phenomenon of dependent joint groups in an SPKC is revealed for the first time.

Modeling and Workplace Analysis of 3T Cable-Driven Parallel Manipulator

2013 ◽  
Vol 415 ◽  
pp. 519-523
Author(s):  
Li Wen Guan ◽  
Cheng Long Mu ◽  
Yu Jian Hu
Keyword(s):  
Numerical Simulation ◽  
Dynamic Modeling ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Comprehensive Analysis ◽  
Dynamics Model ◽  
Set Up

This paper analyzes the dynamic modeling and workplace of the 3T cable-driven parallel manipulator. The mechanism utilizes four cables to driven. Firstly, the kinematics equations and the inverse dynamics model were set up for the analysis. And then, pseudo-drag is a serious problem in cable-driven parallel manipulator, this paper give a method to find the workplace under the condition of pseudo-drag. Finally, through numerical simulation, the workplace of the mechanism satisfying the demand is presented by comprehensive analysis.

A Measure for Evaluation of Maximum Acceleration of Redundant and Nonredundant Parallel Manipulators

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Jun Wu ◽  
Binbin Zhang ◽  
Liping Wang
Keyword(s):  
Dynamic Model ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Maximum Acceleration ◽  
Virtual Work Principle ◽  
Joint Force ◽  
Joint Forces ◽  
Three Degrees Of Freedom

The paper deals with the evaluation of acceleration of redundant and nonredundant parallel manipulators. The dynamic model of three degrees-of-freedom (3DOF) parallel manipulator is derived by using the virtual work principle. Based on the dynamic model, a measure is proposed for the acceleration evaluation of the redundant parallel manipulator and its nonredundant counterpart. The measure is designed on the basis of the maximum acceleration of the mobile platform when one actuated joint force is unit and other actuated joint forces are less than or equal to a unit force. The measure for evaluation of acceleration can be used to evaluate the acceleration of both redundant parallel manipulators and nonredundant parallel manipulators. Furthermore, the acceleration of the 4-PSS-PU parallel manipulator and its nonredundant counterpart are compared.

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

Kinematic analyses of novel translational parallel manipulators

2013 ◽  
Vol 228 (2) ◽  
pp. 330-341 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Horacio Orozco-Mendoza ◽  
Alvaro Sánchez-Rodríguez ◽  
Gursel Alici
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Output Displacement ◽  
Kinematic Analyses ◽  
Linear Actuators ◽  
The One ◽  
Forward Kinematic ◽  
Primary Contribution

This study reports on the kinematic analyses of four translational parallel manipulators (3RPC, SPS + 2RPC, RPPR + 2RPC and RPPR + 2PPP) articulated with linear actuators. They are based on serially connected chains which are connected with cylindrical (C), prismatic (P), revolute (R), spherical (S) and universal (U) joints. Of these manipulators, the one which is a fully decoupled, fully isotropic and singularity-free translational parallel manipulator (RPPR+2PPP) offers a one-to-one correspondence between its input and output displacement. This makes its forward and inverse position analyses simpler with a set of linear equations to be solved. Although the other manipulators have coupled kinematics, they still have simpler forward kinematic equations over other well-known translational parallel manipulators reported in the literature. We also employ screw theory to undertake the velocity and acceleration analyses. The primary contribution of this manuscript is to show how the 3-RPC translational parallel manipulator can be gradually modified in order to obtain a fully isotropic, fully decoupled and singularity-free translational parallel manipulator.

scholarly journals A Five-Bar Planar Parallel Manipulator with Two End-Effectors

2018 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Ramon Rodriguez-Castro ◽  
Luciano Perez-Gonzalez ◽  
Carlos R. Aguilar-Najera ◽  
Alvaro Sanchez-Rodriguez
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Intermediate Step ◽  
Euclidean Group ◽  
Planar Parallel Manipulator ◽  
Special Software ◽  
End Effectors ◽  
Klein Form

Parallel manipulators with multiple end-effectors bring us interesting advantages over conventional parallel manipulators such as improved manipulability, workspace and avoidance of singularities. In this work the kinematics of a five-bar planar parallel manipulator equipped with two end-effectors is approached by means of the theory of screws. As an intermediate step the displacement analysis of the robot is also investigated. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that regard the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) plays a central role. In order to exemplify the method of kinematic analysis, a case study is included. Furthermore, the numerical results obtained by means of the theory of screws are confirmed with the aid of special software like ADAMS.TM

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