Forward and Inverse Acceleration Analyses of In-Parallel Manipulators

1998 ◽  
Vol 122 (3) ◽  
pp. 299-303 ◽  
Author(s):  
Jose´ Marı´a Rico Martı´nez ◽  
Joseph Duffy
Keyword(s):  
Parallel Manipulator ◽  
Computing Time ◽  
Parallel Manipulators ◽  
Simple Expression ◽  
Intermediate Step ◽  
Simple Method ◽  
Dynamics And Control ◽  
Klein Form ◽  
Six Degree Of Freedom ◽  
And Control

Simple expressions for the forward and inverse acceleration analyses of a six degree of freedom in-parallel manipulator are derived. The expressions are obtained by firstly computing the “accelerator” for a single Hooke-Prismatic-Spheric, HPS for short, connector chain in terms of the joint velocities and accelerations. The accelerator is a function of the line coordinates of the joint axes and of a sequence of Lie products of the same line coordinates. A simple expression for the acceleration of the prismatic actuator is obtained by forming the Klein form, or reciprocal product, with the accelerator and the coordinates of the line of the connector chain. Since the Klein form is invariant, the resulting expression can be applied directly to the six HPS connector chains of an in-parallel manipulator. As a required intermediate step, this contribution also derives the corresponding solutions for the forward and inverse velocity analyses. The authors believe that this simple method has applications in the dynamics and control of these in-parallel manipulators where the computing time must be minimized to improve the behavior of parallel manipulators. [S1050-0472(00)01303-9]

An Efficient Inverse Acceleration Analysis of In-Parallel Manipulators

1996 ◽  
Author(s):  
José María Rico Martínez ◽  
Joseph Duffy
Keyword(s):  
Parallel Manipulator ◽  
Computing Time ◽  
Parallel Manipulators ◽  
Simple Expression ◽  
Degree Of Freedom ◽  
Simple Method ◽  
Dynamics And Control ◽  
Acceleration Analysis ◽  
Klein Form ◽  
And Control

Abstract A very simple novel expression for the accelerations of the six prismatic actuators, of the HPS connector chains, of a 6 degree of freedom in-parallel manipulator is derived. The expression is obtained by firstly computing the “accelerator” for a single HPS connector chain in terms of the joint velocities and accelerations. The accelerator is a function of the line coordinates of the joint axes and of a sequence of Lie products of the same line coordinates. A simple expression for the acceleration of the prismatic actuator is obtained by forming the Klein form, or reciprocal product, with the accelerator and the coordinates of the line of the connector chain. Since the Klein form is invariant, the resulting expression can be applied directly to the six HPS connector chains of an in-parallel manipulator. The authors believe that this simple method has important applications in the dynamics and control of these in-parallel manipulators where the computing time must be minimized to improve the behavior of parallel manipulators.

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

Determination of the Workspace of 6-DOF Parallel Manipulators

1989 ◽  
Author(s):  
C. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometrical Properties ◽  
Cartesian Space ◽  
Six Degree Of Freedom

Abstract This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-parallel manipulator.

A Simple Method for Mobility Analysis Using Reciprocal Screws

2006 ◽  
Author(s):  
Z. Huang ◽  
Q. J. Ge
Keyword(s):  
Coordinate System ◽  
Scalar Product ◽  
Simple Procedure ◽  
Parallel Manipulators ◽  
Simple Expression ◽  
Parallel Mechanisms ◽  
Complex Mechanism ◽  
Mobility Analysis ◽  
Simple Method ◽  
Analysis Process

The goal of this paper is to demonstrate that the Modified Gru¨bler-Kutzbach Criterion when combined with a simple procedure for determining the reciprocal screws offers a direct and simple method for analysing highly complex mechanisms including the over-constrained parallel manipulators. Since the scalar product of screws is not dependent on the choice of the origin, one can quickly obtain a simple expression of screws by selecting an appropriate coordinate system. In such simple expression, the coordinates of a screw would include 0 or 1, and thus greatly simplifies the procedure for determine the number of constraints in a mechanism. Seven rules have been presented to help simplify the analysis process. The advocated approach makes it possible to determine, within minutes, the mobility of a highly complex mechanism by using a pencil and a paper. Many over-constrained mechanisms, including three parallel mechanisms, are presented as examples.

Dynamic Performance With Control of a 2DOF Parallel Robot

2012 ◽  
Author(s):  
Gianmarc Coppola ◽  
Dan Zhang ◽  
Kefu Liu ◽  
Zhen Gao
Keyword(s):  
Dynamic Model ◽  
Performance Index ◽  
Parallel Manipulator ◽  
Dynamic Performance ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Performance Study ◽  
Linear Controller ◽  
Reachable Workspace ◽  
And Control

In this work the dynamic performance and control of a 2DOF parallel robot is conducted. The study is partly motivated by large variations in dynamic performance and control within the reachable workspace of many parallel manipulators. The forward dynamic model of the robot is derived in detail. The connection method is directly utilized for this derivation. Subsequently, a dynamic performance study is undertaken. This reveals important information whilst using a forward dynamic model. A performance index is proposed to determine the variability of performance of the parallel manipulator. Then a trajectory-tracking scenario is undertaken using a linear controller. By means of control, the simulations illustrate the validity of the proposed index for parallel manipulators.

Modeling and Control of a Cable-Driven Robot for Inspection of Wide-Area Horizontal Workspaces

2016 ◽  
Author(s):  
Forrest Montgomery ◽  
Joshua Vaughan
Keyword(s):  
Parallel Manipulator ◽  
Large Scale ◽  
Parallel Manipulators ◽  
End Effector ◽  
Modeling And Control ◽  
Oscillatory Dynamics ◽  
Flexible Wire ◽  
Length Changes ◽  
Stiffness And Damping ◽  
And Control

Cable Driven Parallel Manipulators (CDPMs) utilize flexible wire to actuate an end-effector, allowing rapid accelerations across large workspaces. CDPMs are predominantly modeled with rigid cables, greatly simplifying the analysis. This model is satisfactory for small, fixed masses traveling short distances. However, as cable length increases, the flexibility of the cables, including the variation in stiffness and damping as length changes, cannot be ignored. In addition, the end-effector, which may be modeled as a pendulum, will rotate and contribute to the motion. This paper presents the modeling and control of a large-scale, cable-driven parallel manipulator, with application to inspection of large workspaces. The multi-degree-of-freedom model developed takes into account flexibility of cables and the oscillatory dynamics of the end effector. The dominant dynamics are identified and used to design a control system to limit vibration.

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