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.

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]

scholarly journals Acceleration Analysis of 3-DOF Planar Parallel Manipulators by Means of Screw Theory

2016 ◽  
Vol 45 (2) ◽  
pp. 89-95
Author(s):  
Soheil Zarkandi
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Second Order ◽  
Degree Of Freedom ◽  
Planar Parallel Manipulator ◽  
Acceleration Analysis ◽  
Three Degree Of Freedom ◽  
Planar Parallel Manipulators

This paper deals with the second order kinematics of three degree-of-freedom (DOF) planar parallel manipulators. The simple and compact expressions are derived for both the inverse and forward acceleration analyses using screw theory. Moreover, as an example, a 3-DOF planar parallel manipulator is introduced and its kinematics is analyzed using the proposed method.

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.

Motion Performance Analysis of Double-Cylinder Parallel Manipulators

2009 ◽  
Author(s):  
Hong Zhou ◽  
Shehu T. Alimi ◽  
Aravind Ravindranath ◽  
Hareesh Vepuri
Keyword(s):  
Performance Analysis ◽  
Parallel Manipulator ◽  
Critical Role ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Operation Speed ◽  
Transmission Angle ◽  
Motion Performance ◽  
Two Degree Of Freedom

Double-cylinder parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-cylinder parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a critical role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to apply this type of parallel manipulator.

DYNAMICS AND CONTROL OF A TWO-DEGREE-OF-FREEDOM VIBRATION-DRIVEN SYSTEM

2007 ◽  
Vol 40 (14) ◽  
pp. 109-114
Author(s):  
Nikolai N. Bolotnik ◽  
Mikhail Pivovarov ◽  
Igor Zeidis ◽  
Klaus Zimmermann
Keyword(s):  
Degree Of Freedom ◽  
Driven System ◽  
Dynamics And Control ◽  
And Control ◽  
Two Degree Of Freedom

Kinematics of a partially decoupled 3R2T symmetrical parallel manipulator 3-RCRR

2008 ◽  
Vol 222 (2) ◽  
pp. 277-285 ◽  
Author(s):  
S-J Zhu ◽  
Z Huang ◽  
M Y Zhao
Keyword(s):  
Control System ◽  
Cervical Spine ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Short History ◽  
Translational Degree ◽  
And Performance

The 3R2T (three rotational and two independent translational degree of freedom (DoF)) symmetrical parallel manipulator may be adopted in bionics, for example, simulating the motion of a cervical spine based on their mobility property and performance close to isotropic limit. However, up to now, characteristics of this class of manipulators have not been well studied because of its short history. Hence, to study the feasibility of this class of manipulator for bionics, kinematics for 3-RCRR is analysed including position, singularity, velocity, and acceleration. Different from other 3R2T 5-DoF symmetrical parallel manipulators, the mobility of 3-RCRR is partially decoupled, which makes the realization of control system easier than in others.

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.

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