Dynamic Analysis of Closed Loop Mechanisms on the Basis Vectors of Passive Joint Axes

2003 ◽  
Vol 20 (8) ◽  
pp. 501-508 ◽  
Author(s):  
Koichi Sugimoto
Keyword(s):  
Dynamic Analysis ◽  
Closed Loop ◽  
Passive Joint ◽  
Basis Vectors

On the Bases of Wrench Spaces for the Kinematic and Dynamic Analysis of Mechanisms

2003 ◽  
Vol 125 (3) ◽  
pp. 552-556 ◽  
Author(s):  
Koichi Sugimoto
Keyword(s):  
Dynamic Analysis ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Closed Loop ◽  
Computational Procedure ◽  
Analysis Procedure ◽  
Dual Basis ◽  
Passive Joint

The aim of this paper is to find out a computational procedure for the kinematic and dynamic analysis of a mechanism with multiple loops having motion spaces of a Lie algebra or Lie algebras. The basis of a motion space of the loop is determined such that it consists of passive joints axes in a loop, and a basis of a wrench space is determined to be its dual basis. The analysis of a closed loop mechanism can be done by selecting loop-cut-joints and computing values of wrenches acting on these joints from the condition that virtual works of passive joints are zero. By expressing these wrenches in the coordinate vectors on the dual bases, the concise analysis procedure can be obtained. Because a formulation for the analysis is developed based on the bases consisting of passive joint axes and their dual bases, the computational procedure can be applied to a mechanism with any Lie algebras.

Selection of Degrees of Freedom for Dynamic Analysis

1987 ◽  
Vol 109 (1) ◽  
pp. 65-69 ◽  
Author(s):  
K. W. Matta
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
General Purpose ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Large Complex ◽  
Static Condensation ◽  
Basis Vectors ◽  
Selection Of

A technique for the selection of dynamic degrees of freedom (DDOF) of large, complex structures for dynamic analysis is described and the formulation of Ritz basis vectors for static condensation and component mode synthesis is presented. Generally, the selection of DDOF is left to the judgment of engineers. For large, complex structures, however, a danger of poor or improper selection of DDOF exists. An improper selection may result in singularity of the eigenvalue problem, or in missing some of the lower frequencies. This technique can be used to select the DDOF to reduce the size of large eigenproblems and to select the DDOF to eliminate the singularities of the assembled eigenproblem of component mode synthesis. The execution of this technique is discussed in this paper. Examples are given for using this technique in conjunction with a general purpose finite element computer program GENSAM[1].

Kinematic and Dynamic Analysis for Closed-Loop Flexible Manufacturing Systems Using Nonlinear Recursive Method

2006 ◽  
Vol 505-507 ◽  
pp. 1015-1020
Author(s):  
Yunn Lin Hwang ◽  
Shen Jenn Huang
Keyword(s):  
Dynamic Analysis ◽  
Flexible Manufacturing ◽  
Manufacturing Systems ◽  
Manufacturing System ◽  
Closed Loop ◽  
Recursive Method ◽  
Coupled Equations ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Joint Reaction

In this paper, a nonlinear recursive method for the dynamic and kinematic analysis of a closed-loop flexible manufacturing system is presented. The kinematic and dynamic models are developed using absolute reference, joint relative, and elastic coordinates as well as joint reaction forces. This recursive method leads to a system of loosely coupled equations of motion. In a closed-loop manufacturing system, cuts are made at selected secondary joints in order to form spanning tree structures. Compatibility conditions and reaction force relationships at the secondary joints are adjoined to the equations of open-loop manufacturing systems in order to form closed-loop kinematic and dynamic equations. Using the sparse matrix structure of these equations and the fact that the joint reaction forces associated with elastic degrees of freedom do not represent independent variables, a method for decoupling the joint and elastic accelerations is developed. Unlike existing recursive formulations, this method does not require inverse or factorization of large nonlinear matrices. The application of nonlinear recursive method in kinematic and dynamic analysis of closed-loop manufacturing systems is also discussed in this paper. The use of the numerical algorithm developed in this investigation is illustrated by a closed-loop flexible four-bar mechanism.

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