文档介绍：Available online at hanism
and
Machine Theory
Mechanism and Machine Theory 43 (2008) 964–983
ate/mechmt
Kinematic analysis of linkages based in finite elements and
the geometric stiffness matrix
R. Avile´s, A. Herna´ndez *, E. Amezua, O. Altuzarra
Escuela ica Superior de Ingenierı´a, Alameda de Urquijo s/n, 48013 Bilbao, Spain
Received 8 March 2006; received in revised form 19 July 2007; accepted 21 July 2007
Available online 4 September 2007
Abstract
This paper presents a numerical approach to rigid body linkage kinematics, based on a reduced form of the stiffness
matrix and in structural analysis concepts. This matrix may be referred to as geometric stiffness matrix, or simply as geo-
metric matrix. It is derived from basic nodes and length constraints, and provides full information on the kinematic prop-
erties of any linkage, including positions, velocities, accelerations, jerks and singular positions. This approach offers a
number of major advantages, especially where simplicity and generality are concerned. putational cost is also very
low, because of the simplicity of the numerical calculations and the reduced dimensions of the matrices involved.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Kinematics; Linkage analysis; Multibody; Numerical methods
1. Introduction
Methods for kinematic analysis are most often classified according to the type of procedure used to get a
solution, . graphical, analytical, and numerical. Alternatively they can be classified according to the nature
of the kinematic problem, as when a distinction is drawn between methods used for position problems and
others used in the calculation of velocities and accelerations. While the position problem leads to systems
of nonlinear equations with multiple solutions; velocities, acceleration, and jerks analyses are linear problems
with a unique solution.
Many methods found in bibliography can be defined as grapho-analytic, and are based on a geometric