Using the Matrix Method to Compute the Degrees of Freedom of Mechanisms

Ghaemi Osgouie, Kambiz; Gard, Bahman

doi:10.22055/jacm.2017.20542.1085

Using the Matrix Method to Compute the Degrees of Freedom of Mechanisms

Document Type : Research Paper

Authors

Kambiz Ghaemi Osgouie

Bahman Gard

University of Tehran, Kish International Campus, Kish Island, 7941655665, Iran

10.22055/jacm.2017.20542.1085

Abstract

In this paper, some definitions and traditional formulas for calculating the mobility of mechanisms are represented, e.g. Grubler formula, Somov - Malyshev formula, and Buchsbaum - Freudenstei. It is discussed that there are certain cases in which they are too ambiguous and incorrect to use. However, a matrix method is suggested based on the rank of the Jacobian of the mechanism and its application is investigated. It is shown that the matrix method will definitely lead to a correct answer; however, it is lengthy and consumes more computational effort. It is shown that in the cases the traditional formulas give a wrong answer and the matrix method gives the correct mobility. To compare the methods, several examples are given including the four bar planar linkage, the augmented four bar linkage, University of Maryland manipulator, Cartesian parallel manipulator (CPM), delta robot, orthoglide robot, and H4 parallel robot.

Keywords

Degrees of Freedom

Grubler’s exceptions

Jacobian rank

Subjects

Robotics and Control

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