Available online at hanism and Machine Theory Mechanism and Machine Theory 43 (2008) 1175–1185 ate/mechmt A simple method to calculate mobility with Jacobian Dong-Chao Yang *, Jing Xiong, Xiang-Dong Yang Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, China Received 14 January 2007; received in revised form 4 August 2007; accepted 6 August 2007 Available online 21 September 2007 Abstract Although many mobility formulae have been set in the last 150 years, unfortunately, some of them are not fit for many classical mechanisms and some are indigestible. This paper gives a simple method to calculate the mobility of all kinds of parallel mechanisms only with Jacobian matrixes. It can position of degrees-of-freedom and output speeds of moving platform in passing. Furthermore, this method can be used to determine the existence of inactive joints and equiv- alent serial chain plicated parallel chain. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Mobility; Spatiality; Degree-of-freedom; Parallel mechanisms 1. Introduction Many mobility formulae have been set in the last 150 years, for example, the formulae based on theory of linear transformation [1], screw theory [2–5], Lie group and Lie algebra [6–9], theory of topological features [10]. Gogu studied 35 famous mobility formulae in [11], and he grouped formulae into two categories: (a) approaches for mobility calculation based on setting up the kinematic constraint equations and their rank cal- culation for a given position of the mechanism with specific joint location, (b) formulae for a quick calculation of mobility without need to develop the set of constraint equations. The approaches for mobility calculation based on setting up the kinematic constraint equations and their rank calculation are valid without exception. The major drawback of these approaches is that the mobility cannot be determined quickly without setting up the kinemati
