Mobility and Reconfiguration Analysis of Linkages


Mobility and Reconfiguration Analysis of Linkages

Fri, 24/03/2017 - 13:15 to 14:15


Prof Andreas Müller

The degree of freedom (DOF) and the mobility are essential kinematic features of linkages. Although mobility analysis has been at the core of geometry and theoretical kinematics since centuries, it remains to develop generally applicable mobility criteria.

The finite (local) DOF of a linkage is the (local) dimension of its configuration space (c-space) variety whereas the (instantaneous) differential DOF is the dimension of the kernel of the constraint Jacobian. Despite being simple this definition is difficult to use. Recently the concept of tangent cone to the c-space modelled as an analytic variety has been applied noting that its dimension equals the local dimension of the c-space. It will be shown how the tangent cone (an algebraic variety) can be computed from the joint screw coordinates of the linkage.

Most linkages exhibit kinematic singularities. A configuration is a kinematic singularity when the differential DOF changes, otherwise it is a regular configuration. Singular configurations cannot be identified by inspection of the rank of the constraint Jacobian. For instance, the c-space of so-called overconstrained linkages consists of manifolds with rank deficient Jacobian. It is also not sufficient to compare the finite and differential DOF since this can be different in regular configurations of underconstrained (shaky) mechanisms. It will be shown how kinematic singularities can be established using the tangent cone to the varieties of critical points of the constraint mapping. This provides a necessary and sufficient condition, and eventually allows for a reconfiguration analysis of linkages.
The audience is expected to have a background in general kinematics and preferably in screw and Lie group theory.


Andreas Müller was born on 1971 in Nordhausen, Germany. He is full professor and head of the Institute of Robotic at the Johannes Kepler University Linz. He obtained a diploma degree in mathematics at University Mittweida, Germany, a master degree in electrical engineering at University of Northumbria at Newcastle, UK (1998), and a diploma in mechanical engineering at the TU Chemnitz, Germany, where 2004 he also earned a PhD in mechanics. In 2008 he completed his habilitation at the University Duisburg-Essen, Germany. From 1998 until 2008 he worked at scientific assistant at the Institut of Mechatronic e.V. in Chemnitz where he served as deputy CEO from 2011 until 2013. From 2013 until 2014 he joined the Michigan University – Jiao Tong University Joint Institute in Shanghai as associate professor.

Andreas Müller is executive editor of Mechanical Sciences (IFToMM), Transactions on Robotics (IEEE), Robotics and Automation Letters (IEEE), Journal of Mechanisms and Robotics (ASME), Meccanica (IMETA), and was associate editor of Mechanism and Machine Theory (IFToMM).
His research interests cover the holistic modeling and according model-based control strategies for mechatronic systems and robotic systems and human machine interaction and safety. Particular research foci are kinematics and efficient dynamics modeling with application to mobile platforms, redundant serial and parallel kinematics manipulators and flexible lightweight robots.