文档介绍：Mechanism and Machine Theory 44 (2009) 1240–1255
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Mechanism and Machine Theory
journal homepage: ate/mechmt
Generic mobility of rigid body mechanisms
Andreas Müller *
Institute of Mechatronics at the Chemnitz University of Technology, Reichenhainer Straße 88, 09126 Chemnitz, Germany
article info abstract
Article history: In this paper the generic DOF of rigid body mechanisms is investigated. This is the DOF of
Received 13 August 2007 almost all mechanisms that can be built from a given set of kinematic pairs in a certain
Received in revised form 31 July 2008 arrangement, but with arbitrary link geometry. The generic DOF is the most likely DOF
Accepted 4 August 2008
in the presence of link imperfections. Furthermore, we are interested in the generic DOF
Available online 20 September 2008
of different types of mechanisms, . when the link geometries are arbitrary, but in accor-
dance with a certain type (. planar, spherical, spatial).
A widely used mobility criterion is the extended Chebychev–Kutzbach–Grübler (CKG)
Keywords:
formula. It is proven in this paper that the generic DOF of a prising loops
Mobility
Generic mobility of specific motion types, such as planar, spherical, and spacial, is indeed given by the
Configuration space extended CKG formula. In particular, mechanisms with arbitrary link geometry have gener-
Overconstrained ically a DOF d ¼ n À 6c, where c is the number of fundamental loops, and n is the total
Underconstrained number of joint freedoms. That is, almost all mechanisms are trivial (not overconstrained).
Singularities Moreover, such mechanisms have generically no configuration space singularities.
The mobility and the classification of mechanisms as overconstrained, underconstrained,
or kinematotropic is considered in view of the configuration space. It is pointed out that the
local DOF cannot always be inferred from the number of constraints (overconstrained
mecha