Enumeration of kinematic chains and mechanisms
- 1 December 2008
- journal article
- research article
- Published by SAGE Publications in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
- Vol. 223 (4), 1017-1024
- https://doi.org/10.1243/09544062jmes1071
Abstract
A problem still unsolved in kinematics is the enumeration of a complete list of kinematic chains and mechanisms without isomorphisms and without degenerate chains that operate in any screw system. In this paper, a method for the enumeration of kinematic chains without isomorphisms and degenerate chains for all screw systems and a new method of enumeration of kinematic chain inversions (i.e. mechanisms) based on group theory techniques are presented. New concepts of the group theory are introduced and a new method of enumeration of inversions is presented. Kinematic inversions are related to the symmetries of the chain which can be identified analysing the corresponding graph. The symmetry of a graph can be identified for the group of automorphisms of the graph and its orbits provides sets of vertices (links) that are in the same equivalence classes, i.e. they have the same properties of symmetry. The main definitions of group theory and examples of application of the new method of enumeration of inversions are presented. New results are obtained and divided in two classes: original results in non-planar screw systems (λ≠3) and results in agreement with a previously published list for planar kinematic chains and planar mechanisms (inversions). Two tables (1 and 3) are provided, which are up-to-date lists of kinematic chains and mechanisms for several screw systems.Keywords
This publication has 21 references indexed in Scilit:
- Variety and connectivity in kinematic chainsMechanism and Machine Theory, 2008
- Selecting multi-freedom multi-loop kinematic chains to suit a given taskMechanism and Machine Theory, 2001
- Isomorph-Free Exhaustive GenerationJournal of Algorithms, 1998
- Generation of planar kinematic chainsMechanism and Machine Theory, 1996
- Kinematic chains for robot hands—I. Orderly number-synthesisMechanism and Machine Theory, 1995
- Enumeration of Basic Kinematic Chains Using the Theory of Finite GroupsJournal of Mechanical Design, 1989
- Further Applications of Group Theory to the Enumeration and Structural Analysis of Basic Kinematic ChainsJournal of Mechanical Design, 1989
- On graphical partitions and planarityDiscrete Mathematics, 1977
- Type Synthesis of Plane LinkagesJournal of Engineering for Industry, 1967
- Some Applications of Graph Theory to the Structural Analysis of MechanismsJournal of Engineering for Industry, 1967