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Modelling and Simulation in Engineering
Volume 2012 (2012), Article ID 501251, 9 pages
Research Article

High-Order Dimension Synthesis of Planar/Spatial Mechanisms with One-DoF by CAD Variational Geometry

1Parallel Robot and Mechatronic System Laboratory, Hebei Province, Key Laboratory, Advanced Forging and Stamping Technology and Science, Ministry of National Education, and College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China
2Yingkou Equipment Development and Manufacturing Co., Ltd., Liaoning, Yingkou 115004, China

Received 3 April 2012; Accepted 17 September 2012

Academic Editor: Javier Otamendi

Copyright © 2012 Yi Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a (computer aided design) CAD variational geometry approach for the high-order dimension synthesis of one-DoF mechanisms based on the given velocity/acceleration of a moving platform along a prescribed trajectory. The objective of this approach is to determine the reasonable dimensions of the mechanisms when given the velocity or/and the acceleration of the moving platform along a prescribed trajectory. First, some concepts and mathematical foundations are explained for constructing the velocity/acceleration simulation mechanism of a general mechanism. Second, the inverse velocity/acceleration simulation mechanisms of the planar/spatial four-bar mechanisms with one-DoF are constructed by the CAD variational geometry. Third, when given the position and the velocity/acceleration of the coupler along a prescribed trajectory, all the reasonable dimensions of the planar/spatial four-bar mechanisms are solved from their simulation mechanisms.