Optimal Synthesis of the Slider-crank Mechanism for Path Generation Based on the Generalized Kinematic Mapping of Constrained Plane Motions

10.6567/IFToMM.14TH.WC.OS2.008

Gen-Liang Chen；Hao Wang；Wei-Dong Yu；Yong Zhao

Optimal synthesis ； Planar slider-crank mechanism ； Continuous path generations ； Generalized kinematic mapping ； Gradient descent algorithm

Proceedings of the 14th IFToMM World Congress

14th-4（2015 / 11 / 04）

108 - 116

英文

This paper presents a new strategy for the optimal synthesis of the planar slider-crank mechanism for continuous path generations. Based on the generalized kinematic mapping of constrained plane motions, the desired path for the coupler link is mapped into the three-dimensional projective space as a spatial surface, which is regarded as the target kinematic manifold. Also, the potential motions of the coupler link constrained by the crank and the slider are projected on the target manifold in the image space, whose difference can be regarded as an alternative description for the kinematic conflict of the mechanism with the design requirement. Thus, a metric for the structure error between the candidate mechanism and the ideal one for the desired path is set up in terms of the area of a ruled surface, the distance surface intercepted from the target manifold, which is also selected as the objective function for the optimal synthesis. To obtain the final optimum based on the initial design variables with high convergence rate, the gradient descent algorithm is introduced. A numerical example for the optimal synthesis of the planar slider-crank mechanism for an elliptic trajectory is studied to validate the effectiveness of the proposed approach.