This paper presents a single, unified, and efficient algorithm for animating the coupler motions of all four-bar mechanisms formed with revolute (R) and prismatic (P) joints. This is achieved without having to formulate and solve the loop closure equation for each type of four-bar linkages separately. Recently, we developed a unified algorithm for synthesizing various four-bar linkages by mapping planar displacements from Cartesian space to the image space using planar quaternions. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of generalized manifolds (or G-manifolds) that best fit the image points in the least squares sense. In this paper, we show that the same unified formulation for linkage synthesis leads to a unified algorithm for linkage analysis and simulation as well. Both the unified synthesis and analysis algorithms have been implemented on Apple's iOS platform.
A Unified Algorithm for Analysis and Simulation of Planar Four-Bar Motions Defined With R- and P-Joints
Manuscript received September 26, 2014; final manuscript received December 1, 2014; published online December 31, 2014. Assoc. Editor: Carl Nelson.
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Li, X., Ge, X., Purwar, A., and Ge, Q. J. (February 1, 2015). "A Unified Algorithm for Analysis and Simulation of Planar Four-Bar Motions Defined With R- and P-Joints." ASME. J. Mechanisms Robotics. February 2015; 7(1): 011014. https://doi.org/10.1115/1.4029295
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