This paper presents a generalized framework to solve m-pose, n-path-points mixed synthesis problems, known as the Alt-Burmester problems, using a task-driven motion synthesis approach. We aim to unify the path and motion synthesis problems into an approximate mixed synthesis framework. Fourier descriptors are used to establish a closed-form relationship between the path and orientation data. This relationship is then exploited to formulate mixed synthesis problems into pure motion synthesis ones. We use an efficient algebraic fitting based motion synthesis algorithm to enable simultaneous type and dimensional synthesis of planar four-bar linkages.

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