This paper presents the conceptual foundation and analytical techniques for the design of multiple-degree-of-freedom force-generating linkages. Force-generating mechanisms produce a specified quasi-static force or torque as a function of input position with resisting energy supplied to the mechanism from an external energy-storage device, such as a spring or load weight. Multiple-degree-of-freedom force-generating mechanisms provide the tailored resistance force along a design path while incorporating additional mobility, which allows the mechanism to deviate from the path within a local workspace. Although many potential applications for these mechanisms exist, the focus of this research has been on the design of weight-loaded machines for personal strength training, where the additional freedom of motion is valuable for reasons of ergonomic and exercise efficiency. A variety of open- and closed-chain mechanisms are considered as potential candidates for design. Techniques are developed for the closed-form synthesis of simple, two link, open loop chains that are able to produce a specified force component along a prescribed path. This result provides a foundation for designing more useful mechanisms, including doubly weighted symmetric and singly weighted asymmetric 5R linkages. In all cases, closed-form solutions are developed using Burmester-type synthesis procedures and equations of static equilibrium.

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