This paper focuses on preliminary work related to the discovery of single degree-of-freedom mechanism paths useful for dynamic locomotion tasks. The objective is to bridge a gap between kinematic specifications and emerging dynamic behaviors. This is accomplished by formulating a set of ordinary differential equations that includes essential mechanism characteristics (path traced, mechanical advantage) but excludes all physical mechanism parameters (topology, link lengths). The dynamics represent a rotation constrained body propelled by a foot that is attached to that body by a user-defined path. The foot is powered by a series-elastic actuator acting through a mechanical advantage function that is defined across the length of the path. Through this framework, a range of user-defined paths were tested for effective locomotion on flat and complex terrains. Foot paths and mechanical advantage functions exist outside of any mechanical design, with the goal to discover paradigms worth instantiating into physical mechanisms, a task reserved for kinematic synthesis. This work would empower existing kinematic synthesis techniques to achieve dynamic requirements. In other words, kinematic requirements are transformed from an end to a means. Their dynamic utility would be evaluated by the framework presented in this paper rather than pursued by themselves.

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