Continuum Manipulator Statics Based on the Principle of Virtual Work

This paper presents a generalized method of determining the static shape conformation of a continuum robot based on the principle of virtual work. A lumped parameter model is utilized to model a prototypical single-segment manipulator. Elastic effects, gravitational forces and actuation loading are modeled as generalized forces and moments acting along the manipulators at discrete masses. A brief derivation of the governing static equations based on the principle of virtual work is presented, and then applied to the problem of continuum manipulator statics. The numerical method was successfully implemented numerically, capable of determining a system’s static equilibrium given a prescribed actuation.