The minimum form of strength in serial, parallel and bifurcated manipulators

The described mathematical formulations answer the questions “how strong is enough?”, “strong in which direction?”, and “where is the weakest link?” that robot designers face in the early stages of matching tasks with robotic mechanisms. This work produces 3D visualizations of robot strengths and weaknesses across their dexterous workspaces, aiding interactive manipulator joint and kinematic design. Strength is defined here as the maximum force or moment that the robot can exert on the environment at its point of resolution. This strength is a 6×1 vector for spatial mechanisms, comprising forces and moments resolved in a global frame. The three factors studied in this work are the design of the manipulator´s drive trains, the chain´s kinematic parameters, and the articulation of kinematic redundancies as self motion. The mathematical formulation is implemented as a minimum of a set of serial strengths, within which can exist parallel sets as appropriate for the mechanism´s kinematics. The strength model is first developed for serial chains, broadened to the statically indeterminant cases of parallel chains, and then applied to a bifurcated system of chains in development at NASA. This work´s primary objective is to bring to bear in robot design the mathematical principles usually reserved for robot modeling and control. After a robot has been built, it is often too late to fix a mechanism´s many weaknesses. It is our belief that the Jacobian has as much to teach robot designers as it has taught students of dynamics and control theory