Simplified dynamics model of planar two-joint arm movements

A theoretical framework is presented that describes a way in which the inverse dynamics equations of motion of planar two-joint arm movements (EX-model) are reformulated in a simple form. A single point was assumed to define both the wrist and elbow joint centers, and thus the motion of two points in extrinsic space was represented by second-order differential equations to provide the variables in the reformulation (RE-) model. Through an analytical processes, it was shown that the RE-model for reproducing the shoulder joint torque consists of the linearly scaled moment per unit mass responsible for accelerating the wrist and elbow points about the shoulder joint, while that for reproducing the elbow joint torque consists of the linearly scaled moment per unit mass responsible for accelerating the wrist point about the elbow. The scaling factors for variables in the RE-model were based solely on the values for segment lengths, while in the EX-model the inertial parameter data for the segments are involved in its representation. The inertial parameter data of six-arm specimens from the cadaver experiment of Chandler et al. (1975, AMRL Technical Report, Wright-Patterson Air Force Base, OH) were used to develop and verify the numeric solutions of the RE-model. The adequacy of the model varied somewhat among subjects, but minor changes of the physical parameters of the arm segments enabled perfect reformulation, regardless of the specimens. The potential abilities of the RE-model to deal with the complexities in motor control with more simple control schemes are discussed.