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The author has derived the closed-form dynamic equations for a planar musculoskeletal chain composed of a generic number n of rigid links connected by ideal revolute joints. Single-joint and multi-joint muscles have been modeled as linear force actuators that can span from one joint to all the joints of the chain. The generic shape and size of each individual link of the chain accounts for different alignments among the center of mass of the link, the centers of rotation of the joints that articulate the link with its neighbors, and the points of application of the muscle forces and the possible contact external resistances acting on the link. The joint torque and the reaction force acting on each joint have been determined in closed-form by analytical quantification of the unique contribution of each individual kinematic and kinetic variable: (1) force of each single-joint or multi-joint muscle spanning or non-spanning the joint; (2) weight and contact external resistances acting on each individual link of the chain; (3) position, angular velocity, and angular acceleration of each individual link of the chain. The analytical results derived in this study can be applied to multilink musculoskeletal chains with deep/superficial and segmental/global muscles.

Non-Slender n-Link Chain Driven by Single-Joint and Multi-Joint Muscle Actuators: Closed-Form Dynamic Equations and Joint Reaction Forces