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This paper describes a three-dimensional parallel solution scheme for inverse dynamics of link mechanisms, which has already been proposed for the two-dimensional case and applied in several inplane motions. In this theory, the entire system is subdivided into finite elements and evaluated as a continuum. A single-link structure of a pin joint and a rigid bar is expressed using the Shifted Integration (SI) technique, which is conventionally used in finite element analyses of framed structures. This scheme calculates nodal forces by evaluating equations of motion in a matrix form, and thus information from the entire system can be handled in parallel, which is a very useful characteristic when applied in closed-loop or continuously transforming mechanisms. The obtained nodal forces are then converted into the joint torque in the system. Simple numerical tests on two-dimensional and three-dimensional open-loop link mechanisms are carried out for comparison with other schemes. The proposed scheme is implemented in a control system to evaluate the performance in actual control with dynamics compensation, and some control experiments are carried out on an open-loop link mechanism. The results reveal the possibility of using the proposed solution scheme in feed-forward control, independent of the system configuration of link mechanisms.