Rapid efficient algorithms for dynamics, torques, and pin forces are developed for use with synthesis programs. The method can be used to calculate either the motion resulting from given torques and forces or the torque required for a given motion. An interactive computer program has been written for these cases. Experimental data for a four-bar mechanism is compared with the computations. Due to the large number of variables, a systematic nomenclature has been developed suitable for FORTRAN Programs. Methods are given to sequentially number the links of the mechanism and order the equations to obtain the diagonal band array directly.