1992 年 58 巻 549 号 p. 1366-1370
This paper deals with a mathematical model of the mechanics of rigid bodies connected by rotary joints. The method is based on the Lagrangian formulation. The kinetic energy is written in terms of the angular velocities. The expression for the kinetic energy has a homogeneous quadratic form in the angular velocity, the coefficient matrix of which is given by the products of triangular matrices. The equations of motion are derived from the Lagrange's equations for the quasi-coordinates, the angular velocities of the bodies. The equations of motion become recursive forms due to the structure of the expression of the kinetic energy of the system. The algorithm of the inverse dynamics, which follows from the equations of motion, becomes also a recursive form like the algorithm based on the Newton-Euler equations of motion. Since the algorithm is based on the Lagrangian formulation, it can be extended to more complex systems that include flexible bodies, the constraints of which limit the motion of the systems, and so on.