モータ代数とグラフ理論による機構の記述と解析 (第3報)

オープンループ機構の動力学解析

抄録

Equation of motion of an open loop mechanism is formulated by describing the equilibrium of external force and inertia force around each pair-axis. The topology of an open loop mechanism is represented by a tree-path matrix having the stationary link as its root. An inertia force motor on a link is determined by the extended tensor of inertia in 6 × 6 matrix form, the velocity motor and the acceleration motor of the link. The equation of motion is interpreted in two ways. Firstly, it can be used to calculate the driving torque of each pair axis to realize the specified motion of an open loop mechanism. Secondly, relative angular acceleration at each pair is determined through the equation by velocity motors and external forces of all links. A computer program based on the new equation is developed for three-dimensional dynamic analysis of open loop mechanisms. When the initial state of an open loop mechanism and the external force functions are given, the motion of the mechanism can easily be simulated by numerical integration. Application to some typical motion analysis problems proved the effectiveness of the program.