モータ代数とグラフ理論による機構の記述と解析(第6報) : 歯車とカムを含む機構の動力学解析

概要

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A simple and clear algorithm for dynamic analysis of mechanisms using motor algebra and graph theory has been developed. A Iower kinematic pair such as rotational pair, helical pair or translational pair is represented by a pair-axis motor. Higher kinematic pair such as spherical pair or cylindrical pair is represented by a chain of multiple lower pairs having void links between them. Gear pair is represented by a line vector or a screw which is repositioned after every small movement. Cam-follower pair is replaced with an equivalent cross-slider crank chain sized and positioned by the velocity and acceleration functions derived form the cam-diagram. An algorithm for the analysis of jump of cam is also proposed. A closed-loop mechanism and an open-loop mechanism are driven simultaneously to estimate the timing ofjump and strike by comparison of acceleration or displacement between the two. In this paper, a new procedure for the small movement is introduced. Transformational matrix at each pair-axis motor is calculated from the relative angular displacement, then superposed along the tree of link-pair graph to determine the absolute displacement of each link. The computational error is reduced significantly by this procedure, which enables the high-speed dynamic simulation.
社団法人精密工学会の論文
1998-05-05