105 モータ代数を用いた閉ループ機構の可動性判定アルゴリズム(OS1-(2)オーガナイズドセッション《計算力学と数値シミュレーション》)

概要

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This paper proposes a new criterion for mobility calculation of closed loop mechanisms by using motor algebra. We represent a lower pair such as screw, rotational, or prismatic as a motor, and a higher pair, with n DOF, as a serial chain of n lower pairs between which n-1 links are interposed. In contrast to the well-known Jacobian matrix, the constraints imposed by a closed loop mechanism are expressed explicitly by pair loop matrix. By applying Gauss-Jordan elimination to the pair loop matrix of acceleration equation along with velocity equation, the rank of the matrix is obtained. The DOF of a mechanism can be determined from the number of lower pairs along the closed loop and the rank of the pair loop matrix. As far as we are currently aware, the new criterion covers much wider range of planar or spatial closed loop mechanisms and we have not found any exception yet.
一般社団法人日本機械学会の論文
2010-08-27