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複雑システム・ Complex structures
Modelling of tree structures
変更行列
モデル・ models
運動学微分運動学力学
連続チェインと同じ
Modelling of closed chain
特性: Enhanced accuracy and load-carrying capacity of
the robot. L 関節 n + 1 リンク L > n Independent closed loops number is:
B = L – n Joints are either active or passive
N active joints
mj=1 if joint actuated
mj=0 if joint non-actuated
Modelling of closed chain
① Equivalent tree structure with n joints by virtually cutting each closed chain at one of its passive joints. Geometric parameters of the equivalent tree defined as before
② Cut joints numbered n + 1 to L. Each cut joint k, attach Rk fixed on one of the links connected to this joint, link j. The zk axis is taken along the axis of joint k, and the xk axis is aligned with the common normal between zk and zj
③Rk fixed on link j, transformation matrix between Rj and Rk constant.For clearness, this transformation will be denoted jTk+B, with j = a(k+B). The geometric parameters defining this transformation have a subscript k + B. Note that frame Rk+B is aligned with frame Rk, and that both rk+B and θk+B are zero.
Geometric description of a structure with closed loops is defined by an equivalent tree structure that is obtained by cutting each closed loop at one of its joints and by adding two frames at each cut joint. The total number of frames is equal to n + 2B and the geometric parameters of the last B frames are constants.
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