By convention, the links of a flexible manipulator are numbered consecutively from 0 to n starting from the base of the manipulator to the tip of the end effector, where n is the total number of links. We define the coordinate system (Xj, Yj, Zj) on link j with origin Oj at the distal end (farthest from the base), oriented so that the Zj axis is along the axis of joint j + 1. We also define the coordinate system on link j with origin Ôj in such a way that when the link is in its undeformed configuration, a coordinate system is exactly coincident on the other.

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