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A nonlinear Timoshenko beam formulation for modeling a tendon‐driven compliant neck mechanism

In this paper, we consider the dynamical behavior of a tendon‐driven compliant neck mechanism which is used to actuate the head of a humanoid robot as proposed by [1, 2]. The neck is realized as a silicone block mounted onto the robot's torso. At the top end of the silicone block an aluminum plate interconnects the compliant neck with the head. At the same plate, tendons are attached whose actuation causes the soft and flexible block to deform thereby inducing a motion of the robot's head. For workspace design and control of the head's trajectory, a mechanical model is required which appropriately describes the entire neck‐head system. We present a dynamic model of the system in which the silicone block and the head are modeled as a planar nonlinear Timoshenko beam and a rigid body, respectively. The tendon actuations are included as external configuration‐dependent forces.