Model validation of discretized spatial closed elastica

摘要

A closed elastica, which is an elastic rod whose both ends are fixed to prescribed two places, can be found in various situations in robotics. In this paper, we investigate validity of the discretized spatial model of a closed elastica. The discretized closed elastica model can be regarded as a series of rigid bodies connected with passive elastic joints physically, and represented by a set of nonlinear equations derived by discretizing differential equations with boundary conditions as well as Euler equations expressing local minimum elastic energy. The validity of the considered model was studied by comparing the measured shape and the calculated shape from the model. Experimental results using a laser position sensor for shape measurement show that good correspondence between measured and calculated shapes, which supports the validity of the considered model. The constrained force and torque at the tip of an elastica, which can be obtained simultaneously associated with shape calculation, are also verified from measurement by a 6-axes force/torque sensor.