This paper presents a new and comprehensive method of modeling robots having highly flexible members such as flexure joints. An accurate model of large deformat ion bending is important for precisely describing the configuratio n of the flexible member. Additionally, the accuracy of the Jacobian and Hessian of the forward kinematics are critically im portant at large angles for predicting the deformation and the stiffness of the joint under load. The model introduced here is based on the assumption that the curvature of a beam in bending is smooth, and thus can be approximated by low-order, orthogonal polynomials. This produces a parameterized description of flexure motion that can be used as a joint model wh en expressed in Denavit-Hartenberg form, as a transformation from one rigid link to the next in a serial manipulator. We will s how that with only three parameters, this model faithfully reprod uces the elastic deformation of a flexure hinge predicted by the continuum model, even for large angles, without requiring numerical integration or many finite elements. It can also be used to compute the compressive buckling load of the flexure as predicted by the continuum model.
['Lael U. Odhner', 'Aaron M. Dollar']
The Smooth Curvature Flexure Model: An Accurate, Low-Dimensional Approach for Robot Analysis