The Smooth Curvature Model: An Efficient Representation of Euler–Bernoulli Flexures as Robot Joints

Abstract

This paper presents a new method to produce computationally efficient models of robots that have planar elastic flexure joints. An accurate, low-dimensional model of large deformation bending is important to precisely describe the configuration of a flexure-jointed manipulator. The new model is based on the assumption that the curvature of a beam in bending is smooth and, thus, can be approximated by low-order polynomials. This produces a description of flexure motion that can be used as a joint model when expressed as a homogeneous transformation between rigid links-essentially a "drop in" replacement for traditional joint models such as screw coordinates and Denavit-Hartenberg conventions. Derivatives of the joint kinematics such as Jacobians and Hessians are accurate and easy to compute. We will show that with only three parameters, this model faithfully reproduces the elastic deformation of a flexure hinge predicted by the continuum model, even for large angles, without requiring numerical integration or many finite elements. The model can also be used to accurately compute the compliance and compressive buckling load of the flexure, as predicted by the continuum model.

A compliant, underactuated hand for robust manipulation

“…A more accurate model for the i-HY finger, also shown in Fig. 9, would include several higher bending modes of the distal flexure joint as described in [43], and is derived in detail in [56]. For both of these models, the motion of the fingers during the sweeping phase of grasping can be modeled by treating the length of the flexor tendon as a rigid constraint on the system, then by minimizing the elastic energy in the two joints to find the equilibrium finger configuration as the finger closes.…”

Design of the Passive Joints of Underactuated Modular Soft Hands for Fingertip Trajectory Tracking

“…Using a sufficiently high number of modules, the deflection of each joint while the finger is bending is rather low, so that, for each joint, we can use the simplified linear results of beam theory. For higher deflections, a more complete bending model, as the one described in [18] should be adopted. When the actuator applies a force f r,j through the j-th tendon, it produces on the joint i a torque τ i = f r,j h. The corresponding joint rotation angle can be evaluated as…”

Bent Sheet Grasping Stability for Sheet Manipulation

“…L. Sun et al [6] developed a system which can flatten garments by accurate surface analysis using RGB-D images. Odhner [7] proposed a model of robots having planar elastic flexure joints by using the Euler-Bernoulli beam theory.…”