Compliance Analysis of Mechanisms with Spatial Continuous Compliance in the Context of Screw Theory and Lie Groups

This paper investigates the compliance effect on both serial and parallel mechanisms based on study of deflections of a finite segment of elastic beam with spatial compliance and applies eigenvectors and eigenvalues to identify principal screws in the mechanisms and parallel devices with spatial continuous compliance. With the analysis, compliance characteristics of both serial mechanisms and parallel devices can be identified with effect of compliance. Case studies are presented with numerical examples.

Design of a Multi-Directional Variable Stiffness Leg for Dynamic Running

Recent developments in dynamic legged locomotion have focused on encoding a substantial component of leg intelligence into passive compliant mechanisms. One of the limitations of this approach is reduced adaptability: the final leg mechanism usually performs optimally for a small range of conditions (i.e. a certain robot weight, terrain, speed, gait, and so forth). For many situations in which a small locomotion system experiences a change in any of these conditions, it is desirable to have a variable stiffness leg to tune the natural frequency of the system for effective gait control. In this paper, we present an overview of variable stiffness leg spring designs, and introduce a new approach specifically for autonomous dynamic legged locomotion. We introduce a simple leg model that captures the spatial compliance of the tunable leg in three dimensions. Lastly, we present the design and manufacture of the multi-directional variable stiffness legs, and experimentally validate their correspondence to the proposed model.

Spatial Compliances Achieved With Serial Elastic Mechanisms

Previously, the structure of a spatial stiffness matrix and its realization using a parallel elastic system have been addressed. This paper extends those results to the analysis and realization of a spatial compliance matrix using a serial mechanism. We show that, a spatial compliance matrix can be decomposed into a set of rank-1 primitive matrices, each of which can be realized with an elastic joint in a serial mechanism. To realize a general spatial compliance, the serial mechanism must contain joints that couple the translational and rotational motion along/about an axis. The structure of a spatial compliance matrix can be uniquely interpreted by a 6-joint serial elastic mechanism whose geometry is obtained from the eigenscrew decomposition of the compliance matrix. The results obtained from the analysis of spatial compliant behavior and its realization in a serial mechanism are compared with those obtained for spatial stiffness behavior and its realization in a parallel mechanism.

The Duality in Spatial Stiffness and Compliance as Realized in Parallel and Serial Elastic Mechanisms

Spatial elastic behavior is characterized by a 6×6 positive definite matrix, the spatial stiffness matrix, or its inverse, the spatial compliance matrix. Previously, the structure of a spatial stiffness matrix and its realization using a parallel elastic system have been addressed. This paper extends those results to the analysis and realization of a spatial compliance matrix using a serial mechanism and identifies the duality in spatial stiffness and compliance associated with parallel and serial elastic mechanisms. We show that, a spatial compliance matrix can be decomposed into a set of rank-1 compliance matrices, each of which can be realized with an elastic joint in a serial mechanism. To realize a general spatial compliance, the serial mechanism must contain joints that couple the translational and rotational motion along/about an axis. The structure of a spatial compliance matrix can be uniquely interpreted by a 6-joint serial elastic mechanism whose geometry is obtained from the eigenscrew decomposition of the compliance matrix. The results obtained from the analysis of spatial compliant behavior and its realization in a serial mechanism are compared with those obtained for spatial stiffness behavior and its realization in a parallel mechanism.