Planar Compliance Realization with Two 3-Joint Serial Manipulators Connected in Parallel

2021 ◽  
pp. 1-18
Author(s):  
Shuguang Huang ◽  
Joseph Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Geometric Construction ◽  
Serial Manipulators ◽  
Compliant Behavior ◽  
New Synthesis ◽  
Synthesis Procedure ◽  
Serial Mechanism

Abstract In this paper, the realization of any specified planar compliance with two 3R serial elastic mechanisms is addressed. Using the concepts of dual elastic mechanisms, it is shown that the realization of a compliant behavior with 2 serial mechanisms connected in parallel is equivalent to its realization with a 6-spring fully parallel mechanism. Since the spring axes of a 6-spring parallel mechanism indicate the geometry of a dual 3R serial mechanism, a new synthesis procedure for the realization of a stiffness matrix with a 6-spring parallel mechanism is first developed. Then, this result is extended to a geometric construction-based synthesis procedure for two 3-joint serial mechanisms.

Spatial Compliances Achieved With Serial Elastic Mechanisms

2000 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Rotational Motion ◽  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Elastic System ◽  
Compliance Matrix ◽  
Elastic Joint ◽  
Compliant Behavior ◽  
Elastic Mechanism ◽  
Spatial Compliance ◽  
Serial Mechanism

Abstract 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.

Realization of an Arbitrary Planar Stiffness With a Simple Symmetric Parallel Mechanism

2011 ◽  
Vol 3 (4) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
The Other ◽  
New Method ◽  
Compliant Behavior ◽  
Elastic Mechanism ◽  
Symmetric Geometry ◽  
Synthesis Procedure

This paper presents a new method for the realization of a planar compliant behavior with an elastic mechanism. The mechanisms considered are parallel with symmetric geometry. We show that any planar stiffness matrix can be realized using a parallel mechanism with four line springs connected symmetrically. Among the four springs, two are identical parallel springs equidistant from the stiffness center, and the other two identical springs intersect at the stiffness center. A synthesis procedure based on geometry is presented and mechanism compactness is discussed.

Realization of a Planar Stiffness With a Simple Symmetric Parallel Mechanism

2010 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
The Other ◽  
New Method ◽  
Parallel Mechanisms ◽  
Compliant Behavior ◽  
Elastic Mechanism ◽  
Symmetric Geometry ◽  
Synthesis Procedure

This paper presents a new method for the realization of a planar compliant behavior with an elastic mechanism. The mechanisms considered are parallel mechanisms with symmetric geometry. We show that any planar stiffness matrix can be realized using a parallel mechanism with four line springs connected symmetrically. Among the four springs, two are identical parallel springs equidistant from the stiffness center, and the other two identical springs intersect at the stiffness center. A synthesis procedure is presented.

Realization of an Arbitrary Elastic Behavior With an Elastic Mechanism Having Concurrent Axes

2000 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Elastic Behavior ◽  
Unique Point ◽  
Compliance Matrix ◽  
Elastic Mechanism ◽  
Serial Mechanism

Abstract In this paper, synthesis of an arbitrary elastic behavior with an elastic mechanism is addressed. The mechanisms considered are parallel and serial mechanisms with concurrent axes. We show that any stiffness matrix can be realized through a parallel mechanism with all spring axes intersecting at a unique point. This point is shown to be the center of stiffness. We also show that any compliance matrix can be realized through a serial mechanism with all joint axes intersecting at a unique point. This point is shown to be the center of compliance. Synthesis procedures for mechanisms with these properties are provided.

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

2000 ◽  
Vol 124 (1) ◽  
pp. 76-84 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Stiffness Matrix ◽  
Elastic System ◽  
Positive Definite Matrix ◽  
Elastic Behavior ◽  
Compliance Matrix ◽  
Compliant Behavior ◽  
Elastic Mechanism ◽  
Compliance Matrices ◽  
Spatial Compliance ◽  
Serial Mechanism

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.

scholarly journals Geometric Construction-Based Realization of Planar Elastic Behaviors With Parallel and Serial Manipulators

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Elastic Properties ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Geometric Construction ◽  
Elastic Component ◽  
Elastic Behavior ◽  
Serial Manipulators ◽  
New Construction ◽  
Necessary And Sufficient ◽  
Serial Mechanism

This paper addresses the passive realization of any selected planar elastic behavior with a parallel or a serial manipulator. Sets of necessary and sufficient conditions for a mechanism to passively realize an elastic behavior are presented. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. The restrictions on the set of elastic behaviors that can be realized with a mechanism are described in terms of acceptable locations of realizable elastic behavior centers. Parallel–serial mechanism pairs that realize identical elastic behaviors (dual elastic mechanisms) are described. New construction-based synthesis procedures for planar elastic behaviors are developed. Using these procedures, one can select the geometry of each elastic component from a restricted space of kinematically allowable candidates. With each selection, the space is further restricted until the desired elastic behavior is achieved.

A stiffness analysis for a hybrid parallel-serial manipulator

Robotica ◽  
2004 ◽  
Vol 22 (5) ◽  
pp. 567-576 ◽  
Author(s):  
Giuseppe Carbone ◽  
Marco Ceccarelli
Keyword(s):  
Numerical Investigation ◽  
Performance Index ◽  
Stiffness Matrix ◽  
Mechanical Design ◽  
General Procedure ◽  
Design Parameters ◽  
Serial Manipulators ◽  
Stiffness Analysis ◽  
Hybrid Manipulator ◽  
Stiffness Characteristics

In this paper a hybrid parallel-serial manipulator, named as CaHyMan (Cassino Hybrid Manipulator), is analyzed in term of stiffness characteristics as a specific example of a general procedure for analyzing stiffness of parallel-serial manipulators. A formulation is presented to deduce the stiffness matrix as a function of the most important stiffness and design parameters of the mechanical design. A formulation is proposed for a stiffness performance index by using the obtained stiffness matrix. A numerical investigation has been carried out on the effects of design parameters and fundamental results are discussed in the paper.

Stiffness Analysis of 3-RPR Planar Parallel Mechanism to the Stiffness Control

2009 ◽  
Vol 16-19 ◽  
pp. 786-790 ◽  
Author(s):  
Shu Jun Li ◽  
Clément Gosselin
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Stiffness Analysis ◽  
Numerical Examples ◽  
Stiffness Control ◽  
Conservative Congruence Transformation ◽  
Stiffness Characteristics ◽  
External Forces ◽  
Congruence Transformation

The analytical stiffness equations of the 3-RPR planar parallel mechanism are derived in this paper based on the Conservative Congruence Transformation (CCT) stiffness matrix proposed in [1-3]. Stiffness maps of the 3-RPR mechanism are plotted in order to show the behaviour of the stiffness with and without external forces. The stiffness characteristics of the mechanism are analyzed and discussed in details. Numerical examples show that the stiffness in x and in y are well balanced, while the stiffness in tends to be lower.

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