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.

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 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.

Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Elastic Behavior ◽  
Compliance Matrix ◽  
Revolute Joint ◽  
Redundant Mechanism ◽  
Compliance Matrices ◽  
Necessary And Sufficient ◽  
Serial Mechanism

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having three joints, each either revolute or prismatic and each with selectable compliance. The geometry of the mechanism and the location of the compliance frame relative to the mechanism base are each arbitrary but specified. Necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. We show that, for an appropriately constructed serial mechanism having at least one revolute joint, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. For each type of three-joint combination, requirements on the redundant mechanism geometry are identified for the realization of every point planar elastic behavior at a given location, just by changing the mechanism configuration and the joint compliances.

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.

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.

scholarly journals Vibration analysis of nonlinear and linear elastic systems

2021 ◽  
Vol 47 (4) ◽  
pp. 141-150
Author(s):  
A. S. Lichkovakha ◽  
B. A. Shemshura ◽  
S. A. Kuznetsov
Keyword(s):  
Elastic System ◽  
Elastic Characteristic ◽  
Progressive Change ◽  
Vehicle Suspensions ◽  
Linear Elastic ◽  
Eccentric Compression ◽  
Elastic Systems ◽  
Elastic Mechanism ◽  
High Flexibility ◽  
Elastic Elements

Objective. In this study, the task is to establish the theoretical prerequisites for the operability of a regressive-progressive elastic mechanism by comparing the amplitude-frequency characteristics and phase trajectories with a linear elastic system of comparable stiffness in a static equilibrium position.Methods. The article presents a comparative dynamic analysis of vibrations of elastic systems with linear rigidity and regressive-progressive characteristics obtained as a result of the use of elastic elements in the form of high flexibility rods with longitudinal eccentric compression. Such elastic elements in various design variants have been tested and patented as damping elements for use in the construction of vibration dampers for construction structures and vehicle suspensions, and have experimentally shown their effectiveness in damping vibrations.Results. The regressiveprogressive elastic characteristic obtained by the elliptic parameters method and using the ANSIS calculation complex is used in the dynamics equations in an approximated form, which expands the capabilities of the method. It is shown that increasing the energy intensity of a curvilinear system reduces the vibration amplitude.Conclusion. The regressive-progressive change of the stiffness of curvilinear elastic systems can be achieved using an elastic element with eccentric longitudinal compression; the regression plot of elastic properties is achieved due to eccentric compression; the progressive plot – through the use of a guide or other design solutions. The implementation of this characteristic allows using such elastic mechanisms in systems where the accumulation of potential energy occurs with a smaller compression stroke for the same perturbation than for linear systems.

scholarly journals Compliant behaviour of redundant robot arm - experiments with null-space

2015 ◽  
Vol 12 (1) ◽  
pp. 81-98
Author(s):  
Petar Petrovic ◽  
Nikola Lukic ◽  
Ivan Danilov
Keyword(s):  
Stiffness Matrix ◽  
Jacobian Matrix ◽  
Null Space ◽  
Joint Space ◽  
Robot Arm ◽  
Kinematic Redundancy ◽  
Redundant Robot ◽  
Redundant Robots ◽  
Compliant Behavior ◽  
Congruent Transformation

This paper presents theoretical and experimental aspects of Jacobian nullspace use in kinematically redundant robots for achieving kinetostatically consistent control of their compliant behavior. When the stiffness of the robot endpoint is dominantly influenced by the compliance of the robot joints, generalized stiffness matrix can be mapped into joint space using appropriate congruent transformation. Actuation stiffness matrix achieved by this transformation is generally nondiagonal. Off-diagonal elements of the actuation matrix can be generated by redundant actuation only (polyarticular actuators), but such kind of actuation is very difficult to realize practically in technical systems. The approach of solving this problem which is proposed in this paper is based on the use of kinematic redundancy and nullspace of the Jacobian matrix. Evaluation of the developed analytical model was done numerically by a minimal redundant robot with one redundant d.o.f. and experimentally by a 7 d.o.f. Yaskawa SIA 10F robot arm.

scholarly journals Standardized Compliance Matrices for General Anisotropic Materials and a Simple Measure of Anisotropy Degree Based on Shear-Extension Coupling Coefficient

2016 ◽  
Vol 08 (06) ◽  
pp. 1650076 ◽  
Author(s):  
Jia-Min Zhao ◽  
Xiao-Xiong Song ◽  
Bin Liu
Keyword(s):  
Elastic Material ◽  
Coupling Coefficient ◽  
Two Dimensional ◽  
Stiffness Ratio ◽  
Compliance Matrix ◽  
Material Constants ◽  
Isotropic Elasticity ◽  
Compliance Matrices ◽  
Anisotropy Degree ◽  
Correct Measure

The compliance matrix for a general anisotropic material is usually expressed in an arbitrarily chosen coordinate system, which brings some confusion or inconvenience in identifying independent elastic material constants and comparing elastic properties between different materials. In this paper, a unique stiffest orientation-based standardized compliance matrix is established, and 18 independent elastic material constants are clearly shown. During the searching process for the stiffest orientation, it is interesting to find from our theoretical analysis and an example that a material with isotropic tensile stiffness does not definitely possess isotropic elasticity. Therefore, the ratio between the maximum and minimum tensile stiffnesses, although widely used, is not a correct measure of anisotropy degree. Alternatively, a simple and correct measure of anisotropy degree based on the maximum shear-extension coupling coefficient in all orientations is proposed. However, for a two-dimensional constitutive relation, both the stiffness ratio and the shear-extension coupling coefficient can be adopted as proper measures of anisotropy degree.

A Classification of Robot Compliance

1993 ◽  
Vol 115 (3) ◽  
pp. 581-584 ◽  
Author(s):  
T. Patterson ◽  
H. Lipkin
Keyword(s):  
Eigenvalue Problem ◽  
Opposite Sign ◽  
Sufficient Conditions ◽  
New Classification ◽  
Matrix Eigenvalue Problem ◽  
Compliance Matrix ◽  
Matrix Eigenvalue ◽  
Compliance Matrices ◽  
Necessary And Sufficient

The concept of compliant axes is developed from the compliance matrix eigenvalue problem. It is shown that the necessary and sufficient conditions for the existence of a compliant axis are two collinear eigenscrews with eigenvalues of equal magnitude and opposite sign. This leads to a new classification of compliance matrices based on the number of compliant axes. Selected matrices from the literature illustrate both the compliant axis concept and the classification.

Sign in / Sign up

Export Citation Format

Share Document