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

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.

Spatial Compliances Achieved With Serial Elastic Mechanisms

10.1115/imece2000-2392 ◽

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 ◽

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.

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

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1434273 ◽

2000 ◽

Vol 124 (1) ◽

pp. 76-84 ◽

Cited By ~ 21

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 ◽

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.

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

10.1115/1.4004894 ◽

2011 ◽

Vol 3 (4) ◽

Cited By ~ 5

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

Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2010-28329 ◽

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.

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

10.1115/1.4035189 ◽

2016 ◽

Vol 9 (1) ◽

Cited By ~ 5

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 ◽

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.

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

10.1115/1.4053284 ◽

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 ◽

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.

Design and Analysis of a Rigid-Flexible Parallel Mechanism for a Neck Brace

Mathematical Problems in Engineering ◽

10.1155/2019/9014653 ◽

2019 ◽

Vol 2019 ◽

pp. 1-20

Author(s):

Jingfang Liu ◽

Yanxia Cheng ◽

Shuang Zhang ◽

Zhenxin Lu ◽

Guohua Gao

Keyword(s):

Parallel Mechanism ◽

Rotational Degree ◽

Compliance Matrix ◽

Body Model ◽

Rotation Measurement ◽

Rigid Body Model ◽

Compliant Joint ◽

Spherical Parallel Mechanism ◽

Rotation Function ◽

Flexion And Extension

A rigid-flexible parallel mechanism called 3-RXS mechanism as a neck brace for patients with head drooping symptoms (HDS) is presented. The 3-RXS neck brace has a simple and light structure coupled with good rotation performance, so it can be used to assist the neck to achieve flexion and extension, lateral bend, and axial torsion. Firstly, to prove that the X-shaped compliant joint has a rotational degree of freedom (DoF) and can be used in the 3-RRS spherical parallel mechanism (3-RRS SPM), the six-dimensional compliance matrix, axis drift, and DoF of the X-shaped compliant joint have been systematically calculated. Secondly, the 3-RXS mechanism and its pseudo-rigid-body model (PRBM) are obtained by replacing the revolute pair with the X-shaped compliant joint in the 3-RRS SPM. The rotation workspace of the 3-RXS mechanism is also performed. Finally, to verify the rotation function and effect of 3-RXS mechanism for neck-assisted rehabilitation, the kinematics simulations of the 3-RXS and 3-RRS mechanisms are carried out and compared with the theoretical result, and a primary experiment for rotation measurement of 3-RXS mechanism prototype is carried out. All results prove the feasibility of the 3-RXS mechanism for a neck brace.

A Quasi-Static Model for Planar Compliant Parallel Mechanisms

10.1115/1.3046144 ◽

2009 ◽

Vol 1 (2) ◽

Cited By ~ 13

Author(s):

Cyril Quennouelle ◽

Clément Gosselin

Keyword(s):

Parallel Mechanism ◽

Applied Load ◽

Jacobian Matrix ◽

Static Model ◽

Parallel Mechanisms ◽

Compliance Matrix ◽

End Effector ◽

Kinematic Constraints ◽

Compliant Parallel Mechanism ◽

External Loads

In this paper, the mobility, the kinematic constraints, the pose of the end-effector, and the static constraints that lead to the kinematostatic model of a compliant parallel mechanism are introduced. A formulation is then provided for its instantaneous variation—the quasi-static model. This new model allows the calculation of the variation in the pose as a linear function of the motion of the actuators and the variation in the external loads through two new matrices: the compliant Jacobian matrix and the Cartesian compliance matrix that give a simple and meaningful formulation of the model of the mechanism. Finally, a simple application to a planar four-bar mechanism is presented to illustrate the use of this model and the new possibilities that it opens, notably the study of the kinematics for any range of applied load.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.16-19.786 ◽

2009 ◽

Vol 16-19 ◽

pp. 786-790 ◽

Cited By ~ 1

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.

Six-Dimensional Compliance Analysis and Validation of Orthoplanar Springs

Journal of Mechanical Design ◽

10.1115/1.4032580 ◽

2016 ◽

Vol 138 (4) ◽

Cited By ~ 8

Author(s):

Chen Qiu ◽

Peng Qi ◽

Hongbin Liu ◽

Kaspar Althoefer ◽

Jian S. Dai

Keyword(s):

Finite Element ◽

Parallel Mechanism ◽

Fem Simulation ◽

Analytical Models ◽

Compliance Matrix ◽

Out Of Plane ◽

Continuum Manipulator ◽

First Time ◽

Good Agreement

This paper for the first time investigates the six-dimensional compliance characteristics of orthoplanar springs using a compliance-matrix based approach, and validates them with both finite element (FEM) simulation and experiments. The compliance matrix is developed by treating an orthoplanar spring as a parallel mechanism and is revealed to be diagonal. As a consequence, corresponding diagonal compliance elements are evaluated and analyzed in forms of their ratios, revealing that an orthoplanar spring not only has a large linear out-of-plane compliance but also has a large rotational bending compliance. Both FEM simulation and experiments were then conducted to validate the developed compliance matrix. In the FEM simulation, a total number of 30 types of planar-spring models were examined, followed by experiments that examined the typical side-type and radial-type planar springs, presenting a good agreement between the experiment results and analytical models. Further a planar-spring based continuum manipulator was developed to demonstrate the large-bending capability of its planar-spring modules.