Constraint Representation Based on Lie Algebra in a Kinematic Model and Synthesis of Mechanisms

2000 ◽  
Author(s):  
Hitoshi Tokunaga ◽  
Satoshi Imamura
Keyword(s):  
Lie Algebra ◽  
Conceptual Design ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Analysis Procedure ◽  
New Method ◽  
Structural Synthesis ◽  
Synthesis Of Mechanisms ◽  
Mechanical Products ◽  
Synthesis Procedure

Abstract This paper deals with a new method for structural synthesis of mechanisms in a conceptual design as follows: first, using the Lie algebra-based representation of constraint on degrees of freedom, we propose an analysis procedure of the degrees of freedom between components in mechanisms of mechanical products. Second, this analysis procedure makes it possible to propose a structural synthesis procedure. Third, in order to select one of the mechanisms generated by the synthesis procedure, we introduce the concept of manipulatability as a criterion for the evaluation. Finally, to evaluate the usefulness of the proposed method, it is applied to an example of structural synthesis.

Reconfiguration of Kinematic Structure for Changing Motion Requirement Based on Reusability Evaluation in Lie Algebra

2002 ◽  
Author(s):  
Hitoshi Tokunaga ◽  
Norio Matsuki ◽  
Satoshi Imamura ◽  
Fumiki Tanaka ◽  
Takeshi Kishinami
Keyword(s):  
Lie Algebra ◽  
Degrees Of Freedom ◽  
Manufacturing System ◽  
New Method ◽  
Kinematic Structure ◽  
Kinematic Design ◽  
Structure And Motion ◽  
Inclusion Relations ◽  
Requirement Change

This paper presents a new method for adapting the existing manufacturing system for a requirement change, such as the change of a required motion task, by modifying its kinematic structure from the viewpoint of the degrees of freedom of the end effecter of the mechanism. In a previous report, the authors formulated the kinematic structure and motion task using Lie algebra. In this report, using these representations and their inclusion relations, the authors propose a method for evaluating the reusability of a kinematic structure for a newly specified motion task, and then propose a method for reconfiguring the mechanism in Lie algebra according to the result of the reusability evaluation. Finally, in order to evaluate the usefulness of the proposed method, it is applied to a kinematic design example of a mechanism.

scholarly journals Synthesis of Mechanisms by Methods of Nonlinear Dynamics

10.14311/1684 ◽  
2012 ◽  
Vol 52 (6) ◽  
Author(s):  
Michael Valášek ◽  
Zbynek Šika
Keyword(s):  
Dynamical System ◽  
Dissipative System ◽  
New Method ◽  
Time Varying ◽  
Objective Functions ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
Nonlinear Dynamical ◽  
Synthesis Of Mechanisms ◽  
Synthesis Procedure

This paper deals with a new method for parametric kinematic synthesis of mechanisms. The traditional synthesis procedure based on collocation, correction and optimization suffers from the local minima of objective functions, usually due to the local unassembled configurations which must be overcome. The new method uses the time varying values of the synthesized dimensions of the mechanism as if the mechanism had elastic links and guidances. The time varying dimensions form the basis for an accompanying nonlinear dynamical dissipative system and the synthesis is transformed into the time evolution of this accompanying dynamical system. Its dissipativity guarantees the termination of thesynthesis. The synthesis always covers the parametric kinematic synthesis, but it can be advantageously extended into the optimization of any further criteria. The main advantage of the method described here for dealing with mechanism synthesis is that it overcomes the unassembled configurations of the synthesized mechanisms and enables any further synthesis criteria to be introduced, and terminates due to dissipation of the accompanied dynamical system.

Kinematic Synthesis of Deployable-Foldable Truss Structures Using Graph Theory, Part 1: Graph Generation

1995 ◽  
Vol 117 (1) ◽  
pp. 112-116 ◽  
Author(s):  
D. B. Warnaar ◽  
M. Chew
Keyword(s):  
Graph Theory ◽  
Conceptual Design ◽  
Design Process ◽  
Degrees Of Freedom ◽  
Truss Structure ◽  
Truss Structures ◽  
Structural Synthesis ◽  
Deployable Structures ◽  
Kinematic Synthesis ◽  
Graph Generation

Kinematic structural synthesis has been relatively successful when applied to the conceptual design of mechanisms. The approach presented in this paper, however, views the design process from an initial standpoint of a truss structure. First, graphs are generated that represent truss structures with a given number of nodes and links. Each graph is then modified by designating certain edges in the graph to represent links in the structure that incorporate additional degrees of freedom. In so doing, the graph of a structure is transformed into one representing a mechanism. A procedure is presented that enables the exhaustive generation of these graphs for deployable structures of any given number of nodes and links. From these graphs, it is then possible to obtain enumerable novel deployable truss structures as well as those that have been reported in the literature.

Automatic Structural Synthesis of Planar Multiple Joint Kinematic Chains

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Huafeng Ding ◽  
Weijuan Yang ◽  
Peng Huang ◽  
Andrés Kecskeméthy
Keyword(s):  
Degrees Of Freedom ◽  
Characteristic Number ◽  
Structural Synthesis ◽  
Topological Graph ◽  
Topological Graphs ◽  
Systematic Method ◽  
Joint Kinematic ◽  
Kinematic Chains ◽  
Mechanical Products ◽  
First Time

It is of great importance in the conceptual creative design of mechanical systems to synthesize as many feasible kinematic structures of mechanisms as possible. However, the methods for the structural synthesis of multiple joint kinematic chains are seldom addressed in literature even though they are widely used in various mechanical products. This paper proposes an automatic method to synthesize planar multiple joint kinematic chains. First, the bicolor topological graph and the bicolor contracted graph are introduced to represent the topological structures of multiple joint kinematic chains. Then, the characteristic number string of bicolor topological graphs is proposed and used to efficiently detect isomorphism in the synthesis progress. Finally, a systematic method for the synthesis of kinematic chains with one multiple joint is proposed, and the whole families of multiple joint kinematic chains with up to 16 links and all possible degrees of freedom are synthesized for the first time.

scholarly journals Solving the double-banana rigidity problem: a loop-based approach

2016 ◽  
Vol 7 (1) ◽  
pp. 107-117 ◽  
Author(s):  
Florian Simroth ◽  
Huafeng Ding ◽  
Andrés Kecskeméthy
Keyword(s):  
Degrees Of Freedom ◽  
The Body ◽  
Structural Synthesis ◽  
New Approach ◽  
Revolute Joints ◽  
Counter Example ◽  
Synthesis Of Mechanisms ◽  
Joint Decomposition ◽  
Special Case ◽  
Rigidity Condition

Abstract. Rigidity detection is an important tool for structural synthesis of mechanisms, as it helps to unveil possible sources of inconsistency in Grübler's count of degrees of freedom (DOFs) and thus to generate consistent kinematical models of complex mechanisms. One case that has puzzled researchers over many decades is the famous "double-banana" problem, which is a representative counter-example of Laman's rigidity condition formula for which existing standard DOF counting formulas fail. The reason for this is the body-by-body and joint-by-joint decomposition of the interconnection structure in classical algorithms, which does not unveil structural isotropy groups for example when whole substructures rotate about an "implied hinge" according to Streinu. In this paper, a completely new approach for rigidity detection for cases as the "double-banana" counterexample in which bars are connected by spherical joints is presented. The novelty of the approach consists in regarding the structure not as a set of joint-connected bodies but as a set of interconnected loops. By tracking isolated DOFs such as those arising between pairs of spherical joints, rigidity/mobility subspaces can be easily identified and thus the "double-banana" paradox can be resolved. Although the paper focuses on the solution of the double-banana mechanism as a special case of paradox bar-and-joint frameworks, the procedure is valid for general body-and-joint mechanisms, as is shown by the decomposition of spherical joints into a series of revolute joints and their rigid-link interconnections.

STRUCTURAL SYNTHESIS OF MECHANISMS KINEMATICS–TYPE DELTA

2020 ◽  
Vol 339 (1) ◽  
pp. 26-33
Author(s):  
N.A. SAPRYKINA ◽  
◽  
A.V. PROSKOKOV ◽  
A.A. SAPRYKIN ◽  
◽  
...  
Keyword(s):  
Structural Synthesis ◽  
Synthesis Of Mechanisms

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

Cooperation and Null-Space Control of Networked Omni-Directional Mobile Manipulators

2020 ◽  
Author(s):  
Michael John Chua ◽  
Yen-Chen Liu
Keyword(s):  
Degrees Of Freedom ◽  
Null Space ◽  
Kinematic Model ◽  
Mobile Manipulator ◽  
Main Task ◽  
Mobile Manipulators ◽  
Robot Arm ◽  
Task Space ◽  
End Effector ◽  
Mobile Base

Abstract This paper presents cooperation and null-space control for networked mobile manipulators with high degrees of freedom (DOFs). First, kinematic model and Euler-Lagrange dynamic model of the mobile manipulator, which has an articulated robot arm mounted on a mobile base with omni-directional wheels, have been presented. Then, the dynamic decoupling has been considered so that the task-space and the null-space can be controlled separately to accomplish different missions. The motion of the end-effector is controlled in the task-space, and the force control is implemented to make sure the cooperation of the mobile manipulators, as well as the transportation tasks. Also, the null-space control for the manipulator has been combined into the decoupling control. For the mobile base, it is controlled in the null-space to track the velocity of the end-effector, avoid other agents, avoid the obstacles, and move in a defined range based on the length of the manipulator without affecting the main task. Numerical simulations have been addressed to demonstrate the proposed methods.

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