Kinematic Acquisition of Geometric Constraints for Task-Oriented Design of Planar Mechanisms

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
Jun Wu ◽  
Q. J. Ge ◽  
Hai-Jun Su ◽  
Feng Gao
Keyword(s):  
Mechanism Design ◽  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Planar Mechanisms ◽  
Analysis Problem ◽  
Geometric Means ◽  
New Type ◽  
Mechanical Linkage ◽  
Task Oriented

A motion task can be given in various ways. It may be defined parametrically or discretely in terms of an ordered sequence of displacements or in geometric means. This paper studies a new type of motion analysis problem in planar kinematics that seeks to acquire geometric constraints associated with a planar motion task which is given either parametrically or discretely. The resulting geometric constraints can be used directly for type as well as dimensional synthesis of a physical device such as mechanical linkage that generates the constrained motion task. Examples are provided toward the end of the paper to illustrate how geometric constraints acquired can be used for task-oriented mechanism design.

Kinematic Acquisition of Geometric Constraints for Task Centered Mechanism Design

2010 ◽  
Author(s):  
Jun Wu ◽  
Q. J. Ge ◽  
Hai-Jun Su ◽  
Feng Gao
Keyword(s):  
Mechanism Design ◽  
Motion Analysis ◽  
Geometric Constraints ◽  
Planar Motion ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Analysis Problem ◽  
Geometric Means ◽  
New Type ◽  
Mechanical Linkage

A motion task can be given in various ways. It may be defined parametrically or discretely in terms of an ordered sequence of displacements or in geometric means. This paper studies a new type of motion analysis problem in planar kinematics that seeks to acquire geometric constraints associated with a planar motion task which is given either parametrically or discretely. The resulting geometric constraints can be used directly for type as well as dimensional synthesis of a physical device such as mechanical linkage that generates the constrained motion task. Methods for kinematic acquisition of geometric constraints bridge the gap between type and dimensional synthesis and provide the foundation for task centered mechanism design.

Optimum dimensional synthesis of planar mechanisms with geometric constraints

Meccanica ◽  
2020 ◽  
Vol 55 (11) ◽  
pp. 2135-2158
Author(s):  
V. García-Marina ◽  
I. Fernández de Bustos ◽  
G. Urkullu ◽  
R. Ansola
Keyword(s):  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Planar Mechanisms

scholarly journals A Line Geometric Approach to Kinematic Acquisition of Geometric Constraints of Planar Motion

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Jun Wu ◽  
Xiangyun Li ◽  
Q. J. Ge ◽  
Feng Gao ◽  
Xueyin Liu
Keyword(s):  
Geometric Approach ◽  
Geometric Constraints ◽  
Planar Motion ◽  
Constrained Motion ◽  
Discrete Form ◽  
Mechanical Linkage

This paper examines the problem of geometric constraints acquisition of planar motion through a line-geometric approach. In previous work, we have investigated the problem of identifying point-geometric constraints associated with a motion task which is given in a parametric or discrete form. In this paper, we seek to extend the point-centric approach to the line-centric approach. The extracted geometric constraints can be used directly for determining the type and dimensions of a physical device such as mechanical linkage that generates this constrained motion task.

Paper 6: Electronic Instrumentation Techniques in the Development of Pistons and Rings

1965 ◽  
Vol 180 (7) ◽  
pp. 54-69 ◽  
Author(s):  
M. H. Westbrook ◽  
R. Munro
Keyword(s):  
Internal Combustion Engine ◽  
Combustion Engine ◽  
Extreme Conditions ◽  
Dynamic Measurements ◽  
Inductive Transducer ◽  
New Type ◽  
Electronic Instrumentation ◽  
Mechanical Linkage ◽  
Contact Displacement ◽  
Engine Development

Both general and particular aspects of the application of electronic instrumentation in internal combustion engine development are discussed, and the work which has been carried out in the authors' establishment on instrumentation for dynamic measurements on the piston assembly is described, in particular, measurements of engine noise and vibration, and of displacement and temperature during operation, using telemetry systems, and making use of both radio and mechanical linkage techniques. The development of a new type of sub-miniature inductive transducer for non-contact displacement measurement under the extreme conditions inside a working piston is described, and the reasons making its development necessary discussed. Results obtained from a working engine showing piston movements as measured by several inductive transducers and transmitted over the linkage system are shown and compared to block vibration recordings made simultaneously; an initial interpretation of the very recent results is made. Finally, electronic methods developed for the static measurement of piston and ring properties are described and the results obtained discussed.

On nonassembly in the optimal dimensional synthesis of planar mechanisms

2001 ◽  
Vol 21 (5) ◽  
pp. 345-354 ◽  
Author(s):  
R.J. Minnaar ◽  
D.A. Tortorelli ◽  
J.A. Snyman
Keyword(s):  
Dimensional Synthesis ◽  
Planar Mechanisms

Designing Planar Mechanisms Using a Bi-Invariant Metric in the Image Space of SO (3)

1994 ◽  
Author(s):  
Pierre Larochelle ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Numerical Results ◽  
Image Space ◽  
Dimensional Synthesis ◽  
Invariant Metric ◽  
Planar Mechanisms ◽  
Position And Orientation ◽  
Position Synthesis

Abstract In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of SO(3). The optimal linkage is obtained by minimizing this distance over all of the n goal positions. The paper proceeds as follows. First, we approximate planar rigid body displacements with spherical displacements and show that the error induced by such an approximation is of order 1/R2, where R is the radius of the approximating sphere. Second, we use a bi-invariant metric in the image space of spherical displacements to synthesize an optimal spherical 4R mechanism. Finally, we identify the planar 4R mechanism associated with the optimal spherical solution. The result is a planar 4R mechanism that has been optimized for n position rigid body guidance using an approximate bi-invariant metric with an error dependent only upon the radius of the approximating sphere. Numerical results for ten position synthesis of a planar 4R mechanism are presented.

Constraint-Based Virtual Environment for Supporting Assembly and Maintainability Tasks

1999 ◽  
Author(s):  
Terrence Fernando ◽  
Prasad Wimalaratne ◽  
Kevin Tan
Keyword(s):  
Virtual Environment ◽  
Current System ◽  
Research Programme ◽  
Geometric Constraints ◽  
Simulation Environment ◽  
Constrained Motion ◽  
Constraint Management ◽  
Interactive Product ◽  
Assembly Operations ◽  
The University

Abstract This paper presents the design and implementation of a constraint-based virtual environment for supporting interactive assembly and maintenance tasks. The system architecture of the constraint-based virtual environment is based on the integration of components such as OpenGL Optimizer, Parasolid geometric kernel, a Constraint Engine and an Assembly Relationship Graph (ARG). The approach presented in this paper is based on pure geometric constraints. Techniques such as automatic constraint recognition, constraint satisfaction, constraint management and constrained motion are employed to support interactive assembly operations and realistic behaviour of assembly parts. The current system has been evaluated using two industrial case studies. This work is being carried out as a part of a research programme referred to as IPSEAM (Interactive Product Simulation Environment for Assessing Assembly and Maintainability), at the University of Salford.

Dimensional Synthesis and Constrained Motion Interpolation for Planar and Spherical 6R Closed Chains

2008 ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Qiaode Jeffrey Ge
Keyword(s):  
Rational Curve ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Initial Attempt ◽  
Kinematic Constraints ◽  
Constraint Manifold ◽  
Cartesian Space ◽  
Closed Chain ◽  
Kinematic Mapping ◽  
The Given

In the recent past, we have studied the problem of synthesizing rational interpolating motions under the kinematic constraints of any given planar and spherical 6R closed chain. This work presents some preliminary results on our initial attempt to solve the inverse problem, that is to determine the link lengths of planar and spherical 6R closed chains that follow a given smooth piecewise rational motion under the kinematic constraints. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of planar and spherical closed chains in the Cartesian space. By using kinematic mapping and a quaternions based approach to represent displacements of the coupler of the closed chains, the given smooth piecewise rational motion is mapped to a smooth piecewise rational curve in the space of quaternions. In this space, the aforementioned workspace constraints on the coupler of the closed chains define a constraint manifold representing all the positions available to the coupler. Thus the problem of dimensional synthesis may be solved by modifying the size, shape and location of the constraint manifolds such that the mapped rational curve is contained entirely inside the constraint manifolds. In this paper, two simple examples with preselected moving pivots on the coupler as well as fixed pivots are presented to illustrate the feasibility of this approach.

A Unified Kinetostatic Analysis Framework for Planar Compliant and Rigid Body Mechanisms

2014 ◽  
Author(s):  
Omer Anil Turkkan ◽  
Hai-Jun Su
Keyword(s):  
Mechanism Design ◽  
Static Analysis ◽  
Compliant Mechanisms ◽  
Daily Life ◽  
Analysis Framework ◽  
Planar Mechanisms ◽  
Simulation Tools ◽  
Compliant Joints ◽  
Adams Software ◽  
Simulation Results

Although many dynamic solvers are available for planar mechanisms, there is no readily accessible static solver that can be used in analysis of planar mechanisms with elastic components which achieve motion utilizing deformation of elastic members. New simulation tools are necessary to better understand the compliant mechanisms and to increase their usage in daily life. This framework was developed to fill this gap in planar mechanism design and analysis. The framework was written in MATLAB and is capable of kinematic and static analysis of planar mechanisms with compliant joints or links. Detailed information on implementation of the code is presented and is followed by the capabilities of the framework. Finally, the simulation results were compared with the Adams software to test the validity of the framework.

A New Approach for Exact/Approximate Point Synthesis of Planar Mechanisms

2005 ◽  
Author(s):  
Ahmad Smaili ◽  
Nadim Diab
Keyword(s):  
Synthesis Method ◽  
Dimensional Synthesis ◽  
Gradient Search ◽  
Planar Mechanisms ◽  
Simple Method ◽  
New Approach ◽  
Optimum Synthesis ◽  
Approximate Synthesis ◽  
Optimum Solution ◽  
Synthesis Approach

The aim of this article is to provide a simple method to solve the mixed exact-approximate dimensional synthesis problem of planar mechanism. The method results in a mechanism that can traverse a closed path with the choice of any number of exact points while the rest are approximate points. The algorithm is based on optimum synthesis rather than on precision position methods. Ant-gradient search is applied on an objective function based on log10 of the error between the desired positions and those generated by the optimum solution. The log10 function discriminates on the side of generating miniscule errors (on the order of 10−14) at the exact points while allowing for higher errors at the approximate positions. The algorithm is tested by way of five examples. One of these examples was used to test exact/approximate synthesis method based on precision point synthesis approach.

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