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

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.

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.

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.

4MDS: A Geometric Constraint Based Motion Design Software for Synthesis and Simulation of Planar Four-Bar Linkages

2014 ◽  
Author(s):  
Anurag Purwar ◽  
Abhijit Toravi ◽  
Q. J. Ge
Keyword(s):  
Real Time ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Design System ◽  
Dimensional Synthesis ◽  
Complete Control ◽  
Dimensional Changes ◽  
Design Software ◽  
Four Bar Linkage ◽  
Motion Design

This paper presents our recent work on designing and developing a geometric constraint based motion design software system for planar four-bar linkages. Given a motion task, the software computes possible four-bar linkage topologies as well as its dimensions. This capability to analyze the given task and find the best type of the linkage and the dimensions simultaneously sets it apart from any other linkage design software. The Four-Bar Motion Design System (4MDS) makes the synthesis and simulation capabilities available to mechanism designers in an intuitive graphical user interface (GUI) environment. Instead of taking a black box approach to mechanism design, wherein the user simply enters the motion requirements and the software outputs parameters of mechanisms, this software facilitates a dialog with the designer by providing various paths to simulation and synthesis in a design session. The designer has complete control over the specification of motion task, interactive tweaking of the motion, choice of linkage topology computed, dimensional changes, and their apparent effect on motion, all done in real time. This interactivity enhances designers kinematic experience. The underlying theoretical foundation of this paper is based on our earlier work on a task-driven approach to unified type and dimensional synthesis of planar four-bar linkage mechanisms. Instead of treating a planar four-bar mechanism as a set of connected rigid links and joints, we treat them as line or circle constraint generators. With that view, the synthesis problem is reduced to extracting geometric constraints hidden in a given motion task and the simulation is reduced to assembling constraints realizable by mechanical dyads. The algorithm employed is simple and efficient and permits real-time computation, and thus precludes using a limiting database-oriented approach. This tool should make innovation of mechanical motion generating devices accessible to novice and experienced designers alike.

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Locations

2013 ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyads rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed locations to yield designs that exactly reach the prescribed pick & place locations while approximating an arbitrary number of guiding locations. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain; also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. An example that demonstrates the synthesis technique is included.

Formulation of Dimensional Synthesis Procedures for Complex Planar Mechanisms

1987 ◽  
Vol 109 (3) ◽  
pp. 322-328 ◽  
Author(s):  
D. G. Olson ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Dimensional Synthesis ◽  
Planar Mechanisms

This paper presents an overview of a component-based approach for the dimensional synthesis of planar mechanisms. The components on which the approach is based are called triads, dyads, and free vectors, and can be synthesized for up to five precision positions. A straight-forward method for formulating dimensional synthesis procedures for arbitrarily complex planar mechanisms is developed, and demonstrated by an example using inspection. The method utilizes the concept of the directed graph, which is an enhancement of the usual graph theory representation of mechanisms. Because the method is based on graph theory, it is believed that it could be easily automated.

A Computational Geometric Approach for Motion Generation of Spatial Linkages With Sphere and Plane Constraints

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Xiangyun Li ◽  
Q. J. Ge ◽  
Feng Gao
Keyword(s):  
Geometric Approach ◽  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Geometric Framework ◽  
Kinematic Chains ◽  
Kinematic Mapping ◽  
Spherical Linkages ◽  
Spatial Displacements ◽  
The Given

This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.

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