Kinematic Synthesis and Planar Four-Bar Motion Generation

2013 ◽  
pp. 45-75
Author(s):  
Kevin Russell ◽  
Qiong Shen ◽  
Raj S. Sodhi
Keyword(s):  
Motion Generation ◽  
Kinematic Synthesis

An Improved Harmony Search Algorithm for a Planar Parallel Robot Synthesis

2018 ◽  
Vol 35 ◽  
pp. 185-197
Author(s):  
Badreddine Aboulissane ◽  
Dikra El Haiek ◽  
Larbi El Bakkali
Keyword(s):  
Search Algorithm ◽  
Harmony Search ◽  
Parallel Robot ◽  
Harmony Search Algorithm ◽  
Path Generation ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Design Variables ◽  
Joint Coordinates ◽  
Improved Harmony Search

The objective of kinematic synthesis is to determine the mechanism dimensions such as link lengths, positions or joint coordinates, in order to approximate its output parameters such as link positions, trajectory points, and displacement angles. Kinematic synthesis is classified into three categories: function generation, path generation, and motion generation. This paper is dedicated only to path generation. As the number of trajectory points increases, analytical methods are limited to obtain precisely mechanism solutions. In that case, numerical methods are more efficient to solve such problems. Our study proposes an improved heuristic algorithm applied to four-bar mechanism path-generation. The objective of this work is to find optimum dimensions of the mechanism and minimize the error between the generated trajectory and the desired one, taking into consideration constraints such as: Grashof condition, transmission angle, and design variables constraints. Finally, our results are compared with those found by other evolutionary algorithms in the literature.

On Adjustable Planar Four-Bar Motion Generation With Order, Branch and Circuit Defect Rectification

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Qiong Shen ◽  
Wen-Tzong Lee ◽  
Kevin Russell
Keyword(s):  
Nonlinear Equation ◽  
Objective Function ◽  
Inequality Constraints ◽  
Equation System ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Order Branch ◽  
Circuit Defects ◽  
Displacement Model ◽  
Defect Elimination

This work is an incremental extension of adjustable planar four-bar kinematic synthesis theory to consider not only synthesis, but also the elimination of the defects inherent in synthesis. A nonlinear equation system for moving pivot-adjustable planar four-bar motion generation that includes constraints for order defect, branch defect and circuit defect elimination is presented in this work. In the objective function of the equation system, the error between the prescribed and achieved precision positions is minimized. The equation system includes inequality constraints to eliminate order defects and branch defects. The equation system also includes a complete planar four-bar displacement model to eliminate circuit defects.

On a General Method of Spatial Kinematic Synthesis by Means of a Stretch-Rotation Tensor

1969 ◽  
Vol 91 (1) ◽  
pp. 115-121 ◽  
Author(s):  
G. N. Sandor ◽  
K. E. Bisshopp
Keyword(s):  
Mathematical Model ◽  
Kinematic Chain ◽  
Higher Order ◽  
Motion Generation ◽  
Rotation Tensor ◽  
Kinematic Synthesis ◽  
Rotation Operator ◽  
Key Concepts ◽  
The Mathematical Model ◽  
General Method

One of the key concepts in a general method of spatial kinematic synthesis is a stretch-rotation operator applied to members of a general spatial kinematic chain. The latter consists of one or more interconnected loops of successively ball-jointed bar-slideball members. Each member is represented by a vector free to stretch-rotate with the motion of the chain. In the mathematical model of the general chain, displacement is simulated by means of stretch-rotation tensors operating on each member vector. Appropriate mathematical constraints render the general chain and its mathematical model equivalent to a particular mechanism. With this approach and by taking derivatives, first, second, and higher-order loop equations can be developed which form the basis for a general method of spatial kinematic synthesis, applicable to path, function and motion generation (body guidance) with first, second, and higher-order as well as for combined “point-order” approximations.

Principles of a General Quaternion-Operator Method of Spatial Kinematic Synthesis

1968 ◽  
Vol 35 (1) ◽  
pp. 40-46 ◽  
Author(s):  
George N. Sandor
Keyword(s):  
Operator Method ◽  
Kinematic Chain ◽  
Point Theory ◽  
System Of Equations ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Special Cases ◽  
General Complex ◽  
Spatial Method ◽  
Space Mechanisms

The basic concepts of a general method of kinematic synthesis of space mechanisms are developed by means of vectors and quaternion operators applicable to path, function, and motion generation (body guidance) for finite and infinitesimal displacements (point, order, and combined point-order approximations). For writing the position equations, space mechanisms are represented by one or more loops of a general kinematic chain of ball-jointed bar-slideball members. Appropriate mathematical constraints on the relative freedom of these members render the general chain equivalent to the represented mechanism. The method leads to a system of equations of canonical simplicity, uniform for all tasks of finite spatial synthesis, often yielding closed-form linear solutions for small numbers of precision conditions. The same system of equations is then used to refine the solution for greater precision by numerical methods. Typical applications are indicated, some involving the use of a spatial finite circlepoint-center point theory, which includes classical planar Burmester theory as one of its special cases. An earlier general complex-number method of planar synthesis is shown to be a special case of the general spatial method introduced here.

Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
James P. Schmiedeler ◽  
Barrett C. Clark ◽  
Edward C. Kinzel ◽  
Gordon R. Pennock
Keyword(s):  
Undergraduate Students ◽  
Constraint Programming ◽  
Computer Aided Design ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Design Software ◽  
Aided Design

Geometric constraint programming (GCP) is an approach to synthesizing planar mechanisms in the sketching mode of commercial parametric computer-aided design software by imposing geometric constraints using the software's existing graphical user interface. GCP complements the accuracy of analytical methods with the intuition developed from graphical methods. Its applicability to motion generation, function generation, and path generation for finitely separated positions has been previously reported. By implementing existing, well-known theory, this technical brief demonstrates how GCP can be applied to kinematic synthesis for motion generation involving infinitesimally and multiply separated positions. For these cases, the graphically imposed geometric constraints alone will in general not provide a solution, so the designer must parametrically relate dimensions of entities within the graphical construction to achieve designs that automatically update when a defining parameter is altered. For three infinitesimally separated positions, the designer constructs an acceleration polygon to locate the inflection circle defined by the desired motion state. With the inflection circle in place, the designer can rapidly explore the design space using the graphical second Bobillier construction. For multiply separated position problems in which only two infinitesimally separated positions are considered, the designer constrains the instant center of the mechanism to be in the desired location. For example, four-bar linkages are designed using these techniques with three infinitesimally separated positions and two different combinations of four multiply separated positions. The ease of implementing the techniques may make synthesis for infinitesimally and multiply separated positions more accessible to mechanism designers and undergraduate students.

Synthesis With Mixed Motion and Path Generation Position Specifications

1983 ◽  
Vol 105 (4) ◽  
pp. 617-623 ◽  
Author(s):  
J. C. Chuang ◽  
K. J. Waldron
Keyword(s):  
Path Generation ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Position Type

Methods are developed for solving kinematic synthesis problems using precision position type methods for mixtures of motion generation and path generation type position specifications. All possible combinations of specification types for three or four design positions are considered.

Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming

2011 ◽  
Author(s):  
James P. Schmiedeler ◽  
Barrett C. Clark ◽  
Edward C. Kinzel ◽  
Gordon R. Pennock
Keyword(s):  
Constraint Programming ◽  
Computer Aided Design ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Design Software ◽  
Aided Design

Geometric Constraint Programming (GCP) is an approach to synthesizing planar mechanisms in the sketching mode of commercial parametric computer-aided design software by imposing geometric constraints using the software’s existing graphical user interface. GCP complements the accuracy of analytical methods with the intuition developed from graphical methods. Its applicability to motion generation, function generation, and path generation for finitely separated positions has been previously reported. This paper demonstrates how GCP can be applied to kinematic synthesis for motion generation involving infinitesimally and multiply separated positions. For these cases, the graphically imposed geometric constraints alone will in general not provide a solution, so the designer must parametrically relate dimensions of entities within the graphical construction to achieve designs that automatically update when a defining parameter is altered. For three infinitesimally separated positions, the designer constructs an acceleration polygon to locate the inflection circle defined by the desired motion state. With the inflection circle in place, the designer can rapidly explore the design space using the graphical second Bobillier construction. For multiply separated position problems in which only two infinitesimally separated positions are considered, the designer constrains the instant center of the mechanism to be in the desired location. Example four-bar linkages are designed using these techniques with three infinitesimally separated positions and two different combinations of four multiply separated positions.

Computational Creativity via Assisted Variational Synthesis of Mechanisms Using Deep Generative Models

2019 ◽  
Author(s):  
Shrinath Deshpande ◽  
Anurag Purwar
Keyword(s):  
Probability Distribution ◽  
Computational Methods ◽  
Network Architecture ◽  
Generative Models ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
User Input ◽  
Synthesis Of Mechanisms ◽  
End To End ◽  
Salient Features

Abstract Computational methods for kinematic synthesis of mechanisms for motion generation problems require input in the form of precision positions. Given the highly non-linear nature of the problem, solutions to these methods are overly sensitive to the input — a small perturbation to even a single position of a given motion can change the topology and dimensions of the synthesized mechanisms drastically. Thus, the synthesis becomes a blind iterative process of maneuvering precision positions in the hope of finding good solutions. In this paper, we present a deep-learning based framework which manages the uncertain user input and provides the user with a higher level control of the design process. The framework also imputes the input with missing information required by the computational algorithms. The approach starts by learning the probability distribution of possible linkage parameters with a deep generative modeling technique, called Variational Auto Encoder (VAE). This facilitates capturing salient features of the user input and relating them with possible linkage parameters. Then, input samples resembling the inferred salient features are generated and fed to the computational methods of kinematic synthesis. The framework post-processes the solutions and presents the concepts to the user along with a handle to visualize the variants of each concept. We define this approach as Variational Synthesis of Mechanisms. In addition, we also present an alternate End-to-End deep neural network architecture for Variational Synthesis of linkages. This End-to-End architecture is a Conditional-VAE (C-VAE), which approximates the conditional distribution of linkage parameters with respect to coupler trajectory distribution. The outcome is a probability distribution of kinematic linkages for an unknown coupler path or motion. This framework functions as a bridge between the current state of the art theoretical and computational kinematic methods and machine learning to enable designers to create practical mechanism design solutions.

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