Selective Precision Synthesis—A General Method of Optimization for Planar Mechanisms

1975 ◽  
Vol 97 (2) ◽  
pp. 689-701 ◽  
Author(s):  
S. N. Kramer ◽  
G. N. Sandor
Keyword(s):  
Nonlinear Programming ◽  
Computer Aided Design ◽  
Planar Mechanisms ◽  
Small Perturbations ◽  
Function Generation ◽  
Computer Aided ◽  
Stable Solutions ◽  
Precision Synthesis ◽  
Aided Design ◽  
General Method

A general method of optimal design of planar mechanisms is presented here called Selective Precision Synthesis (SPS for short), suitable for path, motion or function generation, with different arbitrary limits of accuracy at various discrete positions. It was found that the method yields fundamentally stable solutions: while in closed-form synthesis, small changes in prescribed values often result in very different solutions or no solutions at all, in SPS small perturbations in problem specifications often produce only small variations in the synthesized linkage dimensions. Such stability is rarely found in Burmester theory and other synthesis techniques. Applying nonlinear programming and introducing the dyadic construction of mechanisms, the SPS technique is applicable to the synthesis of most planar mechanisms including four-bar, five-bar, multi-loop, multi-degree of freedom and adjustable mechanisms. Also, dyadic construction simplifies the optimization process and renders the method readily manageable in interactive computer-aided design. The SPS digital computer programs for batch and tele-processing are made available to interested readers.

Selective Precision Synthesis of the Four-Bar Motion Generator With Prescribed Input Timing

1979 ◽  
Vol 101 (4) ◽  
pp. 614-618 ◽  
Author(s):  
S. N. Kramer
Keyword(s):  
Computer Aided Design ◽  
Unique Feature ◽  
Mechanism Synthesis ◽  
Computer Aided ◽  
Programming Techniques ◽  
Stable Solutions ◽  
Precision Synthesis ◽  
Aided Design ◽  
Error Envelope ◽  
Motion Generator

The recently developed Selective Precision Synthesis technique has been extended to the four-bar motion generating mechanism with prescribed input timing. A designer using this method can determine several mechanisms whose coupler triangle positions and orientations will be coordinated with the input crank rotations. The unique feature in the Selective Precision Synthesis formulation is that the path, orientations and rotations are specified along with allowable limits of accuracy creating an error envelope for each of these parameters. This modification removes the limiting conditions imposed by the precision point approach so that standard nonlinear programming techniques can be used to determine several mechanism solutions. It was found that the method yields fundamentally stable solutions rarely encountered in closed-form methods of mechanism synthesis. The problem of dyadic construction error in the original SPS technique is eliminated and the method developed here is well suited to batch or interactive computer-aided design. The computer program of this method is being made available to interested readers.

A Computer-Aided Design Technique for the Synthesis of Planar Four Bar Mechanisms Satisfying Specified Kinematic and Dynamic Conditions

1987 ◽  
Author(s):  
G. A. Rigelman ◽  
S. N. Kramer
Keyword(s):  
Computer Aided Design ◽  
Dynamic Performance ◽  
Mathematical Formulation ◽  
Average Power ◽  
Optimization Method ◽  
Dynamic Conditions ◽  
Allowable Deviation ◽  
Computer Aided ◽  
Precision Synthesis ◽  
Aided Design

Abstract This paper presents a computer-aided design optimization method for synthesizing planar four bar mechanisms which satisfy specified kinematic and dynamic conditions. The method can be used for path, motion, and function generation as well as for combinations of these. The kinematic conditions consist of combinations of specifications on the position, velocity, and acceleration of the coupler point and the rotations of the coupler and follower links. The dynamic conditions consist of the minimization of the average power consumed by the mechanism as well as a limit on the maximum input torque. The external loads consist of variable forces and moments at the coupler point as well as variable torques on the follower link. The Selective Precision Synthesis (SPS) method is used to express each kinematic condition in terms of a specification plus an allowable deviation or tolerance from the specification. In this manner, the synthesis problem is converted into a nonlinear optimization problem which is solved by using the Generalized Reduced Gradient (GRG) method. In addition, two force balancing routines are included to help the dynamic performance of the mechanism. The mathematical formulation and derivation as well as numerical examples are presented in this paper.

Computer-Aided Design of the RSSR Function Generating Spatial Mechanism Using the Selective Precision Synthesis Method

1987 ◽  
Author(s):  
S. R. Dhall ◽  
S. N. Kramer
Keyword(s):  
Computer Aided Design ◽  
Design Method ◽  
General Procedure ◽  
Mathematical Formulation ◽  
Synthesis Method ◽  
Nonlinear Constraint ◽  
Planar Function ◽  
Computer Aided ◽  
Precision Synthesis ◽  
Aided Design

Abstract Planar function generating mechanisms may be synthesized for a limited number of precision points by carrying out a kinematic inversion about the output link. However, this becomes quite difficult for spatial mechanisms. In this paper the general RSSR spatial function generating mechanism is synthesized using the Selective Precision Synthesis technique. In this computer-aided design method, nonlinear constraint equations relating the generated and desired rotations of the output crank are formulated. These constraints which define accuracy neighborhoods around each of the “n” prescribed output crank rotations, are then solved using the Generalized Reduced Gradient Method of optimization. The mathematical formulation, the general procedure of synthesis and numerical examples are presented in this paper.

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.

An Exploration on Modeling Design Method of Sprinklers Based on Rhinoceros Platform

2011 ◽  
Vol 121-126 ◽  
pp. 687-691
Author(s):  
Yun Feng Zhu
Keyword(s):  
3D Modeling ◽  
Computer Aided Design ◽  
Design Method ◽  
Computer Aided ◽  
Design Software ◽  
Aided Design ◽  
General Method

This paper proves the feasibility of Rhino, a computer aided design software, in modeling design of sprinklers, through an analysis in the establishment of sprinklers’ chassis and an example of 3D modeling, and promotes a general method of shell modeling design of sprinklers based on Rhino.

Computer-Aided Design of Power Transmission Shafts Subject to Size, Strength, and Deflection Constraints Using a Nonlinear Programming Technique

1985 ◽  
Vol 107 (1) ◽  
pp. 133-140
Author(s):  
G. Umasankar ◽  
C. R. Mischke
Keyword(s):  
Nonlinear Programming ◽  
Design Problem ◽  
Computer Aided Design ◽  
Power Transmission ◽  
Programming Technique ◽  
Cost Criterion ◽  
Transmission Shaft ◽  
Computer Aided ◽  
Aided Design ◽  
Np Problem

The problem of synthesis of power transmission shafts supported on two bearings, subject to dimensional, strength, and deflection constraints is posed as a nonlinear programming (NP) problem. The formulation of the design problem and its solution using the gradient projection (GP) algorithm are presented. A computer program for shaft design against a user-definable weight/cost criterion, based on the formulation and solution presented, is made available. A design example illustrating this approach to power transmission shaft design is included.

A Computer-Aided Design Technique for the Synthesis of Planar Four Bar Mechanisms Satisfying Specified Kinematic and Dynamic Conditions

1988 ◽  
Vol 110 (3) ◽  
pp. 263-268 ◽  
Author(s):  
G. A. Rigelman ◽  
S. N. Kramer
Keyword(s):  
Computer Aided Design ◽  
Dynamic Performance ◽  
Mathematical Formulation ◽  
Average Power ◽  
Optimization Method ◽  
Dynamic Conditions ◽  
Allowable Deviation ◽  
Computer Aided ◽  
Precision Synthesis ◽  
Aided Design

This paper presents a computer-aided design optimization method for synthesizing planar four bar mechanisms which satisfy specified kinematic and dynamic conditions. The method can be used for path, motion, and function generation as well as for combinations of these. The kinematic conditions consist of combinations of specifications on the position, velocity, and acceleration of the coupler point and the rotations of the coupler and follower links. The dynamic conditions consist of the minimization of the average power consumed by the mechanism as well as a limit on the maximum input torque. The external loads consist of variable forces and moments at the coupler point as well as variable torques on the follower link. The Selective Precision Synthesis (SPS) method is used to express each kinematic condition in terms of a specification plus an allowable deviation or tolerance from the specification. In this manner, the synthesis problem is converted into a nonlinear optimization problem which is solved using the Generalized Reduced Gradient (GRG) method. In addition, two force balancing routines are included to help the dynamic performance of the mechanism. The mathematical formulation and derivation as well as numerical examples are presented in this paper.

Computer-Aided Design of the RSSR Function Generating Spatial Mechanism Using the Selective Precision Synthesis Method

1988 ◽  
Vol 110 (4) ◽  
pp. 378-382 ◽  
Author(s):  
S. Dhall ◽  
S. N. Kramer
Keyword(s):  
Computer Aided Design ◽  
Design Method ◽  
General Procedure ◽  
Mathematical Formulation ◽  
Synthesis Method ◽  
Nonlinear Constraint ◽  
Planar Function ◽  
Computer Aided ◽  
Precision Synthesis ◽  
Aided Design

Planar function generating mechanisms may be synthesized for a limited number of precision points by carrying out a kinematic inversion about the output link. However, this becomes quite difficult for spatial mechanisms. In this paper the general RSSR spatial function generating mechanism is synthesized using the Selective Precision Synthesis technique. In this computer-aided design method, nonlinear constraint equations relating the generated and desired rotations of the output crank are formulated. These constraints which define accuracy neighborhoods around each of the “n” prescribed output crank rotations are then solved using the Generalized Reduced Gradient Method of optimization. The mathematical formulation, the general procedure of synthesis, and numerical examples are presented in this paper.

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