Selective Precision Synthesis of the Spatial Slider Crank Mechanism for Path and Function Generation

1987 ◽  
Author(s):  
P. Premkumar ◽  
S. R. Dhall ◽  
S. N. Kramer
Keyword(s):  
Closed Form ◽  
Computer Aided Design ◽  
Inequality Constraint ◽  
Function Generation ◽  
Reduced Gradient Method ◽  
Nonlinear Inequality ◽  
Generalized Reduced Gradient ◽  
Precision Synthesis ◽  
And Function ◽  
Crank Mechanism

Abstract Analysis of the RRSC spatial slider crank mechanism for path generation with prescribed input timing and for function generation are presented here in closed form. A computer aided design technique for the synthesis of the RRSC path generating and function generating mechanisms is also being presented using the Selective Precision Synthesis technique. The analysis uses the spatial rotation matrices to obtain a fourth order polynomial for the coupler link rotations with the coefficients expressed in terms of the link lengths and input link rotation. This polynomial is solved in closed form to determine the coupler link rotations which are then used to determine the locations of the path point, the output link rotations and the displacement of the slider at the cylindrical joint. For synthesis, nonlinear inequality constraint equations relating the generated and the desired path points or slider displacements are formulated. These constraints define accuracy neighborhoods around each of the “n” prescribed path points (or slider displacements), and are solved using the Generalized Reduced Gradient method of optimization.

Selective Precision Synthesis of the Spatial Slider Crank Mechanism for Path and Function Generation

1988 ◽  
Vol 110 (3) ◽  
pp. 295-302 ◽  
Author(s):  
P. Premkumar ◽  
S. R. Dhall ◽  
S. N. Kramer
Keyword(s):  
Closed Form ◽  
Synthesis Method ◽  
Inequality Constraint ◽  
Form Analysis ◽  
Function Generation ◽  
Reduced Gradient Method ◽  
Nonlinear Inequality ◽  
Precision Synthesis ◽  
And Function ◽  
Crank Mechanism

A technique for the synthesis of the RRSC spatial slider crank mechanism for path and function generation using the Selective Precision Synthesis method is presented here. Also presented is a closed form analysis technique for this mechanism. The analysis uses the spatial rotation matrices to obtain a fourth order polynomial for the coupler link rotations with the coefficients expressed in terms of the link lengths and input link rotation. This polynomial is solved in closed form to determine the coupler link rotations which are then used to determine the locations of the path point, the output link rotations, and the displacement of the slider at the cylindrical joint. For synthesis, nonlinear inequality constraint equations relating the generated and the desired path points (or slider displacements) are formulated. These constraints define accuracy neighborhoods around each of the “n” prescribed path points (or slider displacements), and are solved using the Generalized Reduced Gradient method of optimization.

Design and Analysis of the HCCC, RCCC, and PCCC Spatial Mechanisms for Function Generation

1990 ◽  
Vol 112 (1) ◽  
pp. 74-78 ◽  
Author(s):  
S. Dhall ◽  
S. N. Kramer
Keyword(s):  
Computer Aided Design ◽  
Inequality Constraints ◽  
Output Displacement ◽  
Reduced Gradient Method ◽  
Synthesis Technique ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Generalized Reduced Gradient ◽  
Precision Synthesis ◽  
Input Position

A computer aided design technique for the synthesis of spatial function generating mechanisms is presented. The Selective Precision Synthesis technique has been extended for the synthesis of the spatial HCCC, RCCC, and PCCC function generating mechanisms. These mechanisms consist of three cylindrical joints (C) and one each of a helical (H), revolute (R), and prismatic (P) joint, respectively. A closed form displacement analysis of the HCCC mechanism has also been presented. In this synthesis technique, for each input position the user specifies accuracy neighborhoods around the desired output rather than exact points. Nonlinear inequality constraints relating the desired output displacement to the actual output displacements are then iteratively solved using the generalized reduced gradient method of optimization, until a good mechanism solution is reached. The analysis uses spatial rotation matrices to solve for the displacement variables.

A Computer-Aided-Design Technique for the Optimum Synthesis of RRSS Path Generating Spatial Mechanisms With Prescribed Input Timing

1986 ◽  
Vol 108 (4) ◽  
pp. 538-542 ◽  
Author(s):  
P. Premkumar ◽  
S. N. Kramer
Keyword(s):  
Computer Aided Design ◽  
Mathematical Formulation ◽  
Nonlinear Constraint ◽  
Reduced Gradient Method ◽  
Synthesis Technique ◽  
Optimum Synthesis ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Precision Synthesis ◽  
Mechanical Devices

With the current emphasis on automation, the need for single actuator mechanical devices that can perform simple repetitive tasks much more economically, energy-efficiently and accurately than multiple-degree-of-freedom, multiple-actuator robotic manipulators is greatly felt. This paper presents an optimum synthesis technique for the RRSS path generating spatial mechanism with prescribed input timing. The selective precision synthesis technique is used to formulate the nonlinear constraint equations involving accuracy neighborhoods and corresponding error envelopes and these are then solved using the generalized reduced gradient method of optimization. The mathematical formulation and derivation as well as numerical examples are presented in this paper.

Position, Velocity, and Acceleration Synthesis of the RRSS Spatial Path-Generating Mechanism Using the Selective Precision Synthesis Method

1989 ◽  
Vol 111 (1) ◽  
pp. 54-58 ◽  
Author(s):  
P. Premkumar ◽  
S. N. Kramer
Keyword(s):  
Synthesis Method ◽  
Nonlinear Constraint ◽  
Spatial Mechanism ◽  
Constraint Equations ◽  
Reduced Gradient Method ◽  
Optimum Synthesis ◽  
Spatial Mechanisms ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Precision Synthesis

The inclusion of velocity and acceleration constraints is a crucial step in the coupling of the dynamics with the kinematics of spatial mechanisms. In this paper, an optimum synthesis technique is presented which allows an arbitrary combination of positions, velocities, and accelerations to be specified along with appropriate tolerances at one or more of the prescribed path points. The method of Selective Precision Synthesis is used to formulate nonlinear constraint equations which are then solved by the generalized reduced gradient method of optimization. This is significant since it paves the way for the coupling of mechanism dynamics with the kinematics of spatial mechanisms. The technique developed herein is general to all spatial mechanisms and is exemplified by the RRSS path-generating spatial mechanism.

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.

Finite Kinematic Synthesis of a Cycloidal-Crank Mechanism for Function Generation

1970 ◽  
Vol 92 (3) ◽  
pp. 531-535 ◽  
Author(s):  
S. N. Kramer ◽  
G. N. Sandor
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Gear Ratio ◽  
Form Solution ◽  
Complex Numbers ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Approximate Function ◽  
Crank Mechanism

The method of complex numbers is applied towards the kinematic synthesis of a planar geared five-bar cycloidal-crank mechanism for approximate function generation with finitely separated precision points. It is shown that up to 10 precision points can be obtained, and a closed-form solution is presented which yields up to 6 different mechanisms with a 6-point approximation. In this method, the designer has control over the design of the cycloidal crank regarding gear ratio and configuration. The method has been programmed for automatic digital computation on the IBM-360 system, and the program is made available to interested readers. An optimization method utilizing iterative application of the closed-form solution is outlined.

Synthesis of Multi-Loop Spatial Mechanisms by Iterative Analysis: The RSSR-SS Path Generator

1990 ◽  
Vol 112 (1) ◽  
pp. 69-73 ◽  
Author(s):  
P. Premkumar ◽  
S. Kramer
Keyword(s):  
Equations Of Motion ◽  
Inequality Constraints ◽  
Reduced Gradient Method ◽  
Spatial Mechanisms ◽  
Analysis Technique ◽  
Analysis And Synthesis ◽  
Method Of Solution ◽  
Equality And Inequality Constraints ◽  
Generalized Reduced Gradient ◽  
Precision Synthesis

This paper presents the synthesis of the RSSR-SS path generating spatial mechanisms. The method of solution involves the Selective Precision Synthesis technique to formulate the equality and inequality constraints which are then solved by the Generalized Reduced Gradient method of optimization. A closed from analysis technique is also developed, and by emphasizing the iterative nature of design, the mathematical complexity of the governing kinematic equations of motion for design are greatly simplified. Numerical examples for both analysis and synthesis are presented.

Optimal Design of Semisubmersible’s Form Based on Systems Analysis

1984 ◽  
Vol 106 (4) ◽  
pp. 524-530 ◽  
Author(s):  
S. Akagi ◽  
R. Yokoyama ◽  
K. Ito
Keyword(s):  
Optimal Design ◽  
Computer Aided Design ◽  
Optimization Problem ◽  
Design Method ◽  
Gradient Algorithm ◽  
Interpretive Structural Modeling ◽  
Reduced Gradient ◽  
Optimal Design Method ◽  
Generalized Reduced Gradient ◽  
Aided Design

With the objective of developing a computer-aided design method to seek the optimal semisubmersible’s form, hierarchical relationships among many design objectives and conditions are investigated first based on the interpretive structural modeling method. Then, an optimal design method is formulated as a nonlinear multiobjective optimization problem by adopting three mutually conflicting design objectives. A set of Pareto optimal solutions is derived numerically by adopting the generalized reduced gradient algorithm, and it is ascertained that the designer can determine the optimal form more rationally by investigating the trade-off relationships among design objectives.

Synthesis of a Large Oscillation Four-Bar Mechanism

1997 ◽  
Author(s):  
Gloria K. Starns ◽  
Donald R. Flugrad
Keyword(s):  
Reduced Gradient Method ◽  
Large Oscillation ◽  
Oscillation Mechanism ◽  
Straight Line ◽  
Transmission Angle ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Angular Oscillations ◽  
Four Bar Linkage ◽  
Effective Transmission

Abstract This paper demonstrates procedures implemented for the synthesis of a four-bar mechanism that produces large angular oscillations of the output member while maintaining effective transmission angles. The mechanisms are modeled as being driven by a force applied at the coupler link. Additionally this force’s line of action is constrained to occur along an approximate straight line. This research was conducted out of the need for a device that is capable of retraction of the horizontal tool bar housed on the back of a tractor. The tool bars accommodate the implements required to accomplish the numerous tasks of the farmer, i.e. row markers, sprayer arms, planters, etc. Upon retraction of the tool bar so that it is parallel to ground, the appropriate tools are lowered to their working position. As the length of these bars increases, a savings of time and increased productivity is realized. Kurt Hain makes the following observation regarding large oscillation mechanisms in [1]: “It would be very difficult to solve this problem with one four-bar linkage, because it is difficult to design a four-bar linkage having such a large oscillation of a crank without running into problems of poor transmission angle characteristics; it might be possible to use linkages in combinations with gears, but this would make the mechanism more expensive, less efficient, and probably noisier.” In this study simulated annealing, a genetic algorithm and the generalized reduced gradient method are used to produce mechanisms with large angular oscillations of the output member and transmission angles that vary by as little as 20° from 90°. A comparative analysis of each of the optimization procedures is presented with observations regarding the efficacy of each method in the solution of the large oscillation mechanism.

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