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.

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.

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.

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.

An inventory model of a three parameter Weibull distributed deteriorating item with variable demand dependent on price and frequency of advertisement under trade credit

2019 ◽  
Vol 53 (3) ◽  
pp. 903-916 ◽  
Author(s):  
Ali Akbar Shaikh ◽  
Leopoldo Eduardo Cárdenas–Barrón ◽  
Asoke Kumar Bhunia ◽  
Sunil Tiwari
Keyword(s):  
Trade Credit ◽  
Inventory Model ◽  
Selling Price ◽  
Credit Policy ◽  
Variable Demand ◽  
Reduced Gradient Method ◽  
Deterioration Rate ◽  
Rate Dependent ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

This paper develops an inventory model for a deteriorating item with variable demand dependent on the selling price and frequency of advertisement of the item under the financial trade credit policy. Shortages are allowed and these are partially backlogged with a variable rate dependent on the duration of waiting time until to the arrival of next order. In this inventory model, the deterioration rate follows a three-parameter Weibull distribution. The corresponding inventory model is formulated and solved by using the well-known generalized reduced gradient method along with an algorithm. To validate the inventory model, two numerical examples are considered and solved. Finally, based on one numerical example, the impacts of different parameters are studied by a sensitivity analysis considering one parameter at a time and leaving the other parameters fixed.

Discussion of Hwang and Chen's constraint equations to eliminate order, circuit and branch defects for the paper: Defect-free synthesis of Stephenson-III motion generators, published in Journal of Mechanical Engineering Science, 2008; 222: 2485–2494

2019 ◽  
Vol 234 (5) ◽  
pp. 1130-1134
Author(s):  
Wen-Yi Lin
Keyword(s):  
Mechanical Engineering ◽  
Optimization Algorithms ◽  
Synthesis Method ◽  
Synthesis Methods ◽  
Engineering Science ◽  
Function Generation ◽  
Constraint Equations ◽  
Optimum Synthesis

Many studies to find solutions for the optimum synthesis problems of linkage mechanisms for path, motion or function generation have appeared in the literature. However, their main focus has been on the development of optimization algorithms or synthesis methods without the handling of the defect problems or only with consideration of the same assembly mode. Hwang and Chen's pioneering work proposed a defect-free optimum synthesis method with constraint equations to eliminate order, circuit and branch defects for Stephenson III six-bar motion generators. However, their proposed constraint equations for the three types of defects are incomplete or not clear enough. In this discussion, we not only examine these faults but also offer the correct and complete constraints to eliminate the three types of defects.

scholarly journals A Mathematical Model for Optimal Strength and Alignment of a Marine Shafting System

1985 ◽  
Vol 29 (03) ◽  
pp. 212-222
Author(s):  
Zissimos Mourelatos ◽  
Panos Papalambros
Keyword(s):  
Mathematical Model ◽  
Nonlinear Programming ◽  
Programming Formulation ◽  
Solution Strategy ◽  
Reduced Gradient Method ◽  
Trade Offs ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Optimal Strength ◽  
Vertical Positioning

The design of a marine shafting system is modeled mathematically in order to perform optimization studies with respect to shaft strength as well as longitudinal and vertical positioning of the bearings. The objective criteria used are minimization of the bearing reaction influence numbers and even distribution of the bearing loading. Design trade-offs can be thus established. The problem is posed in a nonlinear programming formulation and is solved using a standard generalized reduced gradient method (GRG2), but in a specialized solution strategy. Two examples from actual ship designs are presented.

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.

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