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.

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.

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.

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.

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.

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.

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.

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.

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