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.

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.

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.

Optimum Path Planning for Mechanical Manipulators

1981 ◽  
Vol 103 (2) ◽  
pp. 142-151 ◽  
Author(s):  
J. Y. S. Luh ◽  
C. S. Lin
Keyword(s):  
Path Planning ◽  
Feasible Solution ◽  
Computing Time ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Planning Problem ◽  
Linear Inequality Constraints ◽  
Nonlinear Inequality ◽  
Angular Velocities ◽  
Nonlinear Inequality Constraints

To assure a successful completion of an assigned task without interruption, such as the collision with fixtures, the hand of a mechanical manipulator often travels along a preplanned path. An advantage of requiring the path to be composed of straight-line segments in Cartesian coordinates is to provide a capability for controlled interaction with objects on a moving conveyor. This paper presents a method of obtaining a time schedule of velocities and accelerations along the path that the manipulator may adopt to obtain a minimum traveling time, under the constraints of composite Cartesian limit on linear and angular velocities and accelerations. Because of the involvement of a linear performance index and a large number of nonlinear inequality constraints, which are generated from physical limitations, the “method of approximate programming (MAP)” is applied. Depending on the initial choice of a feasible solution, the iterated feasible solution, however, does not converge to the optimum feasible point, but is often entrapped at some other point of the boundary of the constraint set. To overcome the obstacle, MAP is modified so that the feasible solution of each of the iterated linear programming problems is shifted to the boundaries corresponding to the original, linear inequality constraints. To reduce the computing time, a “direct approximate programming algorithm (DAPA)” is developed, implemented and shown to converge to optimum feasible solution for the path planning problem. Programs in FORTRAN language have been written for both the modified MAP and DAPA, and are illustrated by a numerical example for the purpose of comparison.

Optimal Path Planning of Redundant Cooperative Robots Under Equality and Inequality Constraints

2003 ◽  
Author(s):  
Ali Hosseini ◽  
Mehdi Keshmiri
Keyword(s):  
Path Planning ◽  
Optimization Problem ◽  
Search Algorithm ◽  
Minimum Principle ◽  
Optimal Path ◽  
Inequality Constraints ◽  
Optimal Path Planning ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Cooperative Manipulators

Using kinematic resolution, the optimal path planning for two redundant cooperative manipulators carrying a solid object on a desired trajectory is studied. The optimization problem is first solved with no constraint. Consequently, the nonlinear inequality constraints, which model obstacles, are added to the problem. The formulation has been derived using Pontryagin Minimum Principle and results in a Two Point Boundary Value Problem (TPBVP). The problem is solved for a cooperative manipulator system consisting of two 3-DOF serial robots jointly carrying an object and the results are compared with those obtained from a search algorithm. Defining the obstacles in workspace as functions of joint space coordinates, the inequality constrained optimization problem is solved for the cooperative manipulators.

scholarly journals On finding a point in the relative interior of a polyhedral set and degeneracy in geometric programming

1978 ◽  
Vol 20 (4) ◽  
pp. 487-494 ◽  
Author(s):  
T. R. Jefferson ◽  
C. H. Scott
Keyword(s):  
Objective Function ◽  
Geometric Programming ◽  
Dual Problem ◽  
Optimization Theory ◽  
Inequality Constraints ◽  
Linear Constraints ◽  
Relative Interior ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Nonlinear Objective Function

AbstractGeometric programming is now a well-established branch of optimization theory which has its origin in the analysis of posynomial programs. Geometric programming transforms a mathematical program with nonlinear objective function and nonlinear inequality constraints into a dual problem with nonlinear objective function and linear constraints. Although the dual problem is potentially simpler to solve, there are certain computational difficulties to be overcome. The gradient of the dual objective function is not defined for components whose values are zero. Moreover, certain dual variables may be constrained to be zero (geometric programming degeneracy).To resolve these problems, a means to find a solution in the relative interior of a set of linear equalities and inequalities is developed. It is then applied to the analysis of dual geometric programs.

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