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.

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.

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 Methodology to Handle Inequality Constraints in an Interactve Design Process

1991 ◽  
Author(s):  
Natarajan Sridhar ◽  
Rajiv Agrawal ◽  
Gary L. Kinzel
Keyword(s):  
Design Process ◽  
Mechanical Design ◽  
Inequality Constraints ◽  
Inequality Constraint ◽  
Management Problem ◽  
Matrix Formulation ◽  
Equality And Inequality Constraints ◽  
Interchange Algorithm ◽  
Generalized Reduced Gradient ◽  
Occurrence Matrix

Abstract The treatment of mechanical design as a constraint management problem has long been related to equality constraints. Work involving inequality constraints has been generally restricted to optimization and symbolic computation. This paper presents a methodology for handling inequality constraints in an interactive mechanical design process. The presented method is similar to the basis interchange algorithm used in the Generalized Reduced Gradient (GRG) method for constrained nonlinear optimization. The main difference is that our method relies on user guidance to select which specification has to be changed in order to satisfy the violated inequality constraint. Also, the specification is only adjusted; unlike the procedure in the GRG method where the basis is changed. An inequality constraint violation is detected whenever the corresponding slack variable becomes negative. An occurrence-matrix formulation is used to represent both the equality and inequality constraints that govern the design. The work is illustrated for the classical weldment design problem.

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.

Computer-Aided Synthesis of Mechanisms Using Nonlinear Programming

1973 ◽  
Vol 95 (1) ◽  
pp. 339-344 ◽  
Author(s):  
V. K. Gupta
Keyword(s):  
Nonlinear Programming ◽  
Mathematical Programming ◽  
Penalty Function ◽  
Inequality Constraints ◽  
Mathematical Programming Problem ◽  
Spatial Mechanisms ◽  
Synthesis Of Mechanisms ◽  
Computer Aided ◽  
Equality And Inequality Constraints ◽  
Penalty Function Approach

The synthesis of spatial mechanisms is formulated as a mathematical programming problem and solved using a penalty function approach. The objective function as well as the equality and inequality constraints are determined explicitly from conditions such as those required for linkage closure, mobility, and transmissibility.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

Optimization of Dynamic Forces in the Design of Mechanical Hands

1989 ◽  
Author(s):  
M. A. Nahon ◽  
J. Angeles
Keyword(s):  
Equations Of Motion ◽  
Inequality Constraints ◽  
Kinematic Chain ◽  
Programming Approach ◽  
Quadratic Optimization Problem ◽  
System A ◽  
Redundantly Actuated ◽  
Internal Forces ◽  
Constrained Quadratic Optimization ◽  
Mechanical Hands

Abstract Mechanical hands have become of greater interest in robotics due to the advantages they offer over conventional grippers in tasks requiring dextrous manipulation. However, mechanical hands also tend to be more complex in construction and require more sophisticated design analysis to determine the forces in the system. A mechanical hand can be described as a kinematic chain with time-varying topology which becomes redundantly actuated when an object is grasped. When this occurs, care must be exercised to avoid crushing the object or generating excessive forces within the mechanism. In the present work, this problem is formulated as a constrained quadratic optimization problem. The forces to be minimized form the objective, the dynamic equations of motion form the equality constraints and the finger-object contacts yield the inequality constraints. The quadratic-programming approach is shown to be advantageous due to its ability to minimize ‘internal forces’ A technique is proposed for smoothing the discontinuities in the force solution which occur when the toplogy changes.

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