Minimum Error Synthesis of Multiloop Plane Mechanisms for Rigid Body Guidance

1974 ◽  
Vol 96 (1) ◽  
pp. 107-116 ◽  
Author(s):  
K. N. Prasad ◽  
C. Bagci
Keyword(s):  
Rigid Body ◽  
Rigid Bodies ◽  
Type I ◽  
Path Generation ◽  
Relaxation Methods ◽  
Single Degree Of Freedom ◽  
Minimum Error ◽  
Numerical Examples ◽  
Single Degree ◽  
Matrix Iteration

A variational method of synthesizing single-degree of freedom, single or multiloop plane mechanisms to guide rigid bodies through specified planar positions is presented. The optimum set of dimensions of a mechanism is determined by minimizing an objective function, which is the sum of the squared errors in the generated coordinates of two body points. The design equations are solved either by matrix iteration or Gaussian relaxation methods. By introducing constraints necessary to coincide the two body points, the problem is reduced to that of optimizing a plane mechanism to generate a planar path. Stephenson six-bar mechanism of Type I and the 4R plane mechanism are synthesized for rigid body guidance and path generation. Numerical examples are given, where all the geometric inversions of a mechanism are synthesized as distinct mechanisms, thereby eliminating the mixing of the geometric inversions at the design positions, thus assuring the mobility of the resulting mechanisms within the design interval.

On the Motion of Lineal Bodies Subject to Linear Damping

1997 ◽  
Vol 64 (1) ◽  
pp. 227-229 ◽  
Author(s):  
M. F. Beatty
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Rigid Body ◽  
General Class ◽  
Plane Motion ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Damping

Wilms (1995) has considered the plane motion of three lineal rigid bodies subject to linear damping over their length. He shows that these plane single-degree-of-freedom systems are governed by precisely the same fundamental differential equation. It is not unusual that several dynamical systems may be formally characterized by the same differential equation, but the universal differential equation for these systems is unusual because it is exactly the same equation for the three very different systems. It is shown here that these problems belong to a more general class of problems for which the differential equation is exactly the same for every lineal rigid body regardless of its geometry.

Synthesis of Spatial Mechanism UR-2SS for Path Generation

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Wen-Yeuan Chung
Keyword(s):  
Three Dimensional ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Path Generation ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Three Stages ◽  
Moving Platform

This article presents a new spatial mechanism with single degree of freedom (DOF) for three-dimensional path generation. The path can be defined by prescribing at most seven precision points. The moving platform of the mechanism is supported by a U-R (universal-revolute) leg and two S–S (spherical–spherical) legs. The driving unit is the first axis of the universal pair. The U-R leg is synthesized first with the problem of order defects being considered. Precision points then lead to prescribed poses of the moving platform. Two S–S legs are then synthesized to meet these poses. This spatial mechanism with a given input is analogous to a planar kinematic chain so that all possible configurations of the spatial mechanism can be constructed. A strategy consisting of three stages for evaluating branch defects is developed with the aid of the characteristic of double configurations and the technique of coding three constituent four-bar linkages. Two numerical examples are presented to illustrate the design, the evaluation of defects, and the performance of the mechanism.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein ◽  
L. S. Woo
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Static Force ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Torque Analysis ◽  
Basic Concepts

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

An Optimization Approach to Vibration Isolation of Rigid Bodies

1997 ◽  
Vol 25 (3) ◽  
pp. 165-175
Author(s):  
P. S. Heyns
Keyword(s):  
Design Problem ◽  
Vibration Isolation ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Optimization Approach ◽  
Local Minima ◽  
Single Degree Of Freedom ◽  
Single Degree

The conventional single-degree-of-freedom approach to isolator design dealt with in most undergraduate curricula, is not always adequate for the design of practical isolator systems. In this article, an optimization approach to the design problem is presented and the viability of the approach demonstrated. It is, however, also shown that multiple local minima may exist and that due care should be exercised in the application of the method.

ON MOTION GENERATION OF WATT I MECHANISMS FOR MECHANICAL FINGER DESIGN

2008 ◽  
Vol 32 (3-4) ◽  
pp. 411-422 ◽  
Author(s):  
QIONG SHEN ◽  
WEN-TZONG LEE ◽  
KEVIN RUSSELL ◽  
RAJ S. SODHI
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Degree Of Freedom ◽  
Planar Motion ◽  
Motion Generation ◽  
Single Degree Of Freedom ◽  
Closed Loops ◽  
Single Degree ◽  
Mechanical Finger

This work formulates and demonstrates a motion generation method for the synthesis of a particular type of planar six-bar mechanism-the Watt I mechanism. The Watt I mechanism is essentially a “stacked” four-bar mechanism (having two closed loops and a single degree of freedom). Extending the planar motion generation method of Suh and Radcliffe [11] to incorporate relative motion between moving pivots, Watt I mechanisms are synthesized to simultaneously approximate two groups of prescribed rigid-body poses for simultaneous dual motion generation capability. The example included demonstrates the synthesis of a finger mechanism to achieve a prescribed grasping pose sequence.

scholarly journals Sliding-vibrating responses of elastic structures

1988 ◽  
Vol 21 (3) ◽  
pp. 190-197
Author(s):  
Yu-An Fu
Keyword(s):  
Rigid Body ◽  
Harmonic Excitation ◽  
Body Motion ◽  
Shake Table ◽  
Reciprocating Motion ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Analytical Expressions ◽  
Vibrating Response

By using simulated friction forces, analytical expressions were derived from the sliding-vibrating response of a single degree of freedom system under harmonic excitation or the "disadvantageous period reciprocating motion", taking the mass of the sliding base into consideration. Some of the general laws were studied and some new characteristics determined which had previously been ignored by assuming rigid body motion. The analysis methods adopted in this paper have been confirmed in comparison with the results of model tests on a shake table.

A New Design Methodology for Planar Vibration Absorbers

1999 ◽  
Author(s):  
Pat Blanchet ◽  
Harvey Lipkin
Keyword(s):  
Design Methodology ◽  
Exciting Force ◽  
Degree Of Freedom ◽  
Vibration Absorbers ◽  
Specific Design ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Single Degree ◽  
Planar Vibration ◽  
Design Freedom

Abstract A new methodology is presented for the design of planar vibration absorbers. For the most part, previous methods have dealt with systems constrained to a single degree-of-freedom and require the absorber to be along the line of the exciting force. The presented methodology is more versatile and allows the placement of the absorber as a design freedom. Three specific design techniques for force and couple excitations are detailed along with numerical examples illustrating the results.

Four-Position Synthesis for Spatial Mechanisms With Two Independent Loops

1992 ◽  
Author(s):  
Chien H. Chiang ◽  
Wei Hua Chieng ◽  
David A. Hoeltzel
Keyword(s):  
Rigid Body ◽  
Mathematical Models ◽  
Analytical Methods ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Practical Applications ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Position Synthesis ◽  
Independent Loops

Abstract Mathematical models that have been employed to synthesize spatial mechanisms for rigid body guidance have been found to be too complicated to implement in practical applications, especially for four-position guidance synthesis. This paper describes simple analytical methods for synthesizing single degree-of-freedom spatial mechanisms having two independent loops for four precision positions. In addition, prescribed timing has been simultaneously considered for several spatial mechanisms.

Explicit Nonlinear Rotational Controllers Using the Fundamental Equation

2009 ◽  
Author(s):  
Aaron D. Schutte ◽  
Firdaus E. Udwadia
Keyword(s):  
Asymptotic Stability ◽  
Rigid Body ◽  
Fundamental Equation ◽  
Rigid Bodies ◽  
Rotational Dynamics ◽  
Qualitative Behavior ◽  
Constrained Motion ◽  
Numerical Examples ◽  
Nonlinear Controllers ◽  
Quaternion Space

In this paper, we present two explicitly generated nonlinear controllers for rest-to-rest rigid body rotational maneuvers in terms of quaternions. The controllers are brought about by applying the fundamental equation of constrained motion to both the rotational dynamics and rotational control of rigid bodies. The first controller yields asymptotic stability at a desired orientation while allowing the stabilization to occur exactly along a pre-selected trajectory for three of the four components that make-up the quaternion. The second controller provides global stability at the desired orientation allowing stable motion to occur from any point in quaternion space. Numerical examples are provided showing the qualitative behavior that both rotational controllers yield when applied to a rigid body.

scholarly journals On the Optimal Shock Isolation of a System with One and a Half Degrees of Freedom

1999 ◽  
Vol 6 (4) ◽  
pp. 159-167
Author(s):  
D.V. Balandin ◽  
N.N. Bolotnik ◽  
W.D. Pilkey
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Single Degree ◽  
Shock Isolation

The limiting performance of shock isolation of a system with one and a half degrees of freedom is studied. The possibility of using a single-degree-of-freedom model for this analysis is investigated. The error of such an approximation is estimated. Numerical examples are presented.

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