Kinematic Synthesis and Analysis of the Rack and Pinion Multi-Purpose Mechanism

1992 ◽  
Vol 114 (3) ◽  
pp. 428-432 ◽  
Author(s):  
G. K. Ananthasuresh ◽  
S. N. Kramer
Keyword(s):  
General Procedure ◽  
Full Range ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Monotonic Functions ◽  
Transmission Angle ◽  
Velocity Condition ◽  
Method Of Solution ◽  
Design Requirements

The general procedure for synthesizing the rack and pinion mechanism up to seven precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for three precision conditions of path generation, two positions of function generation, and a velocity condition at one of the precision points. This mechanism has a number of advantages over conventional four bar mechanisms. First, since the rack is always tangent to the pinion, the transmission angle is always 90 deg minus the pressure angle of the rack. Second, with both translation and rotation of the rock occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide variety of motion and nonmonotonic functions for a full range of motion as well as nonlinear amplified motions. In this work the mechanism is made to satisfy a number of amplified motions. In this work the mechanism is made to satisfy a number of practical design requirements such as completely rotatable input crank and others. By including the velocity specification, the designer has considerably more control of the output motion. The method of solution developed in this work uses the complex number method of mechanism synthesis. A numerical example is included.

Kinematic Synthesis and Analysis of the Rack-and-Gear Mechanism for Four-Point Path Generation With Prescribed Input Timing

1986 ◽  
Vol 108 (1) ◽  
pp. 10-14 ◽  
Author(s):  
M. Claudio ◽  
S. Kramer
Keyword(s):  
Range Of Motion ◽  
Full Range ◽  
Mechanism Synthesis ◽  
Monotonic Functions ◽  
Transmission Angle ◽  
Wide Range ◽  
Method Of Solution ◽  
Gear Mechanism ◽  
Design Requirements ◽  
Four Bar Linkage

The rack and gear mechanism is synthesized for generating four prescribed path points with input coordination. This mechanism has a number of advantages over the well-known four-bar linkage. First, the transmission angle is always at its optimum value of 90 deg since the rack is always tangent to the gear. Second, with both translation and rotation of the rack occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide range of motion and nonmonotonic functions for the full range of motion as well as nonlinear amplified motions. In this work, the mechanism is made to satisfy a number of practical design requirements such as having a completely rotatable input crank, elimination of the branching defect and others. The method of solution developed in this work employs the Burmester Four-Precision-Point Algorithm with additional relations utilizing the Complex Number Method of Mechanism Synthesis. The solution is programmed on the DEC/PDP 11/70 and is available to interested readers.

Computer Aided Design and Analysis of the Rack and Pinion Mechanism

1992 ◽  
Author(s):  
D. Srinivas ◽  
Steven N. Kramer
Keyword(s):  
Computer Aided Design ◽  
General Procedure ◽  
Full Range ◽  
Fortran Program ◽  
Linkage Mechanism ◽  
Function Generation ◽  
Transmission Angle ◽  
Method Of Solution ◽  
Aided Design ◽  
Four Bar Linkage

Abstract The general procedure for synthesizing the rack and pinion mechanism for six precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for generating both four prescribed path points with input coordination and two positions of function generation. This is the extension of the work reported earlier on this mechanism where only three path precision points were satisfied. The rack and pinion mechanism has a number of advantages over the conventional four bar linkage mechanism. First, since the rack is always tangent to the pinion, the transmission angle has a constant optimum value of 90 degrees minus the pressure angle of the pinion. Second, because both translation and rotation of the rack are possible, multiple outputs are available. Generation of monotonic functions for a wide variety of motion, and nonmonotonic functions for the full range of motion as well as nonlinear motions, are other advantages of this mechanism. The rack and pinion mechanism has applications in the packaging industry, in toys, and automotive steering mechanisms. In this work, the mechanism is made to satisfy a number of practical design constraints such as a completely rotatable input crank and others. Also, structural errors for function generation are calculated to give an estimate of the accuracy of the mechanism. The method of solution developed in this work uses the complex number method of mechanism synthesis and a FORTRAN program is written to find the solutions for any input.

scholarly journals Spherical Mechanism Synthesis in Virtual Reality

1998 ◽  
Author(s):  
Todd J. Furlong ◽  
Judy M. Vance ◽  
Pierre M. Larochelle
Keyword(s):  
Virtual Reality ◽  
Design Space ◽  
Three Dimensional ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
New Approach ◽  
Spherical Mechanisms ◽  
Input Design ◽  
Previous Design ◽  
Spherical Mechanism

Abstract This paper presents a new approach to using virtual reality (VR) to design spherical mechanisms. VR provides a three dimensional design space where a designer can input design positions using a combination of hand gestures and motions and view the resultant mechanism in stereo using natural head movement to change the viewpoint. Because of the three dimensional nature of the design and verification of spherical mechanisms, VR is examined as a new design interface in this research. In addition to providing a VR environment for design, the research presented in this paper has focused on developing a “design in context” approach to spherical mechanism design. Previous design methods have involved placing coordinate frames along the surface of a constraint sphere. The new “design in context” approach allows a designer to freely place geometric models of movable objects inside an environment consisting of fixed objects. The fixed objects could either act as a base for a mechanism or be potential sources of interference with the motion of the mechanism. This approach allows a designer to perform kinematic synthesis of a mechanism while giving consideration to the interaction of that mechanism with its application environment.

On the Synthesis of Straight Line, Constant Velocity Scanning Mechanisms

1991 ◽  
Vol 113 (4) ◽  
pp. 464-472 ◽  
Author(s):  
P. H. Hodges ◽  
A. P. Pisano
Keyword(s):  
Constant Velocity ◽  
Transverse Velocity ◽  
Grid Search ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Velocity Error ◽  
Straight Line ◽  
Transmission Angle ◽  
Point Motion ◽  
Input Motion

This paper presents a kinematic synthesis of constant-velocity, straight-line coupler-point motion of two planar mechanisms. After the derivation of synthesis equations, the numerical results of a grid search to determine the linkage dimensions for maximum constant velocity, with minimal straight line error, are presented. Plots of acceleration magnitude, transmission angles, and transverse velocity are presented as a function of the percentage of the constant velocity portion of a cycle of input motion. For a 5R2P Stephenson 6-bar linkage, normalized velocity errors as small as 2 percent can be maintained over 40 percent, or more, of the input cycle. A 7R Watt 6-bar linkage, while not achieving quite as high values as the 5R2P linkage, nevertheless can maintain normalized velocity errors as low as 2.5 percent over as much as 39 percent of the input cycle. These levels of performance must be weighed against unfavorable transmission angles, and in many cases, other undesirable effects, such as large accelerations and large transverse travel. The results show that, in order to maintain minimally acceptable transmission angle requirements, the velocity error and scan fraction requirements may be as little as 2.0 percent and as much as 35 percent, respectively.

Optimization of Planar, Spherical and Spatial Function Generators Using Input-Output Curve Planning

1994 ◽  
Vol 116 (3) ◽  
pp. 915-919 ◽  
Author(s):  
Zheng Liu ◽  
J. Angeles
Keyword(s):  
Performance Index ◽  
General Scheme ◽  
Optimization Procedure ◽  
Output Curve ◽  
Input Output ◽  
Function Generation ◽  
Spatial Function ◽  
Function Generators ◽  
Design Requirements ◽  
A Performance

A general scheme for the optimization of planar, spherical and spatial bimodal linkages for function generation is proposed. The problem is solved here following two basic steps: (i) planning input-output ((I/O) curves based on design requirements and selecting data from the planned curve; and (ii) setting up an optimization procedure to minimize a performance index.

Kinematic Synthesis of Geared Spherical Five Bar Mechanisms for Function Generation

1975 ◽  
Vol 97 (2) ◽  
pp. 723-730 ◽  
Author(s):  
D. L. Riddle ◽  
D. Tesar ◽  
J. Duffy
Keyword(s):  
Gear Train ◽  
Kinematic Synthesis ◽  
Design Procedures ◽  
Function Generation ◽  
Complete Formulation ◽  
Generation Problem

The synthesis of geared spherical five-bar mechanisms with application to the function generation problem is considered for multiply separated position specifications. Special gear train values reduce the geared five-bar to the elementary spherical four-bar. The planar four- and five-bar become a design subset to the spherical five-bar. Design procedures with complete formulation are outlined in detail.

A Novel Synthesis Method for Nonperiodic Function Generation of an RCCC Mechanism

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Wenrui Liu ◽  
Jianwei Sun ◽  
Bangcheng Zhang ◽  
Jinkui Chu
Keyword(s):  
Synthesis Method ◽  
Normalization Method ◽  
Numerical Examples ◽  
Function Generation ◽  
Novel Synthesis ◽  
Feature Parameter ◽  
Design Requirements ◽  
Mechanism Function ◽  
Relationship Of ◽  
The Relationship

In this paper, the nonperiodic function synthesis of an RCCC mechanism is presented using a wavelet feature parameter (WFP) method. The output function and the sliding displacement of the RCCC mechanism are described by the wavelet approximate and wavelet details. Based on the relationship of wavelet details of the sliding displacement and its scaling, a normalization method for wavelet details of the sliding displacement is presented. The influence of proportional scaling of the linkage lengths is eliminated. An adaptive database is established. The problem of nonperiodic design requirements of RCCC mechanism function synthesis is solved. To demonstrate the feasibility of this method, two numerical examples are proposed. Based on the nonperiodic design requirements, the RCCC mechanisms are designed and simulated using matlab and catia software. The results show that the method proposed is effective for nonperiodic function generation of the RCCC mechanism with multiple positions.

Kinematic Synthesis of Spherical Two-Gear Drives With Prescribed Entire-Motion Characteristics: Displacement Analysis and Dwell Characteristics

1983 ◽  
Vol 105 (4) ◽  
pp. 663-671 ◽  
Author(s):  
T. W. Lee ◽  
E. Akbil
Keyword(s):  
Kinematic Synthesis ◽  
Displacement Analysis ◽  
Gear Drive ◽  
Transmission Angle ◽  
Computer Aided ◽  
Displacement Equation ◽  
Synthesis Procedure ◽  
Motion Characteristics ◽  
Joint Consideration ◽  
Gear Drives

This paper presents an analytical and computer-aided procedure on the kinematic synthesis of the spherical two-gear drive with prescribed dwell characteristics. The first part gives a displacement analysis which includes an investigation of the general case of spherical five-link, 5R mechanisms and the spherical geared five-link case. Two approaches, one making use of the spherical trigonometric relations and the other involving sequential coordinate transformations by real and orthogonal [3 × 3] matrices, yield identical input-output expressions. The remainder of the paper focuses on the dwell characteristics of the spherical two-gear drive using algebraic methods based on the displacement equation. Dwell criteria for the general mth-order dwell are derived. A specific example which involves a joint consideration of other entire-motion characteristics, such as limit positions and transmission-angle variations, is given to illustrate both the theory as well as the computer-aided synthesis procedure.

Planar Four-Linkage Guide Mechanism Synthesis Based on Mechanical Chaos System Methods

2011 ◽  
Vol 55-57 ◽  
pp. 1009-1012
Author(s):  
Xiao Yi Che ◽  
Zhe Ming He ◽  
You Xin Luo ◽  
Qi Yuan Liu
Keyword(s):  
Initial Guess ◽  
Mechanism Synthesis ◽  
One Dimensional ◽  
Function Generation ◽  
Newton Iterative Method ◽  
All Solutions ◽  
Sensitive Dependence ◽  
Simple Realization ◽  
Chaos Sequences ◽  
First Time

The problem of four-linkage guide mechanism synthesis is transformed into nonlinear equations to be found, Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess points. For the first time, the mechanical chaos methods of mechanism synthesis and all solutions of the nonlinear questions of mechanism synthesis were found by utilizing chaos sequences of chaos motions of mechanical system to obtain locate initial points. As an example the problem of function generation for planar four-linkage guide mechanism was considered. This makes that multi-projects selecting could be possible. This method is adaptive to planar multi-linkage and spatial mechanism. This provides a new simple realization method for mechanics design.

Sign in / Sign up

Export Citation Format

Share Document