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.

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.

Function Generation With Finitely-Separated Precision Points Using Geometric Constraint Programming

2006 ◽  
Author(s):  
Edward C. Kinzel ◽  
James P. Schmiedeler ◽  
Gordon R. Pennock
Keyword(s):  
Constraint Programming ◽  
Computer Aided Design ◽  
Linear Equations ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Function Generation ◽  
Design Software ◽  
Aided Design ◽  
Four Bar Linkage ◽  
Non Linear Equations

This paper explains how Geometric Constraint Programming can be applied to solve function generation problems with finitely-separated positions using a number of different mechanisms. Geometric Constraint Programming uses the sketching mode of commercial parametric computer-aided design software to create kinematic diagrams whose elements are parametrically related so that when a parameter is changed, the design is modified automatically. Geometric constraints are imposed graphically through the user interface, and the numerical solvers integrated into the software solve the relevant systems of non-linear equations without the user explicitly formulating those equations. A key advantage of using Geometric Constraint Programming for function generation is that the same approach can be applied to any mechanism, so no unique algorithms are required. Furthermore, because the implementation is relatively straightforward regardless of the chosen mechanism, the designer can quickly and easily generate solutions for a large number of precision points and/or with complex mechanisms to provide a very accurate match to the desired function. Examples of function generation with a four-bar linkage, a six-bar linkage, and a seven-bar linkage illustrate the benefits of the proposed methodology.

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.

Over-Constrained Mechanisms Derived From RPRP Loops

2018 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu
Keyword(s):  
Computer Aided Design ◽  
Random Search ◽  
Modular Approach ◽  
Input Output ◽  
Assembly Strategy ◽  
Revolute Joints ◽  
Computer Aided ◽  
Prismatic Joints ◽  
Aided Design ◽  
Four Bar Linkage

This paper addresses the assembly strategy capable of deriving a family of over-constrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of over-constrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of over-constrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer aided design (CAD) software and their mobility were validated with input-output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of over-constrained mechanisms.

Kinematics Synthesis of Linkage Mechanisms With Cam Integrated Joints for Controlled Harmonic Content of the Output Motion

2004 ◽  
Vol 126 (1) ◽  
pp. 135-142 ◽  
Author(s):  
Lifang Yuan ◽  
Jahangir S. Rastegar
Keyword(s):  
Closed Loop ◽  
Vibrational Excitation ◽  
High Harmonic ◽  
Harmonic Component ◽  
Primary Source ◽  
Effective Length ◽  
Linkage Mechanism ◽  
Function Generation ◽  
Harmonic Content ◽  
Four Bar Linkage

A new method is presented for the modification of the output motion of linkage mechanisms with closed-loop chains using cams positioned at one or more of its joints. As an example and to present the basic concept, the method is applied to a four-bar linkage mechanism that is synthesized for function generation for the purpose of eliminating the high harmonic component of the output link motion. By eliminating the high harmonic component of the output motion of a mechanism, the potential vibrational excitation that the mechanism can impart on the overall system, including its own structure, is greatly reduced. The resulting system should therefore be capable of operating at higher speeds and with increased precision. For mechanisms with rigid links, the primary source of high harmonics in the output motion is the nonlinearity of the kinematics of their closed-loop chains. With the present method, a selected range or ranges of high harmonic motions generated due to such nonlinearities may be eliminated by integrating appropriately designed cams that are used to vary the effective length of one or more of the links during the motion. A numerical example is provided together with a discussion of the related topics of interest.

Overconstrained Mechanisms Derived From RPRP Loops

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Kuan-Lun Hsu ◽  
Kwun-Lon Ting
Keyword(s):  
Computer Aided Design ◽  
Random Search ◽  
Modular Approach ◽  
Input Output ◽  
Assembly Strategy ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Overconstrained Mechanisms ◽  
Aided Design ◽  
Four Bar Linkage

This paper addresses the assembly strategy capable of deriving a family of overconstrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of overconstrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of overconstrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer-aided design (CAD) software and their mobility were validated with input–output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of overconstrained mechanisms.

scholarly journals Modeling of Sewage Networks with Computer Aided Design Software

1970 ◽  
Vol 66 (2) ◽  
Author(s):  
Nicoleta SCARLAT ◽  
Severin CAZANESCU ◽  
Simona MALUREANU MALUREANU
Keyword(s):  
System Design ◽  
Computer Aided Design ◽  
Full Range ◽  
Design Phase ◽  
Engineering Project ◽  
Software Application ◽  
Hydraulic Design ◽  
Computer Aided ◽  
Design Software ◽  
Aided Design

Computer Aided Design (CAD) software plays an important role in the design phase of any engineering project. URBANO software application includes CANALIS - module for wastewater system design. CANALIS is a specialized application developed to help the designer to perform the process of sewage and hydraulic design of network of any size, by the aid of computer. With specific tools and features included, CANALIS offers a full range of possibilities for the designer to draw, label, dimension and plotting the drawings of the sewage networks.

A New Approach for the Reduction of Vibrational Excitation in Kinematics Synthesis of High Speed Linkages

2000 ◽  
Author(s):  
L. Yuan ◽  
J. Rastegar
Keyword(s):  
High Speed ◽  
Closed Loop ◽  
Vibrational Excitation ◽  
High Harmonic ◽  
Harmonic Component ◽  
Primary Source ◽  
Linkage Mechanism ◽  
New Approach ◽  
Function Generation ◽  
Four Bar Linkage

Abstract A new method is presented for the modification of the output motion of linkage mechanisms with closed-loop chains using cams positioned at one or more of its joints. In particular, the method is applied to a four-bar linkage mechanism that is synthesized for function generation for the purpose of eliminating the high harmonic component of the output link motion. By eliminating the high harmonic component of the output motion of a mechanism, the potential vibrational excitation that the mechanism can impart on the overall system, including its own structure, is greatly reduced. The resulting system should therefore be capable of operating at higher speeds with increased precision. For mechanisms with rigid links, the primary source of high harmonic motions is the nonlinearity of the kinematics of closed-loop chains. With the present method, the higher harmonic motions generated due to such nonlinearities are eliminated by the integration of appropriately designed cams that are used to vary the effective link lengths. A numerical example is provided together with a discussion of the related topics of interest.

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.

Analysis and Design of Cam-Driven Mechanisms With Nonlinearities

1973 ◽  
Vol 95 (3) ◽  
pp. 685-694 ◽  
Author(s):  
F. Y. Chen
Keyword(s):  
Computer Aided Design ◽  
Degrees Of Freedom ◽  
Lumped Parameter Model ◽  
Analysis Tool ◽  
Analysis And Design ◽  
Lumped Parameter ◽  
Method Of Solution ◽  
Parametric Studies ◽  
Rational Procedure ◽  
Aided Design

The cam-and-follower mechanism is represented by a lumped parameter model of finite degrees of freedom, in which nonlinear system parameters may be taken into account. An approximate dynamic analysis of the system excited by either functional or numerical form of the base motion of a cam is obtained. The method of solution which uses an interpolating polynomial for approximating the excitation function and mechanical quadrature for evaluating the convolution integral is well suited for computer programming. A digital computer program for analysis based on this scheme is developed. In order to utilize the analysis tool for design purposes, parametric studies are conducted, design stratagems are presented and a rational procedure of closed loop computer-aided design is outlined and discussed.

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