Computer Aided Analysis And Synthesis Of Mechanisms 1r1o69

A TERM PAPER ON

COMPUTER AIDED ANALYSIS AND SYNTHESIS OF MECHANISMS BY

KARTIKEYA

ABSTRACT

This paper deals with the computer aided approach of analysis and synthesis of mechanism. Analysis and Synthesis of Mechanism can be performed using Graphical and Analytical approach. The present paper deal only with Analytical method, Slider Crank Mechanism is analysed and synthesised using computer aided approach.The software package is implemented as a class in C++ with member variables corresponding to the physical attributes of the mechanism and member functions which will enable the to calculate the position, velocity and acceleration of the slider as well as angular positions, angular velocities and angular acceleration at each t for different input angular velocities.

Introduction A machine is a device which receives energy and transforms into some useful work.Each part of a machine, which moves relative to some other part, is known as kinematic link.When the kinematic pairs are coupled in such a way that the last link is ed to the first link to transmit definite motion, it is called a kinematic chain.When one of the links of a kinematic chain is fixed , the chain is known as a MECHANISM.The analysis and synthesis of mechanism plays a very important role in the development of machines.The present paper deals with the analysis and synthesis of mechanisms with help of computer i.e. computer aided analysis and synthesis of mechanism with slider crank mechanism as an example.

Literature Review Arthur G. Erdman, Computer-aided design of mechanisms: 1984 and beyond (1985). Mechanism and Machine Theory, Volume 20, Issue 4, 1985, Pages 245–249 This special issue on computer-aided design of mechanisms has the objective of representing the state-of-the-art in computer-assisted mechanism analysis and synthesis. The events of the past 25 years are reviewed in this article. The brief look at today and the potential future of this fast-growing area are meant to set the stage for this special issue of Mechanism and Machine Theory. Rattan, SS, Theory of Machines 3e (2010). Computer Aided Analysis and Synthesis of Mechanisms, Pages 124-140, 159-175 Analysis and Synthesis of Slider Crank mechanism and Four bar chain mechanism is dealt in the text with analytical methods using computers or desk calculator. Author used complex algebra and vector method for analysis of mechanisms and for synthesis Path generation, Function generation and Motion generation are the topics of prime focus. Proctor, Sean, Nalaka Kahawatte, Design Project - EME 152, Department of Mechanical and Aeronautical Engineering University of California, Davis This report discusses the design of a software package which will be useful in computer -aided design And analysis of a crank slider mechanism similar to one showed in the cover page. The software package is implemented as a class in C++ with member variables corresponding to the physical attributes of the Mechanism and member functions which will enable the to calculate the position, velocity and Acceleration of the slider as well as angular positions, angular velocities and angular acceleration at each t for different input angular velocities. Once the initial attributes of the mechanism such as the link lengths are defined, this software package will enable the to inspect the motion of the mechanism using an animation.

Problem Definition We already knew that graphical methods to determine velocity and acceleration analysis of a mechanism are present.It may be noted that graphical method is only suitable for determining the velocity and acceleration of the links in a mechanism for a single position of the crank in order to determine the velocity and acceleration of the links in the mechanism for different position of crank, we have to draw the velocity and acceleration diagrams for each position of crank which is inconvienent.So, analytical expressions for displacement, velocity and acceleration in of gerneral parameters of mechanism are discussed with help of computers.

Proposed Methodology Performing position, velocity and acceleration calculations by hand while deg a mechanism is tedious and a design iteration involving a minor change is time consuming. Therefore computer-aided design and analysis methods have proven to be the most effective tool for a mechanism designer.A program in C language is compiled to solve the equations for respective values of variables.

Analysis

Slider crank mechanism

Position Analysis

The kinematic analysis is done using vector loop closure method, where each link is represented by vector and equations are written in of these vectors. For example, the position vector of B can be written in 2 ways; r2+ r3 or r1+r4. Therefore first loop closure equation becomes

(1)

Using the same method, using the position vector for point C, the second loop closure equation can be written as (2)

This vector representation can also be written in polar format where a vector can be represented by its length and orientation (counter clockwise angle respect to positive x direction). Hence the above equations can be written as. (3) (4)

Once certain values are known, we can solve for the unknowns using complex numbers. The C++ interpreter, Ch., comes with functions such as complexsolvePP (), complexsolveRR, complexsolvePR () to solve for the unknowns depending on what they are. Please refer to 'The Ch. Language Environment Reference Guide' to learn more about the complex solve functions.

.

Velocity Analysis Working off of the loop closure equations, angular velocities can be found by taking the first derivative. For example, taking the first derivative of equation 3 and 4 will yield,

(5) Since r2, r3, r1, r4 and

are constant, the above equation reduces to (6)

Likewise the derivative of equation (4) can be also be taken as

(7) Since r7, r4, r5 and

are constant, the above equation is simplified to (8)

Please note that for the above mechanism, r8 is not constant, therefore the derivative of r8 stays in the equation. As discussed above, complex solves functions provided with the Ch environment can be used to solve for the unknowns.

Acceleration Analysis To find angular accelerations and slider acceleration, the derivative of equations (6) and (8) can be taken as.

(9) (10) Once the position and velocity calculations are done, there'll be enough known variables to be use Complex solves functions to find unknown angular accelerations and the slider acceleration.

The initial setup file will automatically copy the function file and the header file to appropriate folders inside the Ch directory location the specifies. The following sample program illustrates the use of the CMechanism class and functions.

#include int main (){ CMechanisma; double theta2=45*M_PI/180, omega2=-15, alpha2=0, theta8; double r[1:8], theta1=10*M_PI/180, beta=30*M_PI/180; double rp=2.5, numpts=361, x; double complex z; lot plot; bool unit = false; r[1]=5.5; r[2]=1; r[3]=3; r[4]=4.5; rp=2.5; r[5]=8; r[7]=3; theta8=M_PI/2; a.uscUnit(unit); a.setLinks(r[1], r[2], r[3], r[4], r[5], r[7], rp, theta1, beta); a.setNumPoints(numpts); a.setAngVel(omega2); a.setAngAccel(alpha2); a.plotSliderVel(&plot); a.plotSliderPos(0.0, 360.0); a.animation(); a.displayPosition(theta2, QANIMATE_OUTPUTTYPE_DISPLAY); return 0 ; } Program 1 : Sample Program to show CMechanism functionality

#include includes the header file for CMechanism which includes the class definition. Within the main program , the statement CMechanism a; declares an instance of the crank-slider mechanism. The statement a.uscUnit(1); Specifies whether US customary units or SI units are used to specify

dimensions. The line a.setLinks(r[1], r[2], r[3], r[4], r[5], r[7], rp, theta1, beta); sets the lengths of links 1 through 7, theta1, rp and beta which are constant and known for the mechanism. If not specified, the CMechanism class will assign the following default values to the mechanism Table 2 : Default Values Link 1 2 3 4 5 6

r (m) 5.5 1.0 3.0 4.5 8.0 0.0

mass (kg) -0.8 2.4 1.4 2.0 0.3

Ig(kg · m2) -0.012 0.119 0.038 0.040 0.000

C. G. rg (m) -1.25 2.75 2.5 3.0 0.0

 -300 150 30 0 0 0

The statement a.setNumPoints(numpts); sets the number points which will be used for plotting. Usually for position analysis, theta2 angle is known and for velocity and acceleration analysis, omega2 and alpha2 are specified. The following statements are used to set these known angular velocity and angular acceleration. a.setAngVel(omega2); and a.setAngAccel(alpha2); The lines a.plotSliderVel(&plot); a.plotSliderPos(0.0, 360.0); plots the slider position and velocity with respect to the input link position. Finally the animation for the defined mechanism can viewed by calling a.animation();

Conclusion The functions used in computer program can be identified from the articles in references section. Computer aided approach is gives result of more accuracy than geometrical approach. Equations formed and be solved for variables using computers.

References 1. http://en.wikipedia.org/wiki/Mechanism_(engineering) 2. http://www.brighthub.com/engineering/mechanical/articles/6251.aspx 3. http://www.sciencedirect.com/science/article/pii/0094114X85900291 4. http://www.nakamechatronics.com/projects/coursework/reports/CMechanism_Proctor_Ka hawatte.pdf 5. Khurmi R.S. and J.K. Gupta Theory of Machines, S. Chand Publishers, 2011 6. Rattan S.S. Theory of Machines, Tata McGraw-Hill, 3rd Edition, 2009