## Analysis and Synthesis in Machine Design

written by: naveenagrawal • edited by: Swagatam • updated: 7/28/2009

To obtain the desired motion of a machine, the design has to involve analysis beforehand. Read an introduction to the design of mechanisms by analysis and synthesis.

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<<Previous Article: Kinematics – Design of Machines: Introduction

Having the concept and definition of mechanisms and machines, composed of mechanisms explained, now the discussion for design of mechanisms and machines by combining those mechanisms becomes imperative.

The design of mechanisms has two aspects, analysis and synthesis of mechanisms.

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### Analysis

This is consisted of techniques of determining the positions, velocities and accelerations of certain points on the members of mechanisms. The angular positions, velocities and accelerations of the members of mechanisms are also determined during analysis of mechanisms. By analysis of mechanisms the trajectory of particular points and the orientation of the members at particular points of time are obtained.

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### Synthesis of Mechanisms:

If the desired set of positions/angular positions, velocities/angular velocities and acceleration/angular acceleration at definite points of time are stipulated. Then the synthesis of mechanisms comprises of mathematically determining the geometry of members of mechanisms such as to produce the desired results. When that mechanism is operated it will pass through the stipulated points with the required velocity and acceleration, and the members will have the desired orientation.

Synthesis of mechanisms as per the requirement can be achieved through two ways. First, Rational Synthesis, which consists of standard synthesis techniques developed by kinematicians. Being systematic these techniques can be automated using computer programs. Limitation of rational synthesis technique is that it is applicable only to some specific types of mechanisms.

Second technique commonly used by design engineers is Informal Synthesis. This design procedure involves first a guess of dimensions of members of mechanisms and then checking the resultant performance by analysis. The dimensions are modified based on previous performance and adjusted such that to obtain results close to desired. In this way the process of iterative synthesis and analysis is repeated to obtain acceptable design.

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### Forces in Kinematics:

Although kinematics does not have forces or their analysis in its purview, but velocity profile of mechanisms have symmetry with the force profile. Thus, the construction for analysis of geometry of motion (kinematic analysis) can be appropriately extended to static and dynamic force analysis (Kinetics) of mechanisms.

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### Slider Crank Analysis and Synthesis

To have a clear distinction between the analysis and synthesis procedure let us take a concise of slider crank. Slider crank mechanism has a rotating crank, a reciprocating slider and a coupler connecting crank to the slider.

Analysis of slider crank mechanism: it will involve finding the frequency of oscillation, speed at different positions and range of motion of the slider for given angular velocity of the crank and given lengths of crank and the coupler.

Synthesis of slider crank mechanism: One or more data about the frequency of oscillation, speed at different positions and range of motion of the slider may be provided and the requisite task will be finding the dimensions of the members of the mechanism and position of the slider such as to have the desired motion of the mechanism.

Next Article takes up different types of kinematic joints.

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### References

Book: Theory of Mechanisms and Machines – Ghosh and Mallik

Book: Kinematics, Dynamics and Design of Machinery – Waldron and Kinzel.

#### Kinematics - Design of Mechanisms

Machines as simple as livers, machines such as James Watt’s steam engine and the industrial robots such as PUMA all are composed of mechanisms whether simple, complex or combination of many simple and complex mechanisms. These mechanisms are governed by Kinematics – the study of geometry and motion.
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