21-07-2012, 11:39 AM
Computer Aided Analysis and Synthesis of Mechanisms
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Introduction
We have already discussed in chapters 7 and 8, the
graphical methods to determine velocity and acceleration
analysis of a mechanism. 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 a mechanism for different
positions of the crank, we have to draw the velocity and
acceleration diagrams for each position of the crank which
is inconvenient. In this chapter, we shall discuss the analytical
expressions for the displacement, velocity and acceleration
in terms of general parameters of a mechanism and
calculations may be performed either by a desk calculator
or digital computer.
Theory of Machines
The expressions for displacement, velocity and acceleration analysis are derived as
discussed below :
1. Displacement analysis
For equilibrium of the mechanism, the sum of the components along X-axis and along Yaxis
must be equal to zero. First of all, taking the sum of the components along X-axis, as shown in
Fig. 25.2 (b), we have
Synthesis of Mechanisms
In the previous articles, we have discussed the computer-aided analysis of mechanisms, i.e.
the determination of displacement, velocity
and acceleration for the given proportions
of the mechanism. The synthesis is the
opposite of analysis. The synthesis of
mechanism is the design or creation of a
mechanism to produce a desired output
motion for a given input motion. In other
words, the synthesis of mechanism deals
with the determination of proportions of a
mechanism for the given input and output
motion. We have already discussed the
application of synthesis in designing a cam
(Chapter 20) to give follower a known
motion from the displacement diagram and
in the determination of number of teeth on
the members in a gear train (Chapter 13)
to produce a desired velocity ratio.
Classifications of Synthesis Problem
The problems in synthesis can be placed in one of the following three categories :
1. Function generation ; 2. Path generation ; and 3. Body guidance.
These are discussed as follows :
1. Function generation. The major classification of the synthesis problems that arises in
the design of links in a mechanism is a function generation. In designing a mechanism, the frequent
requirement is that the output link should either rotate, oscillate or reciprocate according to a
specified function of time or function of the motion of input link. This is known as function generation.
A simple example is that of designing a four bar mechanism to generate the function y = f (x).
In this case, x represents the motion of the input link and the mechanism is to be designed so that
the motion of the output link approximates the function y.