Kinematics of Piston
Statement of the problem
This is a simple simulation of crank-shaft system. A major application
of such system is used in the piston. Two rigid rods (Bar 1 and Bar 2)
connected through a pin joint. A mass (Mass 3) pine-connected to the end
of Bar 2 can move only horizontally. A constant torque is applied
at the fixed end of Bar 1, The velocity of Mass 3 and its relation to angular
velocity of Bar 1 are our primary concern. Since these information is very
useful in our calculation of the power needed to drive the piston (Mass
3).
Exercises
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Specify a constant acceleration (constant torque), e.g. 1.57 (rad/s),
by either moving the Slider or entering a number in the box, then
Run the program.
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Stop the program sometime after the system finishes at least one
cycle, check out both the velocity of Mass 3 and angle of Bar 1.
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You can change the acceleration of Bar 1 and let the program run again.
Watch the change of velocity of Mass 3.
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Stop the program again, go to File and Export the
Meter Data to a file then using the Excel to plot the results,
comparing them with the numerical results by the Matlab program.
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Reset the program back to its original state.
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You can try different angular velocity of Bar 1 to see what is the difference
in system response.
Think Twice
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Can you find the position(angle), velocity and acceleration of the joint
between Bar 1 and Bar 2 at any time? The generalized equations for velocity
and acceleration are
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From the above equations, find the relation between displacement of Mass
3 and angular velocity of Bar 1 and compare with your plot.
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