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Vector analysis of Loop 1 yields the following position, velocity, and acceleration equations. Note that we assume the length of b is changing in this vector loop.
Position Equations:
Velocity Equations:
Acceleration Equations:
The next image is of Loop 2:
Vector analysis of Loop 2 yields the following position, velocity, and acceleration equations. Note that l7 and l3 are both changing length.
Position Equations:
Velocity Equations:
Acceleration Equations:
Computing these equations in MATLAB produces the following plots. Note, the input crank rotates 360 degrees at 10rpm (1.04 rad/s):
Plot 1: Link 3 position, angular velocity, and angular acceleration as a function of input crank angle.
Plot 2: Link 4 position, angular velocity, and angular acceleration as a function of input crank angle.
Plot 3: Slider longitudinal velocity and acceleration as a function of input crank angle.
Note, the slider achieves nearly constant velocity for roughly 180 degrees of input crank angle, followed by a quick reset to the home position.
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MATLAB animation of mechanism.