09.4 - Kinematic Analysis
Analysis of Casting Mechanism
Ideal Motion Profiles:
Output Link
The output link for the casting mechanism ideally would start in the back position and once in motion will whip forward to bring the link to the final casting position.
Displacement of Output
Figure 23. Displacement of the Output Link
Linear Velocity of Output
Figure 24. Linear Velocity of the Output Link
Linear Acceleration of Output
Figure 25. Linear Acceleration of the Output Link
Input Link
The input link for the casting mechanism is connected to the ground link that moves with the output link of the positional adjustment mechanism to move the output link of the casting mechanism.
Displacement of Input
Figure 26. Displacement of the Input Link
Linear Velocity of Input
Figure 27. Linear Velocity of the Input Link
Linear Acceleration of Input
Figure 28. Linear Acceleration of the Input Link
Mobility Calculation (Grubler's Equation):
Gruebler's Equation is vital for calculating the mobility of robotic mechanisms. It helps determine a mechanism's degree of freedom by considering the number of links, joints, and their respective degrees of freedom. Below is the calculation to determine the mobility of our casting mechanism design.
Figure 29. Mobility Calculation
Mechanical Advantage of Output/Input
The mechanical advantage of the output was determined using the kinematic velocity data obtained from analysis. By assuming power is preserved throughout the mechanism, we can plot the input velocity divided by the output velocity at each point in time to give mechanical advantage of the mechanism.
Figure 30. Mechanical Advantage of Output/Input
Animation showing linkage operation in the full range
Figure 31. Animation of Casting Mechanism
Analysis of Positional Adjustment Mechanism
Ideal Motion of Link 1:
Figure 32. Animation of Ideal Motion of Positional Adjustment Mechanism
Displacement and Linear Velocity for One Full Rotation of Link 1:
Input - 15 rpms
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Figure 33. Displacement of Positional Adjustment Mech.
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Figure 34. Linear Velocity of Positional Adjustment Mech.
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