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

Figure 33. Displacement of Positional Adjustment Mech. 

Figure 34. Linear Velocity of Positional Adjustment Mech.