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2.3 - Kinematic Analysis

2.3 - Kinematic Analysis

 

This section outlines our kinematic analysis for our final linkage design after initial prototyping phase. Below are the linkage length parameters used in our design.

Final Design Dimensions:

(center to center measure)

L2: 53.6 mm

L3: 66 mm

L4: 99.3 mm (24.4 mm from ground hole)

L5:114.7 mm

L6: 300 mm (97.2 mm from ground hole)

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Figure 1: Revised Mechanism Sketch with Labels

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Figure 2: Animation of New Design Idea

With a new arrangement like this, the output velocity is much greater than that of the prototyped design, allowing for greater shooting power. The output angle is also around 55 degrees, much closer to the optimal launch angle of 45 degrees. Because this new system still has the same number of links and joints, the mobility or degrees of freedom is still one.

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Figure 3: Ball Trajectory Plot

Assuming the motor will spin at 60 RPM, the resulting path of the ball is shown in the graph above. The ball will gain approximately 15 cm of height and travel around 0.5 m.

As the output link is the most important one, the remaining graphs will be focused on that one. Note that the ball will launch when the global input angle is approximately equal to -45 to 0 degrees. A clockwise path is also used for graphing.

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Figure 4: Plot of Output Angle vs. Input Angle

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Figure 5: Plot of Output Angular Velocity vs. Input Angle

Note that the highest magnitude is the point of interest at about 9 rad/sec, which is twice as fast as the old version at about 4.5 rad/sec.

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Figure 6: Plot of Output Angular Acceleration vs. Input Angle

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Figure 7: Plot of Output Angular Velocity Ratio vs. Input Angle

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Figure 8: Plot of Output Linear Acceleration vs. Input Angle

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Figure 9: Plot of Output Linear Velocity Magnitude vs. Input Angle

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Figure 10: Plot of Output Mechanical Advantage vs. Input Angle

Note that the mechanical advantage spikes tremendously at 250 degrees and 10 degrees as the output angular velocity approximates 0 around those times, as well as two links becoming collinear, resulting in a division by a small number inflating the chart.

 

All of these plots consider the end point at the output link where the ball will launch from.