18.3- Kinematic Analysis

Kinematic Analysis:

The primary profiles of interest for our team is the position of the slider joint as a function of the input angle, as well as the force experienced at that joint as a function of the input angle.

• Position: Our plans are to have a total working space of around 8 inches above our bed/conveyor belt. We intend to achieve this by using a 4 inch crank that will revolve a total of an 8 inch swing across its full motion path, but this will be verified by our position analysis.

• Force: Our plans are to attach a probe at the slider joint that will hold a strain gauge or limit switch to determine when sufficient contact is made with the sample. Regardless of the equipment we opt for, we will still need our gauge/switch to be sensitive the the range of forces that we can expect the slider joint to be experiencing. This is where our acceleration analysis will come into play, since we can determine the force using the product of the mass of our probe (estimated to be around half a pound, generously) and the acceleration of the joint.

The results of our kinematic analysis is shown below:

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Figure 1. Kinematic Analysis of 4-Bar Slider Crank Mechanism

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Figure 2. Force Analysis at 4-Bar Slider Joint

From our analysis, we can confirm a total range of motion for our slider crank to be 8 inches, as shown in Figure 1, and from Figure 2 we can obtain the range of forces we need to be sensitive to in terms of contact forces on the probe.

• Geneva Drive: Also shown in Figure 1 is a plot of the input angle to our system as driven by the Geneva Drive as a function of time. This is important since we will be using the fact that a Geneva Drive inherently has a constant timing per cycle to calibrate our height readings. In other words, because the Geneva Drive’s dwell and motion periods follow a consistent pattern, we can determine the amount of time that has passed before our probe contacts the sample at a point and directly convert that timing into a distance reading by cross-referencing the position plot to our timing plot. It’s important to note that the period of the timing plot (i.e. time from dwell to dwell) is based on the angular velocity of the DC motor (from spec) since the DC motor will be a direct input to the Geneva Drive, but the slope of the motion interval will be based on the angular velocity experienced by the slider crank mechanism, which is 1/4 of the angular velocity of the DC motor due to the 1:4 gear reduction.

For our slider crank mechanism, 180 degrees of rotation would attribute towards moving the slider downwards, while the other 180 degrees of rotation would bring the slider back upwards towards the starting position. Currently, our design intends to use only 180 degrees of rotation (and then we will reverse the motor direction) in order to avoid the collinear alignment of all our links which would otherwise produce an indeterminate motion based on our Grashof Condition (Class III).

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