CDM - Kinematic Analysis
- Robert P Lopez
- Yousef S Ahmad
- Shiven Danayak
Crank-Rocker:
We decided on our lengths for the crank-rocker by plugging lengths into a MATLAB program (1) we found online that traces out the motion of a four bar crank-rocker. The combination of lengths that we felt gave us the optimal range of motion (as wide as possible without being obstructed by any shaft) were used for the final mechanism.
Slider-Crank:
We started with a desired sliding length of 3" to deal the cards. We offset the furthest most position of the slider 1.5" from the card dealing joint. This gives us 8.5" of rocker length to base the slider crank off of. Because the travel distance of the slider is double the slider crank length, we got a slider crank length of 1.5", and 7" for the slider coupler.
Figure: Basic vector analysis of the mechanism without link lengths, gear sizes or speeds. In hindsight, this type of analysis was not necessary as we decided against using a quantifiable input such as a motor.
Gear Train:
The gear ratio was chosen such that one revolution of the crank-rocker would revolve the slider-crank four times, dealing four cards along the profile of the rocker. To do this required a 4:1 gear ratio. The distance between the input and output gears needed to be 8.75" because these points are the ground link to the crank-rocker. A simple way to ensure the proper gear ratio and proper distance between centers was to use a middle gear that could take the space between the gears. Our gear ratio calculation is shown below:
(68/32)(32/17) = (68/17) = 4.
Crank Rocker Speed Analysis:
The image above shows a velocity vs time analysis of the rocker. The graph shows the response of the mechanism through two whole cranking cycles. It should be noted that this graph assumes known input velocities and accelerations, inputs that are not easily quantified in a hand-cranked mechanism such as our's, meaning that the numerical side of this analysis is not worth much to us. Nevertheless, this type of analysis gave us an idea of the relative speeds of the mechanism at different stages of rotation, something that can impact the way we choose to modify our input and could point towards possible future improvements.
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