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We used Matlab to find the proper link lengths for this linkage. The requirements were as follows:
The mechanism must be Grashof (because the linkage works with a single continuously-rotating motor)
The ground link must be no 12 inches long (to fit within device bounds)
The limits of the joint motion must be 180 degrees apart.
By using the last requirement, the Pythagorean theorem can give the relationship between three lengths: the ground link, output link,
and the sum of the coupler and driving link. The Grashof condition puts limits on the link lengths but does not dictate the lengths, so this is a bounded system
of equations that has infinite solutions. We chose an input link length of 4 inches and output length of 5 inches to maintain a reasonable mechanical advantage.
Toggle Position
Our mechanism had trouble making it through its toggle position, as shown in this video:
Given the amount of issues that we had with this particular portion of the design, we strongly suggest against designing a linkage to pass through a toggle position.
Gear Train
The gear train includes two bevel gears, one of which is attached to the coupler of the 4-bar mechanism. The second bevel gear connects to a drive shaft which
drives a 3:1 spur gear. The spur gear turns the driving link of the 6-bar mechanism, which is designed with gear teeth on the back end.
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