Day 11 - Calculate the Lever Arm
Each cup weighs about 75 grams, including the gravel inside. But you will need to apply more than 75 grams of force to lift each cup due to the effect of mechanical advantage. Normally we apply mechanical advantage so that the output force will be greater than the input force - indeed, that is the way many hydraulic systems are structured. but with hydraulic arms, we have syringes that are positioned close to pivot points so that our output distance is as big as we can achieve using syringes. As a reminder, the mechanical advantage of a lever is equal to the length of the input arm divided by the length of the output arm. In this case, the input arm is actually shorter than the output arm, meaning that we are going to apply more than 75 grams of force to lift the cup.
Today you are expected to frame up the arm of your device and measure the distance of both the input and output arms for each part of your device. The input arm is measured from the pivot point to the location where the syringe pushes on the arm; the output arm is measured from the pivot point out to where the cup is. Although you have not begun to build the end of the arm, you should still be able to determine the distance from the base of the arm to the cup - and thus you can calculate the maximum force required to lift any of the 5 cups and drop it in the bin.
I should also point out that the work submitted on your hydraulic worksheets reflected a poor grasp of the concept of hydraulics and that means we're going to have to do more work on it - leading up to a test. I need you to understand how mechanical advantage shapes hydraulic design work and how it affects (and limits) the performance of your hydraulic arms. We'll save that for Day 18 of this unit (Pascal Review) and then we'll test on Day 20. Just know this stuff is coming....
Hydraulic calculations
- calculate the area of a circle (Acircle = πr2).
- calcuate the mechanical advantage of a system (M.A. = Fout/Fin)
- know that in general, output distance traveled must be multiplied by M.A. of the system to know input distance traveled
- calculate the volume of a cylinder (Vcylinder = πr2h)
- calculate the radius of a circle given its diameter (r = d/2, or d = 2r)
- know that in general, M.A. = Fout/Fin = Aout/Ain = Δhin/Δhout
- hydraulics
- the branch of engineering concerned with the conveyance of liquids through pipes and channels, especially as a source of mechanical force or control.
