Now for the problem: Consider a crank mechanism with the following geometry and running condition: a = 75mm, 1 = 250mm,

N = 6000rpm constant, and mass of the piston, m = 0.1kg. For simplicity let & = a/l.

a) Calculate and show on a graph the position (the y-coordinate) of the piston as a function of the crank angle for two crank

rotations (0 = 0 to 4m) but show 8 in degrees using a crank angle increment of A0 = 4 degrees. Also, calculate the time, At, it takes

for the crank to rotate by this 4 degrees.

b) Calculate and show on a graph the piston velocity. Calculate the velocity two ways: first, the time derivative of the piston

s-sing

position is V== (1+; . Second, by using a numerical approximation V₁ = +1-1, where subscript i refers

24t

Ecose

√1-sin³6

2

to a crank angle step, while (i-1) and (i+1) refer to the previous and following crank positions; 8-18₁-A and 0+1 = 0₁ +48.

Show both results on the same graph.

c) Calculate and show on a graph the piston acceleration also two ways. You will need to derive the exact equation for

acceleration. In addition, find the approximate values of acceleration using the numerical approximation: a = -

24t

d) Knowing the mass, calculate and show on a graph the force required to accelerate the piston as a function of crank angle.

Use Excel to answer the following questions. Start from a blank Excel document; do not share

your file; do not use a shared document.

Question a: plot y(0) for 0 = 0 ... 720 with a step of 4 degrees

Question b: plot V(0) calculated two ways: using the provided equation, and using the

numerical derivative approximation

Question c: plot a(0) using the numerical approximation only

Question d: calculate and plot the force F(0)

Question e: Not included in this assignment.

A significant part of this assignment (not all) will be done during the lab time with the

instructor's assistance.