Draw a Spinning Pinwheel
Python 2 535 517 473 468 bytes

Saved 5 bytes thanks to @Easterly Ink!

Input expected to be comma separated (i.e., numArms,armLength,numRots)

Golfed Version

n,l,t=input()
b=[7,3,1,5,0,4,2,6][:n]
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
 g=[[' 'for _ in[1]*w]for _ in[1]*h];a=j%2;b=[(k+1)%8for k in b];print''
 if a:g[Y][X:X+2]='/\\';g[Y+1][X:X+2]='\\/'
 else:g[Y][X+1]='_';g[Y+1][X:X+3]='|_|'
 for k in b:k=k+8*a;x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X;y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y;exec"g[y][x]='|/_\\\\'[k%4];x+=d[k%8];y+=d[(k-2)%8];"*l
 for k in z(h):print''.join(g[k])


Ungolfed Version

numArms, armLength, rotAmount = input()

# Choose which arms to draw
arms = [0,4,2,6,1,5,3,7][:numArms]
for i in xrange(rotAmount+1):

    # Set up the grid spacing
    maxWidth = 5 + 2 * armLength
    maxHeight = 2 + 2 * armLength
    grid = [[' ' for x in xrange(maxWidth)] for y in xrange(maxHeight)]

    # Add the base square
    angle = i%2
    startX = len(grid[0])/2
    startY = len(grid)/2 - 1
    if angle:
        grid[startY][startX:startX+2] = '/\\'
        grid[startY+1][startX:startX+2] = '\\/'
    else:
        grid[startY][startX+1] = '_'
        grid[startY+1][startX:startX+3] = '|_|'

    for armNum in arms:
        # Determine where this arm starts
        armIdx = armNum + 8*angle;
        armX = [0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][armIdx] + startX
        armY = [0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][armIdx] + startY

        # Determine the direction it travels
        d = [0,1,1,1,0,-1,-1,-1]
        dirX = [0,1,1,1,0,-1,-1,-1][armIdx%8]
        dirY = [-1,-1,0,1,1,1,0,-1][(armIdx)%8]
        sym = '|/_\\'[armIdx%4]

        # Draw the arm
        for i in xrange(armLength):
            grid[armY][armX] = sym
            armX += dirX
            armY += dirY

    # Increment which arms to draw next
    arms = [(a+1)%8 for a in arms]
    for i in xrange(len(grid)):
        print ''.join(grid[i])
    print ''


Explanation

Pretty simple when it's broken down. First figure out how big of grid is required, then plot the base square or diamond.

Each arm's starting location, symbol and direction is hardcoded in for each of the 8 possible arms for the square and diamond base. Then, drawing them is easy enough.

To rotate everything, I simply switch between the square and diamond base, then increment each of the arms, rotating them clockwise once.