Three blocks a, b, and c and a grooved block d have dimensions a, b, c, and d as follows: a 5 1.500 6 0.001 in b 5 2.000 6 0.003 in c 5 3.000 6 0.004 in d 5 6.520 6 0.010 in d a b b c d a w c (a) determine the mean gap w and its tolerance. (b) determine the mean size of d that will assure that w $ 0.010 in.

solution:

a) The mean value of gap w̅ is given by,

w̅ = d̅ - a̅ - b̅ - c̅

w̅=06.520-0.150-2.000-3.000

w̅=0.020 in

bilateral tolerances of the gap is given by,

tw = ∑t

tw = 0.001+0.003+0.004+0.010 = 0.018 in

w = 0.020 ± 0.018 in

b) if wmin = 0.010 in, then

w̅ = wmin + tw

w̅ = 0.010 + 0.018=0.028 in

mean size of d is

d̅ = a̅ + b̅ + c̅ + w̅

d̅ = 1.500+2.000+3.000+0.028

= 6.528 in