1. Based on the 2D tolerance analysis techniques [1,2], we can determine the
spatial variations of kinematic dimensions. In particular, we can use the
sensitivity ∂Tu/∂TT analysis [1,2] to identify key component dimensions in any
design. This will allow us to focus on the key dimensions that affect the
assembly dimensions u. The new technique can guide us to a new domain where
we can improve our design to achieve high product quality without significant
increase in cost. It is a new kind of design optimization, where we can achieve
an optimal balance between product quality and production cost.
(1) Select a suitable design, where nf =6 or greater and nv=2 or greater, for 2D
precision analysis. Provide assembly drawing and also component drawings for
your design and determine x. Describe your design (See the example below)
and the assembly dimensions u. Also determine nJ, nf, nv, vector chain L, Ix, Iu,
table, Φ, Φk, Φf, Ik, If, n, m, q, total number of unknowns for nv.
(2) Discuss each of assembly dimensions, ui, i=1,2,…,m+q, and explain how
quality or performance of your design is affected if ui, i=1,2,…,m+q, is changed.
(3) Identify the key component dimensions [1,2] to demonstrate the usefulness and
applicability of the lecture contents [1,2]. Determine H, ua-n,. Φka-n, Δx, Δu, ΔH,
each A element, A, each B element, B, Ti table, T0, Tu0, u, Φk, ∂Tu0/∂T0T. Based
on x, give a list of key dimensions. Also, based on T0 for making x, determine
the total manufacturing cost cm0  for making x.
Consider two approaches:
(a) The precision of each key component dimension is increased by 30%, which is
the new approach, based on the common approach of T0. For the new approach,
the total manufacturing cost cm(a)  for making x is to be examined. Based on
T0, give T(a). Also, base on T(a), determine Tu(a).
(b) The precision of every component dimension x is increased by 30%, which is
the traditional approach, based on the common approach of T0. For this
approach, the total manufacturing cost cm(b)  for making x is to be examined.
Based on T0, give T(b). Also, base on T(b), determine Tu(b).
Now compare the two approaches, (a) and (b), in terms of assembly’s precision
or quality, specifically, in terms of Tu, and in terms of total manufacturing cost
cm  for x.
(4) Determine the total manufacturing cost increase Δcm(a/b), Δcm(a/b) = cm(a/b) – cm0,
and the kinematic spatial error reduction ΔTu(a/b), ΔTu(a/b) = Tu0 – Tu(a/b). Study
the precision improvement per unit cost increase ΔTu(a)/Δcm(a). and ΔTu(b)/Δcm(b).
(5) Give your recommendation on choice of precision design approach, based on
your analysis, when upgrading product quality.
The work in (6) is optional:
(6) Based on the 2D tolerance analysis techniques together with the sensitivity
∂Tu/∂TT analysis technique [1,2], a nice precision design work can be done as
in (1)-(5). In addition, a new kind, one step further, of good design work can
also be done. This is precision based design optimization: Consider several
designs under a particular set of design specifications, try to conduct the 2D
sensitivity analysis and compare the elements in ∂Tu/∂TT and select the best
design among the several available designs.