A System for Automated Fixture Planning with Modular Fixtures

33.1. Application of Screw Theory
Screw theory can be applied to check part rotation due to active hture components after the part is
located and supported by passive fixture components. Here, we have only considered fixture plans with
overhead clamps and future plans with a vise. While fixture plans with overhead clamps or a vise
kinematidy allow translation onto the plane X-Y and romtion about the Z axis. these motions are
resuained by friction berween fixulre components and the part (Figure 3-4). Also, the configuration of
fixture components in fixture plans with overhead clamps ot a vise always resuains uanslation along the Z
axis. Thus, it is only necess;ny to check whetha a clamp 01 a vise can rotate the part about the X OT Y axis.
When a part is subject to a set of external forem (meaches), a pmsible motion can be represented by a
mew t=(t,.r2,r3;t4.t5.t~ where tl. $* and $ represents rotational motion about the X. Y and Z axis
respectively and h. 4, and represents tmslationaJ motion along the X, Y and Z axis respectively. For an
active fixture component not to rotate tbe part, components t, and 5 in t should have only trivial solutions,
since non-trivial values in any component of a twist represeot the exiSrence of motion caused by a set of
wrenches.
A fix- plan with clprmps ~ A
X
t
thm. plan wi tha vise
Figure 3-4: Unreslrained motions in tixm plans with overhead ciamps or a vise
A fixture plan with overhead clamps
Wbenapartissu~byabsseplateorasubplate,eachvertwofreference~touchinga~
plaeorasubplate can be described by a wreoch (see Figure3-5). When apart is qprted by a few
suppas, each support can be described by a wrench. In addition, a candidate clamp loation can also be
described by a wrench.
From resuits of mew theory, geomemic reasoning can be used to detect part rotanon due to clamping.
The part will rotate if the projection of the clamp location to tbe base plate lies outside of a convex polygon