16] the cylindroid. 23
parallel to OR. It is desired to find the cylindroid determined by these two
screws.
In the plane POR draw OS perpendicular to OP and denote Z.ROS
by X.
The translation of length p along OR may be resolved into the components
P sin X, along OP and p cos X along OS.
Erect a normal OT to the plane of POR with a length determined by
the condition
wOT = p cos Å.
The joint result of the two motions is therefore a twist of amplitude <o
«■bout a screw 0 through T and parallel to OP.
The pitch p0 of the screw is given by the equation
wpe = a>p + p sin X,
whence pt -p = OT tan X.
In Fig. 3 we show the plane through OP perpendicular to the plane POR
in Fig. 2. The ordinate is the pitch of the screw through any point T.
If p0 = 0 then 0T=- OH. Thus H is the point through which the one
screw of zero pitch on the cylindroid passes, and we have the following
theorem;
If one screw on a cylindroid have infinite pitch, then the cylindroid
reduces to a plane. The screws on the cylindroid become a system of parallel
lines, and the pitch of each screw is proportional to the perpendicular distance
from the screw of zero pitch.
MM■!■HB