Our latest technical report "Scaling Direct Drive Robots" by R. S. Wallace and
J. M. Selig is now available on-line. file://cs.nyu.edu/pub/tech-reports/
tr669.ps.Z

Abstract:

Recent experimental and analytical evidence indicates that direct drive robots
become very practical and economical at miniature and microscopic scales, so it
is interesting to understand quantitatively the properties of direct drive
robots under scaling transformations. This leads to a study of how screws and
their dual co-screws behave under the group of similarity transforms. This
group is the group of isometries together with dilations. Several different
representations are found on the space of screws and complementary
representations are found on the dual space of co-screws. From the
electromagnetic theory of the force and torque on a magnet in a magnetic field,
we derive the scaling properties of the electromagnetic wrench. Hence, these
results can be directly applied to the scaling of direct drive motors. We
conclude by proposing a scale-invariant measure for direct drive actuator
performance.