Contiuously Variable Transmission for Serial Link Cobot Architectures
1
Carl A. Moore
Masters Thesis, Northwestern University
1997 NWU
http://lims.mech.northwestern.edu/camoore-lib/cvtthesis.pdf
There are robotic applications in which the human user works in direct
physical contact with the robot.  Examples include surgical robotics,
haptic display, and trajectory enhancing systems. Because safety and
stability are of major concern in these systems, passive robots, which
are intrinsically safe and stable, are attractive solutions. A cobot
is a new type of passive robotic device created for use in these
applications.  Cobots have no joint actuators. Instead, they employ
nonholonomic joints that redirect undesirable user motions rather than
fight them.

The scope of this thesis is the creation and study of a nonholonomic
joint called a continuously variable transmission (CVT). The CVT will
be used to create cobots with serial link architectures. A cobot with
n links uses n-1 CVTs to couple the rotations of each consecutive pair
of joints. Each CVT is computer controlled to set the angular velocity
ratio of the two joints that are coupled to it. With all the cobot's
joints set to rotate in a particular ratio, its end point is
constrained to a particular trajectory through space.

Cobots aid the user in task completion by providing virtual
constraint surfaces that guide the user's motion.  For example, a
cobot could be used to constrain the motion of a surgeon's cutting
tool to a trajectory that was programmed pre-operatively. Or as part
of a haptic display system, a cobot could provide virtual walls for a
person pushing on its end effector.

When a force on a cobot's end effector is applied perpendicular to a
constraint surface, torques are created in the cobot's joints. These
torques produce joint angular velocity error causing the end effector
to leave the desired path and penetrate the constraint surface. At
some value of applied force, the torques become too great, and the
constraint surface is catastrophically violated.

In this thesis, a model of the friction forces that support joint
torques is developed. From the model, equations are derived to relate
joint angular velocity error to joint torque magnitude. The maximum
sustainable joint torques are also calculated. I find that the
relationship between joint angular velocity error and joint torque is
a function of the angular velocity ratio of the joints. Experiments
have been done to test the friction model and to yield additional
information on CVT dynamics and resulting cobot performance. The
results are used to determine what design changes can engender the
creation of robust constraints.