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Intrinsic Reference Frame for the Sphere
In order to define the Zero Plane Map, we need to define a reference frame
for the sphere. This reference frame is intrinsic to the joint chain itself.
A sphere can be defined by the center, the horizontal plane, and the meridian
(zero longitude). The center is assigned to the start joint.
The pose when all the joint angles assume preferred angles is particularly
important. Lets call it the preferred pose.
We use the solver plane at the preferred pose as the horizontal plane. Since
the swivel angle is used to control the start joint, the preferred angles at the
start joint are not so intrinsic. It is also reasonable to define the horizontal
plane with the solver plane that is derived by assigning zeroes to the start
joint and preferred angles to the other joints.
The EE axis defines the meridian. The sphere is now defined as shown in the
following figure:
1. EE axis
All the joints assume preferred angles. The Zero Plane Map is to be defined
on this sphere.
3400 | Chapter 15 Animation