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Lecture 13: Understanding IK solvers 

Taken from the Maya Help Documentation 
IK solvers
IK solvers are the mathematical algorithms behind the IK handles. IK solvers calculate the rotations
of all the joints in a joint chain controlled by an IK handle. The effect an IK handle has on a joint
chain depends on the type of IK solver used by the IK handle.
IK solver calculations
When you move an IK handle, the solver performs the appropriate calculations to move and rotate
all the joints in its IK chain accordingly. First, the solver looks at the position (Translate X, Y,
and Z attributes) and orientation (Rotate X, Y, and Z attributes) of the IK handle. Next, the solver
calculates how to move the position and orientation of the end effector as close to the IK handle's
position and orientation as possible. To do that, the solver calculates how to best rotate the joints
in the IK handle's joint chain. Finally, the solver then rotates all the joints in the joint chain so
that the end effector reaches the IK handle's position and orientation.
Single Chain solver
A single chain IK handle uses the single chain solver to calculate the rotations of all the
joints in the IK chain. Also, the overall orientation of the joint chain is calculated directly by
the single chain solver.
Difference between single chain and rotate plane IK handles
The difference between a single chain IK handle and a rotate plane IK handle is that the single
chain IK handle's end effector tries to reach the position and the orientation of its IK handle,
whereas the rotate plane IK handle's end effector only tries to reach the position of its IK handle.
Since the rotate plane IK handle's end effector only tries to reach the position of its handle, the
resulting joint rotations are more predictable. For the rotate plane IK handle, the orientation of
its entire joint chain is controlled by the twist disc manipulator.
Note
If your joint chain is suffering from flipping, use the rotate plane solver instead of the single
chain solver. The rotate plane solver was introduced with the pole vector to control the flipping of
IK chains that you sometimes get with the single chain solver.
Handle Wire
The handle wire is the line that runs through all the joints and bones in a joint chain controlled
by an IK handle. The handle wire begins at the start joint's local axis and ends at the end joint's local axis.
Handle vector
The handle vector is the line drawn from the start joint of the IK chain to the IK handle's end joint
(end effector). This is the axis used by the rotate plane.
Rotate Plane solver
A rotate plane IK handle uses the rotate plane solver to calculate the rotations of all the
joints in its IK chain, but not the joint chain's overall orientation. Instead, the IK rotate
plane handle gives you direct control over the joint chain's orientation via the pole vector and
twist disc, rather than having the orientation calculated by the IK solver. The single chain solver
and rotate plane solver differ in this respect.
The rotate plane solver is ideal for posing joint chains (such as arms and legs) that you want to
stay in the same plane. For example, the shoulder, elbow, and wrist joints of an arm driven by a
rotate plane IK handle all stay within the same plane as the elbow rotates. The plane itself can be
rotated from the shoulder joint by the pole vector.
Rotate Plane IK handle components
Twist disc
The twist disc is a manipulator that you can use to twist or rotate the joint chain. The twist
disc is located at the end joint of the IK chain.
Translating the pole vector often leaves the IK chain pointing in the wrong direction. You can
use the twist disc to reorient the plane after you move the pole vector to prevent flipping.
Joint chain plane
The joint chain plane is the plane that contains all the joints in the joint chain and poses
through the axis. The joint chain plane rotates about the handle vector. When you manipulate the
pole vector, you are rotating the joint chain plane about the handle vector.
Reference plane
For the joint chain plane to rotate and twist the joint chain, the plane must rotate relative to
some other plane so that the degree of twist can be measured. The plane that the joint chain plane
rotates relative to is the reference plane.
Pole vector
The pole vector is a manipulator that lets you change the orientation of the IK chain. The pole
vector also lets you control flipping.
Since moving the pole vector changes the orientation of the reference plane, moving the pole
vector can also change the orientation of the joint chain directly; just as manipulating the twist
disc can change the orientation of the joint chain. This is because the joint chain's degree of
orientationor twistis defined as the difference in orientation between the reference plane and
the joint chain plane.
Warning
When positioning your IK handle, if the handle vector and the pole vector cross each other or
point in exact opposite directions, the joint chain can suddenly flip. You can prevent this
flipping by moving the pole vector so that the handle vector does not cross it or point in the
opposite direction from it.
Rotation disc
The rotation disc is an indicator that displays how much the IK chain has been rotated by the
twist disc. The rotation disc is located at the start joint of the IK chain.
Reference plane indicator
The reference plane indicator is the green dot on the rotation disc that moves to reflect the
movements of the pole vector.
Twist indicator
The twist indicator is the green arc between the reference plane indicator and the joint chain
plane indicator on the rotation disc. The twist indicator displays the orientation of the joint chain
relative to the reference plane.
Joint chain plane indicator
The joint chain plane indicator displays the orientation of the joint chain plane relative to the
reference plane. The joint chain plane indicator appears in the rotation disc.


