apply the inverse kinematic tranformation?

[Mike Betts]

Formal kinematics for robotics is a rigorous treatment to handle any robotic system, regardless of how complex it may be.

Most college courses in robotics start with position rather than velocity. They also start with forward kinematics as it yields a unique result.

In a forward kinematic equation, you can find the position of the tool tip (the end effector of your arm) given the angles of each joint. However, the inverse kinematic, calculating the joint angles for a desired tool tip position, is much harder. For a non-trivial arm, there are usually several solutions to the inverse kinematic. Many of these positions would require the arm to be in positions that are nonsensical in the real world.

Once you have positional kinematics in hand, you move on to velocity and acceleration. Figuring these out usually require calculus.

The math and physics involved is not for the fainthearted... If someone is handing you the equations for a given task, I would look hard at the gift...

JMHO,

Mike