Kinematic Chain

The order of matrix multiplication is crutial for obtaining correct orientation and position information. The kinematic chain is the order that the transformation matrices are multiplied in order to move between coordinate systems.

The haptic device has an internal kinematic chain that we will not explore, but we will use the haptics coordinate at (0,0,0) using the right hand rule and with no rotation. Having the haptic device directly in front of you. The x-axis is positive to the right. The y-axis is positive to the ceiling. The z-axis is positive in the direction away from the haptic device.

The haptics has a base coordinate system that we will use as the world coordinate system. Transformations are calculated in the following ways

Haptics (World Zero) -- This is identity 4x4 matrix
Stylus (Center of Rotation) -- Calculated and Returned from HD - HD_Current_Transform
Tool Tip (TCP) -- Calibrated from reading in points
WorkPiece (Orientation) -- Read in from calibration subroutine

Kinematic Chain
Tool Tip to Haptics

T = Tool Tip x Stylus

Tool Tip to WorkPiece

T = Tool Tip x Stylus x inverse(WorkPiece)