Tangent System Kinematics


Application Note Nov-2004 Tangent Following Kinematics

A common class of applications involves the requirement to keep a rotary tool tangent (or at some other fixed angle) relative to the path described by two Cartesian axes, as in the cutting blade of a jigsaw. In these applications, the path program typically only describes the path of the Cartesian axes (e.g. X and Y); it is up to the controller to derive the angle of the rotary axis from internally generated path information. If the rotary axis trajectory simply follows the XY path, and never affects the XY path or speed along the path, then the rotary axis can be put in a separate coordinate system running simple program that simply calculates the present path angle from X and Y motor registers and commands a move to this angle. That case is covered in a separate example.

However, there are a couple of reasons why the rotary angle can affect the XY path and/or speed on that path. First if the tool tip is offset from the center of rotation of the axis, the position of the X and Y-axes must be changed depending on the rotary angle. Second, if the rotary axis path required for proper

tracking of the XY path can cause the rotary axis to exceed its velocity or acceleration limits, then the XY path must be slowed to keep the rotary axis within its limits.

Both of these cases can be handled in a Turbo PMAC by putting all three axes in the same coordinate system and deriving their relationships with kinematic algorithms. Once the angle of the rotary axis is computed, the required change to the XY path location can be calculated. Because the resulting action of all 3 motors can be passed through the lookahead algorithm, all motion can be slowed in a coordinated fashion if any of the motors, including the rotary motor, is asked to exceed a performance limit. Mechanism Description

In this basic example, there is a standard XY Cartesian table using Motors 1 and 2 on Turbo PMAC, each with 1-micron count resolution. The tool is on a rotary head whose axis of rotation is about the Z-axis, so by convention, it is called the C-axis. It has a resolution of 100 counts per degree. The contact edge of the tool is offset from the C-axis center of rotation by 5 mm in the direction of motion.

Tangent System Kinematics

+X The forward-kinematics algorithm, which computes the starting axis positions of the tool edge as a function of the motor positions, can be described by the following equations:


Xmotor=Xtool ToolOffset*cos(C)

Ymotor=Ytool ToolOffset*sin(C)

To implement these equations in a Turbo PMAC forward-kinematic program for Coordinate System 1 that uses Motor 1 for X, Motor 2 for Y, and Motor 3 for C, the following setup and program could be used: Macro Substitution Definitions

Status/Control Bits using Suggested M-Variable Definitions #define Mtr1Homed M145


#define Mtr2Homed M245

Mtr2Homed->Y:$000140,10,1 ; Motor 1 home complete bit ; Bit 10 in Motor 1 status word ; Motor 2 home complete bit ; Bit 10 in Motor 2 status word

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