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Involute Interpolation Help


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hii everyone,


i am using Geobrick Turbopmac2 4 axis, and need to move tool on precise Gear Involute profile Path using Rotary Axis (c ) and Radial Axis (Y). Need to know if there is any Involute Interpolation available.

Y Axis Position = R(Theta)sin(Theta)

C Axis Position = Tan(Theta)-Theta

where (Theta) is the Roll Angle of the Gear in Radians with ® as the Base Circle Radius of the Gear.


Thanks & Regards




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PMAC does not have an 'Involute Interpolation' function, but you do have a number of choices to execute an involute curve.


1) Implement equations exactly as you have shown them, as a parametric set using theta as the parametric variable. Place these equations in a loop within a motion program using "linear blended mode" and solve for the axis values as you increment 'theta' each pass through the loop. Path speed may be an issue as you will not have direct control over this. By calculating the derivative and changing the increment of theta each pass to keep the velocity vector magnitude constant you could in effect control path velocity at the possible expense of path smoothness. Theta actually becomes a function of the unit velocity vector direction, with constant servo increment each pass.

Increasing servo loop frequency will improve smoothness by increasing how often the parametric equ's are executed. Servo loops will need to be retuned if you do alter the servo interrupt.


2) Generate a series of points by parametric method similar to #1 (NOT every interrupt, maybe 20-100 pairs) and feed these into the PVT mode, or either of the Spline modes. This may afford better path velocity control, especially in PVT mode and Spline2 mode. You'll still need to calculate the derivitives and magnitude to calculate & control path velocity. Since PMAC will be generating intermediate points by a spline algorithm, you will not need to calculate new points each interrupt. A precalculated array might be ok.


3) Use PMAC's kinematic motion capability, and program moves in PVT mode (or Spline2 ?)

This is probably the best solution if you are familiar with developing forward and inverse kinematic equations. I believe your involute path will require an iterative approach to solving the kinematics as there may not be an easy closed form solution.(?) If this is the case, three to five passes of a Newton-Raphson algorithm should do it.

You would have an R-Theta mechanism programmed in X-Y coordinates. PMAC would then take care of tool path velocity in X-Y space.


Looks like you are using an R-Theta mechanism, that is my assumption from your comments. If you are using an X-Y mechanism, then PMAC can control vector path velocity directly. Otherwise, the kinematic approach that transforms the R-Theta mechanism into X-Y will allow you to take better advantage of PMAC capabilities.


See the Turbo PMAC User Manual starting at pp259 (kinematics), 289 (spline), & 292(PVT)

also see Isx13 Segmentation Time in the "Software Users manual"

Keep in mind that whatever approach you take, new points are generated every servo interrupt; no more, no less. In #1 you are calculating them directly from your parametrics. In #2 you are generating much more coarse waypoints and then PMAC interpolates a smooth spline each servo.

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