LinuxCNC S-Curve Accelerations
- Aciera
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05 Apr 2026 08:14 #345191
by Aciera
Replied by Aciera on topic LinuxCNC S-Curve Accelerations
I agree.The proposal on the table is a new modal G64.1 P Q
jerk-aware continuous path mode that behaves like G64 P Q but adds automatic full stop fallback when the jerk-constrained cornering velocity rounds to zero. Off by default to preserve existing behavior, opt-in for integrators who need provably clean command streams or are running drives without internal interpolation. That seems like the right balance between being true to the physics and being useful across the wide range of hardware LinuxCNC runs on.
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- ewlsey
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05 Apr 2026 15:47 #345201
by ewlsey
Centripetal acceleration is v^2/r and centripetal jerk is v^3/r^2.
My back of the envelope math says the maximum velocity at a 45 degree junction with .01mm deviation would be .0056 m/s or .336 m/min to keep centripetal acceleration at 5 m/s^2. That would produce a centripetal jerk of 4568 m/s^3, which is an order of magnitude over the limit.
To keep the jerk within the limit, the maximum velocity at the junction would be .001243 m/s or .0745 m/min. At that velocity it would take 8ish servo cycles to traverse the radius.
But, for all intents and purposes, it's basically a full stop.
Wouldn't it be pretty simple to find the maximum junction velocity to keep both jerk and acceleration within the limits of each axis? We have everything we need to make that calculation. Interestingly, since corner tolerance, max accel, and max jerk are constants, this velocity limit is only dependent on the angle. That would make it pretty easy to use a look up table generated by the tolerance setting.
onehossshay.wordpress.com/2011/09/24/imp...cornering_algorithm/
Replied by ewlsey on topic LinuxCNC S-Curve Accelerations
I don't think it's actually zero, but it's pretty close.@ruediger123
For your exact parameters: 1ms cycle, 50 m/s³ jerk, 5 m/s² acceleration, P0.01 on a 45° corner, the only cornering speed that mathematically fits within the jerk limit on a 1ms grid is zero.
Centripetal acceleration is v^2/r and centripetal jerk is v^3/r^2.
My back of the envelope math says the maximum velocity at a 45 degree junction with .01mm deviation would be .0056 m/s or .336 m/min to keep centripetal acceleration at 5 m/s^2. That would produce a centripetal jerk of 4568 m/s^3, which is an order of magnitude over the limit.
To keep the jerk within the limit, the maximum velocity at the junction would be .001243 m/s or .0745 m/min. At that velocity it would take 8ish servo cycles to traverse the radius.
But, for all intents and purposes, it's basically a full stop.
Wouldn't it be pretty simple to find the maximum junction velocity to keep both jerk and acceleration within the limits of each axis? We have everything we need to make that calculation. Interestingly, since corner tolerance, max accel, and max jerk are constants, this velocity limit is only dependent on the angle. That would make it pretty easy to use a look up table generated by the tolerance setting.
onehossshay.wordpress.com/2011/09/24/imp...cornering_algorithm/
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