Re: homing and stopping distance
To clarify:
All homing moves use a single-joint trajectory
planner (simple_tp) that implements a trapezoidal
velocity profile using specified maximum speed and
acceleration (vmax,amax).
Code:
if (v < vmax): v = amax * t (fixed accel phase)
then : v = vmax (fixed vel phase)
So starting (from 0 speed to vmax)
or stopping (from vmax to 0 speed)
the time taken is:
tstop = tstart = vmax/amax
Speed is the derivative of position (x) or,
alternately, position is the integral of speed
so the distance traveled while in the fixed accel
phase is:
x = Integral(v dt)
= Integral(amax*t dt)
= 0.5 * amax * tstart^2 (similary for tstop)
x = 0.5 * amax * (vmax/amax)^2
x = 0.5 * vmax^2 / amax
Example:
vmax = 500 units/sec
amax = 5000 units/sec^2
tstart = tstop = 500/5000 = 0.1
( = time to reach full speed from 0)
(or time to stop from full speed)
xstart = xstop = 0.5 * 500^2/5000
= 25 units
( = distance traveled to reach full speed)
( = or distance to stop from full speed)
Note: Velocity is a vector quantity, speed is a scalar
measure of velocity magnitude. The terms are commonly
interchanged and misused in Linuxcnc documents and pin
names.
