[time-nuts] Sensing pendulum position, speed, or height

[Dr Bruce Griffiths]

Hal Murray wrot
> The hardware used for bar code scanners might be a useful starting place.  I 
> assume you would have to hack the firmware/whatever to output time/position 
> info rather than bar code data.
>
>
>
> My initial thought was that you would put one read head directly under the 
> middle of the pendulum path.  That gives you a "tick" each half cycle.
>
> With two sensors, I think you can measure the height of the swing.  It's not 
> measuring the actual height but relative to some target.  2 sensors gives you 
> 4 chunks of time per cycle: A-B, B-B, B-A, and A-A.  If you position the 
> sensors along the path symmetrically on opposite sides of the center then A-A 
> + B-B can match A-B + B-A and you can servo the kicker to produce that.  If 
> you want the swing to be higher, move A and B farther apart.  If they are off 
> center, A-A will be different from B-B and the servo filter will have some 
> lower frequency junk to filter out.
>
> Sounds like a fun tar pit.  :)
>   
Hal

A typical bar code sensor (eg HBCS1100) has a photo transistor output 
and a transition region about 200um wide.
Obtaining sufficiently stable gain to interpolate reliably will be 
difficult. A sensor like a HEDS1500 which uses a photodiode sensor would 
be a better choice as it is intended for use with a transimpedance 
amplifier. The gain of such a sensor will be more stable and 
interpolation by a factor of 10 or more should be feasible.

However a better approach is to use a grating in front of the sensor and 
a matching one on the end of the pendulum. resolution is then limited 
only by the grating period, the interpolation technique and not the 
sensor size. If one uses a pair of gratings and sensors with a 
displacement of an odd integral multiple of a 1/4 the grating period 
between the 2 detector gratings then interpolation to better than 1/100 
of a grating period is relatively easy. Averaging over several grating 
lines reduces the sensitivity to grating irregularities.

In fact a linear optical encoder (either incremental with an index 
position or absolute) would be easier to use and some encoders are 
capable of submicron resolution.

Bruce