Motion sensor that senses motion not the change in temp

I'd also go with "have you tried it"?
or/ Hang a bulb off the wooden arm.

 

You could mount a resistor on the lever arm, in view of the PIR sensor, and provide enough current to it to raise its surface temperature above ambient by a few degrees... amount necessary depends on sensitivity of the PIR.

You may possibly not understand how a PIR sensor works. Typically there are two pyroelectric sensing elements connected in series opposing. Here is a link to a website that has a basic explanation.

Each sensor element produces an electrical output only when its temperature is changing. That means they cancel each other out when their common ambient temperature rises or falls. However, the field-of-view (FOV) of each sensor element is slightly different, by virtue of the two elements being physically separated and a plastic Fresnel lens focusing two slightly different (displaced) images on the sensors. When motion occurs in the FOV, one sensor will produce an output signal that is the opposite polarity to the other sensor. Since they are connected in series opposing, this differential signal represents motion across the FOV. In actuality there are many Fresnel lenses, arranged to cover a volume of space with overlapping FOVs, for any practical PIR. You can cover individual lenses with aluminum foil to limit the motion detection area and therefore prevent false-positive motion detection.

 

Instead of having a heater on the arm you could illuminate it with an IR LED so that reflected IR gets to the PIR sensor.

 

That is a good idea, but I am not sure it would work because of the way pyroelectric detectors respond to infrared radiation: their bulk temperature changes, which is what causes their embedded charge to change. An IR LED might not provide enough power to significantly raise the temperature of the pyroelectric. It's worth a try however!

If the IR LED doesn't work with a PIR sensor, it might still work with an IR photodiode by specular reflection from a small mirror attached to the wooden lever arm. Or, perhaps a small incandescent radiant heat source (a tungsten lamp perhaps?) could be used to raise the temperature of the wooden lever arm high enough above ambient for motion detection by a PIR sensor.

 

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I would use ultrasonic sensor or laser if the sensor can be installed close to the lever.

 

A couple of questions; I'm guessing that all you need is to tell whether the arm has moved, is that right? Also that you don't want to connect anything to the arm. How about a magnet fitted to the arm and a Hall Effect device? Very cheap and reliable.