Do I get it right that the pedals move, but don't stay in place?
Most timpani I know, work with an internal spring.
Normally the tension of that spring must equal the head tension, resulting in a pedal that stays where you want it to be, holding the tone you want.
If your pedals moves back / forth, you will likely have unequal spring / head tension, so you need to adjust one of the two.
I'd always first check the head tension, as this is usually the one that deviates the earliest / most.
To determine if your head tension is too low:
Check the tonal range of your timpani:
- If you can't find the highest tone that should be there normally according to the size of the timpani => head tension is too low
- If you can't find the lowest tone that should be there normally according to the size of the timpani => head tension is too high
- If the lower and upper tones are playable => timpani is in tune => head tension is correct => adjust the spring tension
Good luck and have fun!