I'm going to demonstrate something I stole from Mike Essoudry at Carleton Jazz Camp this week. Mike explained the idea of playing any rhythm and alternating between all 4 limbs in a predetermined order. He was talking about using it for reading studies but I thought I would apply it to standard melodies.
There's a few things about this that are cool:
1. It helps strengthen your knowledge of whatever melody you're playing.
If you don't know the tune really well, the whole thing will fall apart very quickly.
2. It gets you used to playing the rhythm of a melody, without necessarily playing its pitch contour.
You're almost assigning the rhythm of the melody to different pitches. (Which, by the way, is a concept Hal Galper talks about as a way of having hip rhythms in a solo.)
3. It gets you used to memorizing (by both sound and feel) repeating pitch patterns.
This will help you be ready to repeat ideas, even while improvising.
Here's the first example. One chorus of the melody to "Straight, No Chaser". The limb pattern is LF, RH, LH, RF. You could also sing the sound of the pitch pattern as ti,ss,pa, doom or something like that to help you memorize the sound.
Here's another example. This is "Billie's Bounce" with a RH, LH, RF, LF limb pattern. The cool thing about this melody is each chorus it starts on the next limb of the cycle, so I played it 4 times to start from each place.
Obviously there many other orders of limbs you can try. You can also split up melodies between 3 limbs and use the remaining limb in a more static, timekeeping way.
That's what music is, you continually walk towards the horizon, and it just keeps moving back on you! Good luck.