Closed-loop belt differential actuator

Let me start a discussion about pros and cons of the interesting linear belt drive kinematics.

Assumptions:

• Static plate with two motors with timing pulleys ( A, B ) and two idlers;
• Moving plate with two idlers;
• Closed-loop belt;
• Moving plate is constrained in single axis.

This system has several modes of operation based on the difference of rotational speeds of motors.

1. If A and B have the same angular speed (same RPM if pulleys have same number of teeth), then moving plate position is not changed, belt just runs through the loop. This is a useless mode.

2. If one pulley is spinning, while the other is blocked - this is a simple block and tackle mechanism, so the moving plate will travel for a half of pulley circumference.

3. If pulleys are spinning in the same direction, but with the small difference in angular speeds - the amount of belt passed through the each side will be slightly different and the moving plate will move the half of this difference.
For example, the GT2 40 teeth pulley on motor A will move 80mm of the belt, while the same pulley on motor B will spin faster and move 82mm of the belt (one tooth more). This will take 2mm of belt from one side and push it to another, and this will cause the moving plate to change its position for 1mm. The system acts as a reducer - the movement of 82mm of belt is transformed to 1mm.

4. Last mode is when the pulleys spinning in opposite directions - this will cause the loop halves to change their lengths faster that for 2nd mode, but limited with the sum of angular speeds of both pulleys.

Result:
In such configuration this linear actuator can provide reduction rates (from pulley surface speed to moving plate speed) from 1 to "infinity".



Also it can be reworked to the rotational joint with the same properties:




Pulleys can be arranged for fixed reduction rates and be driven with a single motor with the same RPM, but with different amount of teeth (eg 40 and 41).

I did a version with coaxial pulleys with moving idlers in the perpendicular plane to join two stacking halves of the drive, but it is a hell to create a drawing for it. I'll try if it will gather some interest.

Different arrangement with fixed reduction ratio: