• In wearable robots, number of the actuators is important because the users should carry the robot.

• Therefore, researchers have used numerous tendon routings that enable using fewer actuators (Fig.S0.1).

Fig. S0.1 Previous tendon routings used to reduce the number of actuators

(a) a red line shows an active tendon that pulls serially connected joints and a green dotted line shows a passive tendon attached at the back of the finger; (b) shows bi-directional transmission routed by constraining both position and force; (c) shows position-constrained routing for multiple fingers;  (d) shows position-constrained routing for a single finger; (e) shows force-constrained routing for a single finger; (f) to (h) show force-constrained routing for multiple fingers with movable pulley, fixed pulley, and remote mechanism, respectively. The dark-gray thick line in (h) represents the Bowden cable used to locate the actuator far from the robot. The dotted lines in (b) and (d) represent that the tendon is routed at the back of the finger. A large circle on the right side of (f) represents a movable pulley. 

0.2.1. Prior knowledge

• Designing tendon routing is about finding the proper relationship between three vector spaces (Fig. S0.2): 

1) Joint space, 2) Tendon space, and 3) Actuation space.

• The tendon space acts as a mediator between the joint space and the motor space.

0.2.2. Constrained routings for fewer actuator use

• The relationship between vector spaces  aids in understanding how the robot can move with fewer actuators:

The tendons apply force or position constraints to the joints to move joints with fewer actuators.  

• Routing variations (that reduce the actuator counts) apply position or force constraints to the joints - In this paper, we refer to these routings that enable using fewer actuators as Constrained Tendon Routing (CTR)*. 

• We also classify CTRs using the constraints applied to the joints in this paper as they highly affect the robot's motion characteristics.

* Some readers might confuse CTR with under-actuated tendon routing. Force-constrained tendon routing is the same as under-actuated tendon routing. However, we used different terminology to also introduce position-constrained tendon routing. The position constraints reduce the actual degrees of freedom to move more joints with fewer actuators; Force constraints don't reduce.