Embedded Files
1.1 Classification of
Contribution 1.1
Contribution 1.1
The paper classifies the tendon routings that enable using fewer actuators.
Please refer to the full analysis of the constrained tendon routing here.
1.1. Definition of constrained tendon routings (CTRs) to use fewer actuators
1.1. Definition of constrained tendon routings (CTRs) to use fewer actuators
We should apply position or force constraints when designing the robots (to move joints with fewer actuators) (Fig. S1.1).
When PTR is used, the motor pulls multiple tendons with fewer motors (Fig. S1.2).
When FTR is used, the motor pulls a single tendon but this tendon moves multiple joints (Fig. S1.3).
Fig.S1.1 Relationship between joint space, tendon space, and actuator space when Position-constrained Tendon Routing (PTR) or Force-constrained Tendon Routing (FTR) are used.
Position-constrained Tendon Routing (PTR)
Position-constrained Tendon Routing (PTR)
Fig. S1.2 Schematic of Position-constrained Tendon Routing (PTR)
When the motor pulls multiple tendons, the pulled length of each tendon is constrained.
One possible way is to use parallel spool as shown in the figure.
This routing has been named postural synergy or coupling in previous research.
Force-constrained Tendon Routing (FTR)
Force-constrained Tendon Routing (FTR)
Fig. S1.3 Schematic of Force-constrained Tendon Routing (FTR)
When the motor pulls a single tendon that passes multiple joints, the joint torque is constrained.
This routing has been named a differential mechanism, under-actuated tendon routing, and adaptive synergy previously.
* We wanted to use name "FTR" instead of previous names to integrate position-constrained tendon routings and make a bigger category: constrained tendon routing.
1.2. The actuation characteristics of PTR and FTR
* Please read our paper for a detailed mathematical analysis of why CTRs show the below characteristics.
1.2. The actuation characteristics of PTR and FTR
* Please read our paper for a detailed mathematical analysis of why CTRs show the below characteristics.
1.2.1 Robots with PTR may generate more accurate motions than the robots with FTR.
1.2.1 Robots with PTR may generate more accurate motions than the robots with FTR.
The kinematic relationship between joint angle and tendon length is well-defined in PTR as shown in Table 1.
Therefore, we can control the joint angle with the motor when we use PTR.
1.2.2 Robots with FTR generate adaptable motions.
1.2.2 Robots with FTR generate adaptable motions.
However, in the robots with FTR, null space exists in the kinematic relationship. Therefore, we cannot control (or estimate) the joint angle here.
Undefined joint angles provide one benefit and one drawback:
It enables adaptable motions: See our simulation result for this motion characteristic.
However, it becomes difficult to estimate posture when there is unwanted friction.
To leverage the benefit of adaptable motion, many robots have been developed using FTR. See our simulation results for this benefit.
1.2.3 Important characteristics of FTR: Force capability
1.2.3 Important characteristics of FTR: Force capability
FTR is not the perfect solution: The robot with FTR has a limited achievable torque manifold. Often, it is expressed as the robot has limited force capability. Therefore, the researchers should think about force capability. See our simulation result for further information.
Position constraints (PC)
We can estimate the joint angle from motor data.
However, we cannot estimate the tendon tension from the motor torque.
Force constraints (FC)
Due to null space, the joint angle cannot be estimated from the motor data.
The null space enables adaptable motion; for this reason, many researchers developed robots with FC.
However, it may not suitable when accurate posture is important.
* For more details on actuation characteristics and their derivation, please see our main paper.
1.3. Extension of CTRs to the multi-finger robots for further simplification
1.3. Extension of CTRs to the multi-finger robots for further simplification
Constrained tendon routings (CTRs) can be extended to the multi-finger robots to simplify them.
In practice, CTRs for multi-finger robots can be implemented in various ways as described below.
Fig. S1.4. Classification of the tendon routing that enables to use fewer actuators
(a) shows the overall view of the classification and (b) - (i) show brief schematic of each tendon routing. (b) shows how passive tendons are used. A green dotted line shows a passive tendon attached at the back of the finger and a red line shows an active tendon that pulls serially connected joints; (c) shows position-constrained routing for a single finger; (d) shows bi-lateral transmission routed by constraining both position and force constraint; (e) shows force-constrained routing for a single finger; (f) shows position-constrained routing for multiple fingers; (g) - (i) show force-constrained routing for multiple fingers with movable pulley, fixed-pulley, and remote mechanism, respectively. The dark-gray thick line in (i) represents the Bowden cable used to locate the actuator far from the robot. The dotted lines at (b) and (d) represent that the tendon is routed at the back of the finger. A large circle at the right side of (g) represents a movable pulley.
1.4. Comparison between CTRs for multi-finger robots in practice
1.4. Comparison between CTRs for multi-finger robots in practice
Four CTRs (Fig. S1.4f - Fig. S1.4i) can be used for multi-finger robots. In practice, these four CTRs have benefits and drawbacks as explained below (Fig. S1.5 - Fig. S1.8)
(NOT contribution of this paper) For this reason, the authors of this paper also proposed "Dual-Tendon Routing" in another paper, to relieve the drawbacks of CTRs [R1.1].
Exo-Glove Pinch, a robot introduced in this paper, also uses Dual-Tendon Routing. Since this is not a contribution of this paper, we do not emphasize it in our paper.
[R1.1] Byungchul Kim, Useok Jeong, and Kyu-Jin Cho, “Dual-Tendon Routing: Tendon Routing for Under-actuated Tendon-Driven Soft Hand-wearable Robot,” IEEE Robotics and Automation Letters, Feb. 2025.
Fig. S1.5 P-FTR that uses a parallel spool
Pros
Simple: Easy to pull by using more tendons.
Scalable: Easy to increase the number of fingers
Cons
Less adaptable: The position constraints harm the adaptability.
Requires customization: Should customize a ratio between radii of the two spools.
Fig. S1.6. F-FTR that uses a movable pulley
Pros
Adaptability: F-FCR all has adaptability.
Less friction: Bearings at movable pulley induce less friction.
Cons
Relatively bulky size: It requires space for pulleys to move.
Less scalable: Requires many movable pulleys when the number of fingers increases.
Not used in wearable robots (only used in gripper/robotic hand)
Fig. S1.7 F-FCR that uses fixed pulleys
Pros
Adaptability: F-FCR all has adaptability.
Compact size: It doesn't need space for pulleys to move.
High actuation stiffness: It transmits higher force to the finger.
Cons
High friction: Tendon passes many curves, and the friction accumulates at these curves.
Used in wearable robots with the name of "soft tendon routing"
Fig. S1.8. F-FCR that uses a remote mechanism
Pros
Adaptability: F-FCR all has adaptability.
Compact size and less friction: Unlike the previous cases, it has less friction and doesn't require space for movable pulleys at the wearing part.
Cons
Small actuation stiffness: It necessarily uses Bowden cables (Darg gray lines) and this requires a longer tendon. Increased tendon length reduces actuation stiffness.
Page updated
Google Sites
Report abuse