a Department of Mechano-Informatics, The University of Tokyo, Japan b AI Center, The University of Tokyo, Japan
This study proposes a multi-objective optimization method for tendon-driven arm design, addressing the inherent trade-off between joint torque and arm thickness through tendon wrapping and shortcut effects. We formulate the problem to simultaneously maximize torque and minimize thickness, solved using NSGA-II. The algorithm optimizes tendon routing, pulley configurations, and attachment points. Results reveal Pareto-optimal designs with effective moment arm expansion via strategic shortcuts, providing practical guidelines for compact high-torque arms. The optimized configurations demonstrate non-trivial patterns beyond conventional design intuition, offering new insights for engineering efficient robotic systems.
Designing tendon-driven arms that balance joint torque and arm thickness.
Design optimization considering tendon wrapping and shortcut
Tendons can wrap around joint pulleys or shortcut them as the arm bends. Wrapping maintains a moment arm determined by the pulley, while a shortcut can increase the effective moment arm and the available joint torque. The same shortcut can also increase the arm’s thickness. Our method models these routing changes explicitly and searches for designs that balance the two objectives.
Arm model: pulley radii, tendon attachment points, and routing around each joint are design parameters.
For each sampled posture, we determine the valid tendon path, accounting for wrapping and shortcut transitions, and calculate the muscle-length Jacobian. Joint torque capability is evaluated from the feasible tendon-tension space; arm thickness is evaluated from the distance of pulleys and tendons to the arm links.
Checking whether a tendon wraps around a pulley.Checking whether a tendon shortcuts a pulley.
NSGA-II jointly optimizes pulley radii, the links and positions of tendon start and end points, and the side on which each tendon passes each joint. The resulting Pareto front offers multiple design candidates, allowing designers to choose a balance between torque and compactness.
Experiments: optimized tendon configurations
We evaluate a two-joint arm with three tendons and a four-joint arm with eight tendons, using 20,000 optimization samples for each case. Link lengths and tendon tensions are normalized, and designs are evaluated at nine representative postures.
Two joints, three tendons.Four joints, eight tendons.
The blue points show sampled designs, and the red points show the Pareto front. A representative solution is selected from the trade-off region. The simple case recovers an intuitive tendon configuration; the more complex case combines tendons spanning one and two joints to increase torque while limiting excessive shortcuts.
Experiments: different numbers of joints and tendons
We compare arms with two to five joints, varying the tendon count from one to four more than the number of joints. For the two-, three-, and four-joint systems, increasing the number of tendons generally improves torque capability at the same thickness.
The five-joint system exposes the difficulty of exploring a larger design space with a fixed sample budget. Increasing the sample count to 40,000 for the nine-tendon case improves its performance beyond the eight-tendon case, highlighting the importance of sufficient optimization samples.
