cs.ROOct 7, 2026

Design optimization of tendon-driven robots considering tendon wrapping and shortcut

Authors: Yuta Sahara, Kento Kawaharazuka, Kei Okada

Organizations: Department of Mechano-Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan. · AI Center, Graduate School of Information Science and Technology, The University of Tokyo, Japan.

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Abstract

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.

Figures & tables

Figure 1: The overview of this study. Design optimization of tendon-driven arms that take advantage of tendon wrapping and shortcuts through multi-objective optimization that considers trade-offs in joint torque and arm thickness.
Figure 2: The example of the model of the arm. The number of joints is Njoint=3N_{\text{joint}}=3 and the number of tendons is Ntendon=5N_{\text{tendon}}=5 .
Figure 3: The range of PjstartP^{\text{start}}_{j} is limited to rSjstart−1<Pjstart<LSjstart−rSjstartr_{S^{\text{start}}_{j}-1}<P^{\text{start}}_{j}<L_{S^{\text{start}}_{j}}-r_{S^{\text{start}}_{j}} by the radii of the pulleys at both ends of the linkSjstart{link}_{S^{\text{start}}_{j}} .
Figure 4: The example of the tangent line between pulleys. This is the case when the tendon passes through the upper side of the left pulley and the lower side of the right pulley. The red line represents the tendon between the two pulleys, the blue line represents the tendon between the starting point and the pulley, and the green line represents the tendon between the end point and the pulley. The dashed line represents a common tangent line other than the one the tendon actually passes through.
Figure 5: The examples on checking assumptions about whether the tendon wraps around each pulley.
Algorithm 1 The algorithm to check if is_wrapi\text{is\_wrap}_{i} , the assumption about which pulley the tendon wraps around, is correct.
Figure 6: The example of theta listing for a 4-joint case. The angles shown in the figure go into all elements of theta.
Figure 7: (1) The result of the multi-objective optimization. The blue points are the sampling points, and the red points are the Pareto fronts. The horizontal axis is the minimum distance between the surface of the demonstrable joint torque space and the origin in each posture, and the vertical axis is the arm thickness. (2) An example of a solution with both dSd_{S} and tarmt_{\text{arm}} moderately superior among Pareto fronts. It shows the arm’s posture and tendons at each θ\bm{\theta} , its posture-specific dSd_{S} , and tarmt_{\text{arm}} . The blue circles indicate pulleys and the yellow areas indicate areas where the distance from the arm is less than the arm’s thickness.
Figure 8: The optimization result of the multi joints arm with different number of tendons. Only Pareto solutions are plotted.

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