Tendon-Actuated Robots with a Tapered, Flexible Polymer Backbone: Design, Fabrication, and Modeling

Abstract

This paper presents the design, modeling, and fabrication of 3D-printed, tendon-actuated continuum robots featuring a flexible, tapered backbone constructed from thermoplastic polyurethane (TPU). Our scalable design incorporates an integrated electronics base housing that enables direct tendon tension control and sensing via actuators and compression load cells. Unlike many continuum robots that are single-purpose and costly, the proposed design prioritizes customizability, rapid assembly, and low cost while enabling high curvature and enhanced distal compliance through geometric tapering, thereby supporting a broad range of compliant robotic inspection and manipulation tasks. We develop a generalized forward kinetostatic model of the tapered backbone based on Cosserat rod theory using a Newtonian approach, extending existing tendon-actuated Cosserat rod formulations to explicitly account for spatially varying backbone cross-sectional geometry. The model captures the graded stiffness profile induced by the tapering and enables systematic exploration of the configuration space as a function of the geometric design parameters. Specifically, we analyze how the backbone taper angle influences the robot's configuration space and manipulability. The model is validated against motion capture data, achieving centimeter-level shape prediction accuracy after calibrating Young's modulus via a line search that minimizes modeling error. We further demonstrate teleoperated grasping using an endoscopic gripper routed along the continuum robot, mounted on a 6-DoF robotic arm. Parameterized iLogic/CAD scripts are provided for rapid geometry generation and scaling. The presented framework establishes a simple, rapid, and reproducible pathway from parametric design to controlled tendon actuation for tapered, tendon-driven continuum robots manufactured using fused deposition modeling 3D printers.

Figures (8)

• Figure 1: The proposed 3D-printed continuum robot design featuring a tapered, flexible TPU backbone, an integrated electronics base housing, and three tendons equally spaced along the circumference.
• Figure 2: Actuation and sensing electronics housing located at base of the tapered backbone with a subspace for endoscopic tool actuation.
• Figure 3: Cosserat rod free body diagram where $\{x, y, z\}$ denotes the coordinate frame attached to the proximal (mounted) end of the robot, and $\{x^b, y^b, z^b\}$ denotes the local coordinate frame at backbone arc length $s$. The action $g(s)$ represents the transformation from the proximal end to the cross-section pose at $s$.
• Figure 4: Simulated backbone shape as a function of taper angle and cable tension. A single cable is tensioned from 0–12 N, modeled using a TPU Young's modulus of 67 MPa, a backbone length of 34.5 cm, and a base radius of 1.11 cm.
• Figure 5: Cost function values over a range of tendon tensions for an optimal taper angle of $\alpha^* = 1.08^\circ$.