Tendon-driven Continuum Robots (TDCRs) are promising candidates for applications in confined spaces due to their unique shape, compliance, and miniaturization capability. Non-parallel tendon routing for TDCRs have shown definite advantages including segments with higher degrees of freedom, larger workspace and higher dexterity. However, most works have focused on parallel tendons to achieve constant-curvature shapes, which yields analytically simple kinematics but overly restricts the design possibilities. We believe this under-utilization of general tendon routing can be attributed to the lack of a general kinematic model that estimates shape from only tendon geometry and displacements. Cosserat rod-based models are capable of modeling general tendon routing, but they require accurate tendon tension measurements and extensive system identification, hindering their usability for design purposes. Recent attempts in developing a kinematic model are limited to simple scenarios like actuation with a single tendon or tendons on perpendicular planes. Moreover, model formulations are often disconnected from hardware, making designs challenging to build under manufacturing constraints. Our first contribution is a novel design for TDCRs based on a synovial universal joint module, which provides a mechanically discretized and feasible design space. Based on the design, our second contribution is the formulation and evaluation of an optimization-based kinematic model, capable of handling actuation of multiple general routed tendons. Lastly, we present an example application of a TDCR designed for gaited locomotion, demonstrating our method's potential for an unified model-based design pipeline.

Parallel Continuum Robots (PCR) are closed-loop mechanisms but use elastic kinematic links connected in parallel between the end-effector (EE) and the base platform. PCRs are actuated primarily through large deflections of the interconnected elastic links unlike by rigid joints in rigid parallel mechanisms. In this paper, Cosserat rod theory-based forward and inverse kinetostatic models of 6-RUS PCR are proposed. A set of simulations are performed to analyze the proposed PCR structure which includes maneuverability in 3-dimensional space through trajectory following, deformation effects due to the planar rotation of the EE platform, and axial stiffness evaluation at the EE.