Continuum robots stand out due to their high dexterity, which allows them to effectively navigate in confined spaces and dynamic environments. At present, motor‐controlled tendons represent the most prominent actuation method used in continuum robots which require large drive units, increasing the overall system size and weight. A potential alternative technology to overcome those limitations is represented by shape memory alloy (SMA) wire actuators, which are characterized by extremely high energy density and flexibility, leading to a reduction of the size, weight, and design complexity of continuum robots. The complex thermomechanical behavior of SMA wires, however, makes the design of SMA‐based applications a challenging task, and systematic approaches to design SMA‐driven continuum robots are poorly understood. To overcome this issue, this article presents a novel systematic methodology for designing SMA‐driven continuum robots capable of motion in a three‐dimensional environment. First, the kinematic relationship between SMA wires and continuum robot deformation as well as the required actuator force in quasi‐static conditions, is mathematically described based on the assumption of a constant curvature deformation. Subsequently, the model is validated by in‐plane experiments for different design parameters. Based on the results, a fully integrated, antagonistic SMA continuum robot is built and validated.
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