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Continuum robot is a new kind of bionic robot, and it is the beneficial supplement to the traditional joint-type robot. This paper presented a design scheme of Hook Joint type continuum robot, and fully discussed its structure and mechanism connection mode. An exponential product based matrix transformation is used to describe the position and orientation of the end-effector. The forward kinematics is also discussed in this paper. Numerical examples are completed with Matlab M language and simulation results indicate the validity of the proposed analysis method.