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This paper presents a general framework for the motion design of cam mechanisms using Non-Uniform Rational B-Spline (NURBS). The follower motion is described by the NURBS function. To establish motion curves, the system of linear equations is set up by arbitrary boundary conditions of the follower motion on displacements, velocities, accelerations, and jerks. Moreover, the computation of the NURBS parameters (the knot vector and the weight factor) is formulated in order to reduce peak values of the acceleration and jerk. The example demonstrates that the motion curves used by NURBS obtain advantageous characteristics and the maximum values of the acceleration and jerk on the motion curves decrease considerably compared with the polynomial and B-spline functions. Therefore, inertial forces and the tendency of vibration can be reduced in cam dynamics of high-speed cam systems. The results show that using NURBS for synthesizing motion curves is robust and effective because this can be applied for arbitrary motion curves of cam mechanisms.

This paper proposes a vertical planar 2 P RP-2 P PR parallel manipulator along with a serial planar RRR passive orthosis (exoskeleton/supporting system) for performing sitting/lying type (stationary trainer) lower limb rehabilitation therapies in the sagittal plane. Proposed system's kinematic arrangement along with forward and inverse solutions is presented. System dynamics is derived to understand the behavior of the over-constrained manipulator-orthosis system. Further, a robust motion control scheme is proposed and the motion control scheme is based on non-singular fast terminal sliding mode control along with a nonlinear disturbance observer. The effectiveness and usefulness of the proposed manipulator is shown with the implementation of the motion controller through computer based numerical simulations using a clinical gait motion pattern. The proposed motion control scheme is also validated on an in-house fabricated prototype through motion control experiments. The controller parameter sensitivity and controller robustness are further analyzed at different working conditions. In comparison to the conventional controllers, the proposed control scheme possess few advantages namely better robustness, less chattering, high precision and fast finite time convergence, and can work in the presence of parameter uncertainties. From the demonstration, the proposed manipulator has certain advantages over existing stationary lower limb rehabilitation trainers namely, simple design, larger workspace, higher stiffness, modular design and low cost.