# Motion design of cam mechanisms by using non-uniform rational B-Spline

• Bewegungskurven von Kurvengetrieben unter Verwendung von Non-Uniform Rational B-Spline

Nguyen, Thi Thanh Nga; Corves, Burkhard (Thesis advisor); Hüsing, Mathias (Thesis advisor)

Aachen (2018)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2018

Abstract

The follower of cam mechanisms may flexibly perform its movement based on the shape of the cam element and the direct contact with the cam. With this feature, it is convenient to design a cam mechanism when an output motion is given by working requirements of machines. The follower motion is characterized by the displacement, velocity, acceleration, and jerk functions. The acceleration is related to inertial forces of the follower. When an acceleration curve has abrupt changes, i.e., peak values, this will lead to large inertial forces. Therefore, contact stresses at the bearing and on the cam surface also change abruptly, which causes noise and surface wear. Additionally, the peak value of the jerk curve is also important in cam design since it determines the tendency of vibration in cam-follower systems. Thus, selecting a mathematic function to describe the motion of the follower is an important step in cam design. In this thesis, Non-Uniform Rational B-Spline (NURBS) is used to describe motion curves of the follower. With the properties of NURBS, the motion curves including peak values of the acceleration and jerk are shown to have advantageous characteristics compared to classical approaches. To do this, the displacement, velocity, acceleration, and jerk functions are represented by NURBS curves. These curves are then determined by solving the system of linear equations under given boundary conditions of the displacement, velocity, acceleration, and jerk. Moreover, the main advantage of NURBS compared with other functions is that the NURBS curve can be controlled by its parameters such as weights and the knot vector. In this thesis, the computation of the knot vector is presented to evaluate its effect on motion curves. Furthermore, finding values of the weight factor to reduce peak values of the acceleration and jerk, the multi-objective functions depended on the weight factor are expressed. For solving this problem, the simulated annealing algorithm is used to get the optimal value of weights. Results of this thesis demonstrate that using NURBS for synthesizing motion curves is robust and effective because this may apply any motion curves of cam-follower systems. In addition, the kinematics of cam mechanisms is improved by controlling NURBS’s parameters.

Institutions

• Chair and Institute of Mechanism Theory, Machine Dynamics and Robotics [411910]