Use of Kane’s Method for Multi-Body Dynamic Modelling and Control of Spar-Type Floating Offshore Wind Turbines

This paper demonstrates the use of Kane’s method to derive equations of motion for a spar-type floating offshore wind turbine taking into account the flexibility of the members. The recently emerged Kane’s method reduces the effort required to derive equations of motion for complex multi-body systems, making them simpler to model and more readily solved by computers. Further, the installation procedure of external vibration control devices on the wind turbine using Kane’s method is described, and the ease of using this method has been demonstrated. A tuned mass damper inerter (TMDI) is installed in the tower for illustration. The excellent vibration mitigation properties of the TMDI are also presented in this paper.

Kinetics Study in Parachute Landing Fall Technique by Comparing Professional and Amateur Malaysian Army Parachutists Using Kane’s Method

This paper discusses the torque data during Parachute Landing Fall (PLF) activity on the sagittal plane by applying Kane’s method. The value of torque is determined in order to identify the movement of extension and flexion at every joint-segment on the parachutist during landing. Data were obtained from three professional and eighteen amateur parachutists, each with three consecutive landings. Quintic Biomechanics Software v26 was selected to capture motion analysis. The mathematical model for the PLF technique was presented based on a two-link kinematics open chain in a two-dimensional space using Kane’s method. The t-test result showed the p-value of torque at each joint between professionals and amateurs (p ≤ 0.05). According to the torque result, the professional parachutists extended their arm then flexion their elbow, shoulder, hip, knee and the ankle plantar flexion during the foot strike phase. The professional demonstrated a perfect PLF technique by identifying the flexion and extension on each joint segment that was involved during landing activity. The value of torque at each joint segment from professional parachutists may be used as a guideline for amateurs to perform optimal landing and minimise the injury.

Comparison of Kane’s and Lagrange’s Methods in Analysis of Constrained Dynamical Systems

SUMMARYDynamic modeling is a fundamental step in analyzing the movement of any mechanical system. Methods for dynamical modeling of constrained systems have been widely developed to improve the accuracy and minimize computational cost during simulations. The necessity to satisfy constraint equations as well as the equations of motion makes it more critical to use numerical techniques that are successful in decreasing the number of computational operations and numerical errors for complex dynamical systems. In this study, performance of a variant of Kane’s method compared to six different techniques based on the Lagrange’s equations is shown. To evaluate the performance of the mentioned methods, snake-like robot dynamics is considered and different aspects such as the number of the most time-consuming computational operations, constraint error, energy error, and CPU time assigned to each method are compared. The simulation results demonstrate the superiority of the variant of Kane’s method concerning the other ones.

A Multibody Model of Tilt-Rotor Aircraft Based on Kane’s Method

A tilt-rotor aircraft can switch between two flight configurations (the helicopter configuration and the fixed-wing plane configuration) by tilting its rotors. In the process of rotor tilting, the nacelles which drive the rotors tilt together with the rotors. Because the mass of the nacelles cannot be ignored compared to the mass of the whole aircraft, the tilting of the nacelles is a coupling motion of the body and the nacelles. In order to better character the aircraft dynamics during the nacelle tilting, a multibody model is established in this paper. In this multibody model, Kane’s method is used to build a dynamic model of a tilt-rotor aircraft. The generalized rates are used to describe the movement of the body and the nacelles (with rotors). The generalized active forces and generalized inertial forces of both the body and the nacelles (with rotors) are obtained, respectively, and the first-order differential equations of the generalized rates are obtained. The longitudinal trim of the XV-15 aircraft is calculated according to the single-body model and our multibody model, in this paper, and the results verify the correctness of the multibody model. In the process of nacelle inclination angle command tracking, the multibody model can provide more information about the disturbance torque of the nacelle than the single-body model, and model inversion control based on the proposed multibody model can obtain a better tracking result than a PID control method only using nacelle angle feedback information.