Kane's Method Research Articles

Dynamic model and control for a cable-driven continuum manipulator used for minimally invasive surgery.

Due to its unique flexible and dexterity, continuum robot has been widely used in small constrained environment. However, those advantages also bring that motion modelling and accurate control for the continuum robot is more complicated and tedious. A dynamic model and control strategy is presented for improving its control performance. The kinematics and velocity model of the robot are derived. The inertial force, elastic force, gravity and actuation force applied to the continuum robot are analysed. Meanwhile, the friction in drive system is investigated, and dynamic model is established by the Kane's method. Finally, a motion control strategy is proposed based on this model to verify the dynamic model. Results of the simulation and experiment of a prototype verify the proposed model and its control method. The proposed model and control strategy can be used to achieve the bending deformation of the robot.

Multibody dynamic modeling and controlling for unmanned bicycle system

The accurate mathematical model of the dynamic multi-rigid-body mechanical system of unmanned bicycle is established by using the Kane method, and the derivation is presented in detail. And then, the stability of the unmanned bicycle system is analyzed based on the obtained model. In addition, the influence factors to the stability which is caused by changing of the structure parameters of wheelbase, centroid of the bicycle, head fork angle, fork trail and the velocity of the bicycle are analyzed. The balance mechanism of unmanned bicycle is revealed based on the analysis, and the reasonability of the key structure revolution in the development history of bicycle is explained. The model of unmanned bicycle provided solid theory evidences for the optimization of the bicycle structure parameters. Four universal laws for balancing the bicycle are summarized by system analyzing, and the full state feedback control which combines the correcting function of velocity with optimum control is presented. The results of simulation and physical experiment show that the correctness of the dynamic model of the unmanned bicycle and the validity of the control strategy.

Comparison of accuracy of different intraocular lens power calculation methods using artificial intelligence.

To assess the accuracy of the intraocular lens (IOL) power calculation based on three methods using artificial intelligence (AI) and one formula using no AI. During cataract surgery on 114 eyes, one type of IOL was implanted, calculated with the Hill-RBF 2.0 method. The theoretical postoperative refractions were calculated using the Kane and the Pearl-DGS methods and a vergence based formula (Barrett Universal II, BUII). The differences between the manifest and objective postoperative refractions and the predicted refractions were calculated. The percentage of eyes within ±0.5 D and ±1.0 D prediction error (PE), the mean, and the median absolute errors (MAE and MedAE) were also determined. The mean age of the patients was 69.48 years; the axial length was between 21.19 and 25.39 mm. The number of eyes within ±0.5/±1.0 D PE was 96/108 (84.21%/94.73%) using the Hill-RBF 2.0 method, 92/107 (80.70%/93.85%) with the Kane method, 91/107 (79.82%/93.85%) with the Pearl-DGS method, and 91/106 (79.82%/92.98%) with the BUII formula, using subjective refraction. With objective refractometric data, PEs were within ±0.5 D in 88 (77.19%), 83 (72.80%), 82 (71.92%), and 80 (70.17%) cases (Hill-RBF, Kane, Pearl-DGS, BUII, respectively). MAE and MedAE were also best with the Hill-RBF 2.0 method (0.3 D; 0.18 D). Better accuracy of PE might be obtained by the Hill-RBF 2.0 method compared with BUII. The Kane and Pearl-DGS methods showed similar accuracy when compared with BUII.

Dynamic modelling, simulation and experiments of a micro-cutter with applications to cell perforation

The nonlinear three-dimensional dynamic equations of motion of a micro-cutter driven longitudinally at ultrasonic operating frequencies are derived using Kane's method. The micro-cutter is assumed to be immersed in a fluid, and in contact with an oocyte, which is to be perforated by the micro-cutter. The micro-cutter is modelled as an Euler-Bernoulli cantilever beam attached to a moving base. The shear and rotary inertia effects are neglected by considering a slender-shaped beam with homogeneous and isotropic material properties. It is assumed that there is no slip between the micro-cutter tip and the embryo membrane. The model presented demonstrates that the longitudinal excitation input of a micropipette results in excitation of out-of-plane, lateral motion due to the nonlinear dynamic coupling of the dynamics. Experimental results of membrane perforation are presented in the work supporting oocyte micro-cutter observations regarding suitable frequencies of excitation for effective oocyte membrane perforation.

DYNAMIC MODELING AND STABILITY CONTROL OF FOLDING WING AIRCRAFT

During the deformation process, the dynamic modeling of the folding-wing aircraft presents the characteristics of multi-rigid、multi-degree of freedom and strong nonlinearity. At the same time, parameters such as aerodynamics/torque, pressure center, centroid and moment of inertia will also change greatly, which will seriously affect Flight stability. Therefore, this paper will mainly study the multi-rigid dynamics modeling and deformation stability control of the folding wing aircraft. The multi-rigid dynamic model of the folding wing aircraft is established based on the Kane method with the additional force and moment expressions. The functional relationship between the aerodynamic parameters and the folding angle is fitted through aerodynamic calculations. and the longitudinal dynamic characteristics of the aircraft at different folding angular speeds are analyzed. It is shown that the speed, height and pitch angle of the folding wing aircraft will change during the deformation process by analyzing the longitudinal dynamic characteristics, and the aircraft cannot maintain stable flight. A stability control method is proposed for the deformation process of the folding-wing aircraft based on the active disturbance rejection control theory. The nonlinear terms, coupling terms and parameter time-varying terms are regarded as the total internal and external disturbances in the longitudinal nonlinear dynamic model of the folding-wing aircraft, using the extended state observer to estimate and compensate the total disturbance in real time. The PD controller is proposed for compensated systems to realize decoupling control of speed channel and height channel. The stability of the system is proved by Lyapunov stability theory, and mathematical simulation is used to verified the stability of the folding wing aircraft. The simulation results show that the stability controller based on the active disturbance rejection control theory can solve the problems of strong nonlinearity and time-varying parameters caused by aircraft deformation, and ensure the high-precision and stable control of the aircraft.

Kinematics and Dynamics of Flexible Robotic Manipulators Using Dual Screws

In this article, we present a new procedure for the derivation of the linearized kinematics and dynamics of a flexible industrial robotic manipulator. We introduce the Lie groups of dual rotation and dual homogeneous transformation matrices, which are the basis for the derivation of dual twists. In addition, dual screws and dual screw transformation matrices are introduced, which are used for the development of a general and systematic linearization procedure for both kinematics and dynamics. This leads to expressions that are linearized in all the states associated with the elastic motion. The dynamic modeling procedure is based on Kane's method, where the partial velocities and partial angular velocities are given as dual screws arranged as columns of dual projection matrices. The elasticity of the links is modeled by the assumed mode method. The presented procedure is implemented numerically for a 4-degrees of freedom manipulator and the simulation results are given.

Design, Kinematic, Dynamic and Stiffness Analysis of a 5-DOF Single-incision Laparoscopic Surgery Robot

In order to further reduce the incisions of laparoscopic surgery and the possibility of infection, the organic combination of single-incision laparoscopic surgery (SILS) and robotics has made the degree of minimally invasive surgery further improved. A new 5-DOF single-incision laparoscopic surgery robot was designed based on Axiomatic Design Theory, whose structure consisting of the movement mechanism, the endoscope and the position and pose adjustment mechanism. The robot parts are connected in series and parallel, allowing a pivotal motion of the endoscope in the center of the robot for realizing the incision. In order to achieve a performance optimization and a dynamic control of the single-incision laparoscopic surgical robot, the kinematics and dynamic modeling and dynamic stiffness analysis of the robot are especially important. The forward kinematics equation, inverse kinematics equation and Jacobian matrix of the SILS robot are derived based on D-H method and geometric method, and the kinematics numerical simulation is carried out by Matlab. The dynamic equation of the robot is derived by Kane method. Subsequently, a numerical simulation of the robot dynamics equation is performed, with its virtual prototype utilized to set the motion plan of the robot mechanism. After robot’s dynamic simulation, the numerical changes of the driving force and torque for each robot’s moving mechanism are obtained. The performed simulation results further verify the correctness of the established robot’s dynamic model. Finally, utilizing the above methods, the dynamic stiffness model and evaluation index of the robot are determined, and the dynamic stiffness of the robot is analyzed and evaluated. The results of the kinematics, dynamic and stiffness analysis of the SILS robot further validate that the 5-DOF SILS robot has a reasonable structure, motion and sufficient stability to meet the needs of single-incision laparoscopic surgery.

Tethered towing of defunct satellites with solar panels

Space debris is becoming an increasingly serious threat to human space activities. Active debris removal by connecting a space tug to debris by means of tethers is one of the promising techniques to constrain the debris population. Connection between the tether and the debris is preferred to be realized by tether net, since the tether net have multiple attachment points on the debris, which can damp debris' rotations passively. However, the computation of contact dynamics is very complicated and time-consuming for tether net, especially when the debris is a defunct satellite with solar panels. In this study, a tethered towing system which incorporates the flexibility of solar panels and, in the meantime, has multiple fixed attachment points is proposed. Equations of motion are obtained via Kane's method, and dynamical behaviors are discussed. Numerical results verify the validity of the proposed system, and find that the flexibility of the solar panels improves the passive rotation damping ability of the towing system.

Dynamic modeling of helicopter-slung load system under the flexible sling hypothesis

A physics based and comprehensive model for helicopter with external load is established via Kane's Method in this paper. The weight and flexibility of the cable are taken into account using spring-mass-damper model. The dynamic stability and flight quality of the helicopter-flexible sling-external load system are analyzed and verified through available reference data. Finally, the influences of the flexibility of the sling are discussed through the comparison of the flexible sling model and rigid sling model. The result shows that the rigid sling model is imprecise as the flexible sling will worsen the system's performance in dynamic stability and flight quality.

Dynamic modelling of a railway wheelset based on Kane's method

This study applies Kane's method to generate the equations of motion for a railway wheelset moving on a tangent track at a constant speed. Since the wheel and rail close contact conditions are used to obtain two nonholonomic constraint equations, the lateral vibration of the wheelset can be proven as a nonholonomic system possessing two degrees of freedom. Moreover, using Kane's approach to derive the linearised equations, we can take advantage of bypassing the full nonlinear equations and getting two equations with dynamic decoupling. When the set of equations in this work is compared with those in the literature, we found that two gyroscopic effect terms exist and yaw gravitational stiffness disappears, so that the critical speeds calculated in this work are always lower than those in the literature for the same numerical cases. At last, the contact conditions along with the creepages between wheels and rails can be directly expressed in terms of generalised speeds by using Kane's method. It shows that Kane's method focuses on motions rather than on configurations.

Dynamic modelling of a railway wheelset based on Kane's method

Dynamic modelling of a railway wheelset based on Kane's method

Influence of ocean currents on the stability of underwater glider self-mooring motion with a cable

The underwater glider mooring motion with a cable has its unique advantages and is gradually gaining attention. The influence of ocean currents on its residence stability cannot be ignored. To analyze the impact of ocean currents on the stability of the underwater glider self-mooring motion, the multi-body dynamics is solved. In this paper, the lumped mass method is utilized to discretize the cable into a series of lumped mass points and massless springs, which considers the nonlinear forces acting on the cable. The kinematic and dynamic models of the underwater glider resident process are established by the KANE method and the generalized force method, respectively, which fully considers the interactions of the underwater glider, cable and anchor. The simulations are conducted by applying fourth Runge–Kutta method in the time domain. The results show that the numerical method proposed is reasonable, and it is observed that the ocean currents with different speeds and directions affect the stability of the underwater glider in the self-mooring motion with a cable. In addition, the length of the cable in the same ocean current environment will also have a certain impact on the stability of the underwater glider.

Dynamics of a debris towing system with hierarchical tether architecture

Use of a debris-tether-tug (DTT) system has been recognized as one of the most promising techniques for space debris removal. Attitude motion of the debris may give rise to severe disturbances to the debris removal system. In this case, a conventional DTT system with a single tether may no longer be capable of removing the debris in a stable manner. A hierarchical tether architecture is proposed to stabilize the debris with a main tether from the tug branched into multiple sub-tethers attached to the edges of the debris. The primary goal of this paper is to study the dynamics of a DTT system consisting of a tug, a rigid debris and the proposed tether architecture. First, a three-dimensional dynamics model is developed using Kane's method. A simplified model is studied analytically to determine the equilibrium configurations and their stability, and the frequencies of oscillation about the stable equilibrium points. Numerical simulations are then conducted to verify the analytical results with both rigid and elastic tethers. Additionally, the stabilization effect of the branched tether system is investigated considering various debris angular velocities.

Modelling and simulation for the vibration of a plate with three axes maneuvering

In super-maneuvering flight, aircraft often bears high accelerations and high jerks. To ensure the safety of the aircraft, it is necessary to carry out the ground test to simulate the flight loads and the responses of the aircraft. In this paper, mechanical model of the accelerations are established, the distribution characteristic of the accelerations on the plate is explored and the consistency conditions for the centrifugal load and flight load are studied. The dynamic equations of a rectangular thin plate in three-axis centrifugal environment are established by Kane method, and the responses of the plate are calculated. The model established and the results obtained can be used to reflect the responses of the plate in the flight environment.

Vibration control of gyroelastic spacecraft using input shaping and angular momentum devices

This paper studies the vibration control of gyroelastic spacecraft. The dynamics of gyroelastic spacecraft considering the angular momentum devices are derived using Kane's method. A novel control strategy combining input shaping (IS) and variable-speed control moment gyros (VSCMGs) is proposed to suppress the flexible vibration of gyroelastic spacecraft. Input shaping technique is used to suppress the flexible vibration due to attitude motion. An adaptive controller is designed to further reduce the residual vibration using VSCMGs. Considering that the modal variable cannot be measured in practice, a novel modal observer is designed to estimate the modal variables for vibration control. Simulations are conducted to verify the effectiveness of the proposed control strategy.

Finite-Time Trajectory Tracking Control of Space Manipulator Under Actuator Saturation

This paper proposes a finite-time trajectory tracking controller for a space manipulator under model uncertainty, external disturbance, and actuator saturation. The dynamics of space manipulator is derived using Kane's method. Considering the model uncertainty that may exist when the manipulator captures an unknown payload, a radial basis function neural network (NN) is used to estimate the uncertain model of the space manipulator. An auxiliary system is designed to compensate the actuator saturation. Then a NN-based adaptive terminal sliding mode controller is proposed for trajectory tracking of a space manipulator. The stability of the proposed controller is analyzed using Lyapunov theory. Numerical simulations are conducted to verify the effectiveness of the proposed controller.

Effects of magnetization conditions on dynamic characteristics of spacecrafts with superconducting flux pinning docking interfaces

Depending on the self-stable levitation characteristics of superconductors with trapped magnetic flux, superconducting flux pinning docking interfaces (FPDIs) provide a promising approach for space applications. In this paper, we investigate the influence of magnetization conditions on the dynamic response between two satellites equipped with FPDIs. The flux pinning interactions between a high-temperature superconductor and a source magnet are approximated using a frozen image model. An analytic model of the docking process is derived based on the Kane method to simulate the dynamic response. A linearized dynamic model is derived, and linear quadratic regulator (LQR) control is applied to the FPDI to minimize the relative attitude deviations. The results show that improving the frozen magnetic flux density of superconductors is beneficial to the capture ability of the FPDI. Increasing the damping coefficient is also an efficient approach to improving the docking performance, but this approach is limited by the field cooling height. Damping materials with a lower density and a higher damping coefficient are proposed to be employed in the FPDI. The LQR control contributes to suppressing the amplitude of the oscillation and reducing the settling time in the docking process. Although the amplitude of oscillation in a noncontrol scheme converges more slowly than the LQR control scheme, it does not require the high dynamic response speed of a control system like the LQR control scheme, which contributes toward simplifying the structure of the FPDI. The principles presented above provide a guide for the design and implementation of FPDI in space docking missions.

PD CONTROL WITH DESIRED GRAVITY COMPENSATION FOR A NOVEL DYNAMIC BRACE

A novel dynamic brace for the treatment of idiopathic scoliosis based on parallel-actuated robotic system is proposed in this paper. The new brace can apply corrective forces on patients’ spine actively to correct the abnormal spine. However, the gravity of the dynamic system results in some adverse impacts, such as reducing comfort degree of patients, accuracy loss of rehabilitation force control, big error in direction and value of force. To overcome this problem, a new active force control strategy, proportional-derivative (PD) control with desired-gravity-compensation (DGC), is proposed to improve the effectiveness of scoliosis rehabilitation. Considering the electrically driven system and the environment contacting with the brace, the dynamic model of the active brace system is derived using Kane method. Based on the above mentioned, the force controller with DGC is designed for the brace system to compensate the impact of system gravity. The brace experiment system is built and various experiment tests are performed to verify the proposed control strategy. Experiment results demonstrate that the proposed control strategy, PD control with DGC, can distinctly reduce the influence of the brace system gravity and has more efficient control effectiveness compared with the classical PID controller.

Floating Ice Load Reduction of Offshore Wind Turbines by Two Approaches

The offshore wind turbines (OWTs) constructed at the northern sea areas under cold climate are frequently subjected to floating ice loads. It is imperative to reduce the damage owing to the floating ice with some appropriate approaches. The purpose of this paper is to ascertain the effectiveness of the tuned mass damper (TMD) and the ice-breaking cone for reducing floating ice loads on OWTs. The National Renewable Energy Laboratory's (NREL) 5 MW OWT, which is treated as a multibody system with rigid and flexible parts, is adopted as the example model here. The multiple loads taken into consideration in the fully coupled simulation include floating ice and turbulent wind. The aerodynamic load acting on the blades is solved by the blade element momentum method based on a full-field turbulent wind farm generated by the Kaimal spectrum. The Matlock model and the Ralston model are adopted for evaluating the floating ice loads on the cylindrical and conical structures, respectively. The TMD system in the nacelle and the ice-breaking cone on the tower at the mean sea level are the two load reduction approaches of concern in this paper. A weak aeroelastic simulation of the OWT model is conducted. The solution of flexibility effectiveness depends on some accurate mode shapes by the linear modal representation. Finally, Kane's method is used for predicting the motion of the whole OWT. The relevant results reveal some positive effectiveness of the TMD system and the ice-breaking cone for reducing the floating ice load. The displacement of tower top decreases significantly with the utilization of the two approaches. The TMD system has a better performance for the side-side displacement than the fore-aft displacement. By switching the ice failure mode from crushing to bending, the ice-breaking cone reduces the floating load more effectively than the TMD system. It affects equally significantly the fore-aft and side-side displacements.

Dynamics of flexible multibody systems with variable-speed control moment gyroscopes

This paper presents a generic global matrix formulation for the dynamics of flexible multibody systems with variable-speed control moment gyroscopes (VSCMGs). The flexible bodies are assumed to exhibit only small deformation, and they are connected in a tree topology by hinges permitting large rotation and translation. A cluster of VSCMGs is mounted on each body for actuation; it is assumed that the VSCMGs are statically and dynamically balanced, and their rotors are axisymmetric. A minimum set of dynamic equations are derived systematically via a mixed use of Kane's method and Newton–Euler equations. The parameters of each flexible body are augmented to take into account the inertias of the attached VSCMGs. Moreover, a skew-symmetric gyroscopic matrix and three control-input-mapping matrices are defined to represent the passive and the active gyroscopic torques of the VSCMGs in a global matrix manner. Three examples are given to show the usefulness, versatility, and correctness of the proposed formulation. As an additional contribution, also presented are linear dynamic equations for a spacecraft with flexible appendages and embedded VSCMGs.