Multi-body Kinematics Research Articles

Multibody Dynamics on Differentiable Manifolds

Abstract Topological and vector space attributes of Euclidean space are consolidated from the mathematical literature and employed to create a differentiable manifold structure for holonomic multibody kinematics and dynamics. Using vector space properties of Euclidean space and multivariable calculus, a local kinematic parameterization is presented that establishes the regular configuration space of a multibody system as a differentiable manifold. Topological properties of Euclidean space show that this manifold is naturally partitioned into disjoint, maximal, path connected, singularity free domains of kinematic and dynamic functionality. Using the manifold parameterization, the d'Alembert variational equations of multibody dynamics yield well-posed ordinary differential equations of motion on these domains, without introducing Lagrange multipliers. Solutions of the differential equations satisfy configuration, velocity, and acceleration constraint equations and the variational equations of dynamics, i.e., multibody kinematics and dynamics are embedded in these ordinary differential equations. Two examples, one planar and one spatial, are treated using the formulation presented. Solutions obtained are shown to satisfy all three forms of kinematic constraint to within specified error tolerances, using fourth-order Runge–Kutta numerical integration methods.

A Track Geometry Measuring System Based on Multibody Kinematics, Inertial Sensors and Computer Vision.

This paper describes the kinematics used for the calculation of track geometric irregularities of a new Track Geometry Measuring System (TGMS) to be installed in railway vehicles. The TGMS includes a computer for data acquisition and process, a set of sensors including an inertial measuring unit (IMU, 3D gyroscope and 3D accelerometer), two video cameras and an encoder. The kinematic description, that is borrowed from the multibody dynamics analysis of railway vehicles used in computer simulation codes, is used to calculate the relative motion between the vehicle and the track, and also for the computer vision system and its calibration. The multibody framework is thus used to find the formulas that are needed to calculate the track irregularities (gauge, cross-level, alignment and vertical profile) as a function of sensor data. The TGMS has been experimentally tested in a 1:10 scaled vehicle and track specifically designed for this investigation. The geometric irregularities of a 90 m-scale track have been measured with an alternative and accurate method and the results are compared with the results of the TGMS. Results show a good agreement between both methods of calculation of the geometric irregularities.

Analysis and correction of geometrical error-induced pointing errors of a space laser communication APT system

The geometrical error caused pointing error is an inevitable problem in space satellite laser communication terminals which can affect the pointing accuracy of the APT (acquisition pointing and tracking) system greatly, in order to facilitate the assembling of the APT system and improve the performance of the laser communication system, the geometrical error sensitivity about the APT pointing accuracy is analyzed based on multi-body kinematics method in this paper, the error transformation matrix is derived and the geometrical error is analyzed, the simulation results provide some pointing error distribution regulars which are conductive to assembling. Based on the above research, the geometrical error correction experiment is performed and the pointing accuracy of the APT system is tested, the expectation value of the pointing error can reach 29.9 µrad which is greatly improved. This research can provide technical references for the design and analysis of space laser communication terminals.

Dynamic analysis and decoupled control of a heavy-duty walking robot with flexible feet based on super twisting algorithm

In this paper, the dynamics and control strategies of a biped robot with 6-DOF parallel leg mechanism are studied. Firstly, the multi-body kinematic model and dynamic model of the robot are established. Secondly, the insufficient stiffness of robot’s feet and the coupling effect between the kinematic chains are considered in dynamics modeling, and the rigid-flexible coupling model is established by using ADAMS and finite element method. Finally, aiming at the position deviation and system vibration caused by the flexible foot, a strategy based on the combination of a computed torque controller (CTC) and a second-order sliding-mode super twisting algorithm (STA) is designed. At the same time, the control strategy based on CTC and PID and the control strategy based on CTC and sliding mode control (SMC) are designed to compare with CTC-STA. The results show that CTC-STA has faster regulation ability and stronger robustness than CTC-SMC and CTC-PID.

Reliability and global sensitivity analysis for an airplane slat mechanism considering wear degradation

This paper focuses on the issue of reliability and global sensitivity analysis for an airplane slat mechanism considering the uncertainties in the wear process of mechanical components. First, the multi-body kinematic model of the slat mechanism is built in the ADAMS software. The geometrical sizes of the roller wheels after wear degradation are considered as input variables and the angle the slat should turn is considered as the output response. To accurately identify the influential roller wheels to the reliability and robustness of the slat mechanism, the failure probability based sensitivity and variance-based sensitivity indices are introduced. Comprehensive analysis of the results have shown that the reliability analysis and global sensitivity theory can help engineers find significant parts by their contributions, thus provide guidance for mechanical design and maintenance.

Does double calibration coupled with a closed loop multibody kinematic optimization improve scapular kinematic estimates?

Assessment of scapular kinematics has been a challenging topic for several decades. While invasive procedures, such as biplanar fluoroscopy or intra cortical pins, have showed high accuracy to meas...

Skidding research of a high-speed cylindrical roller bearing with beveled cage pockets

PurposeThis study aims to uncover the influencing mechanism of the tilt angles of the cage pocket walls of the high-speed cylindrical roller bearing on the bearing skidding.Design/methodology/approachA novel cylindrical roller bearing with the beveled cage pockets was proposed. Using the Hertz contact theory and the elastohydrodynamic and hydrodynamic lubrication formulas, the contact models of the bearing were built. Using the multibody kinematics and the Newton–Euler dynamics theory, a dynamics model of the bearing was established. Using the Runge–Kutta integration method, the dynamics simulations and analysis of the bearing were performed.FindingsThe simulation results show that the effects of the tilt angles of the front and rear walls of the pocket on the bearing skidding are remarkable. Under a 5° tilt angle of the front wall of the pocket and a 10° tilt angle of the rear wall, the bearing skidding can be effectively decreased in the rotational speed range of 10,000-70,000 r/min.Originality/valueIn this paper, a novel cylindrical roller bearing with the beveled cage pockets was proposed; a dynamics model of the bearing was established; the influence mechanism of the tilt angles of the front and rear walls of the pocket on the bearing skidding was investigated, which can provide fundamental theory basis for optimizing the pocket.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-01-2020-0035/

Dynamic Analysis of Tram Vehicles Coupled With the Track System Based on Staggered Iterative Algorithm

Abstract In recent years, a large number of tram–tracks have been constructed in typical soft soil area of China. Infrastructure defects due to the differential foundation settlement are serious issues in this area. To ensure the operation safety of the tram, the influence of different infrastructure defects on the dynamic response of the tram–track system has been investigated in this paper. A dynamic model of a five-module 100% low-floor tram vehicle coupled with a slab track system is developed based on a finite element (FE) method and multibody kinematics. The articulation between different vehicle modules, the wheel–rail nonlinear contact, pad failures, and a cavity in the subgrade have been taken into account in this model. The dynamic response of the vehicle–track coupling system to different operation speeds and infrastructure defects are calculated. Results indicate that the vibration energy of the vehicle body is mainly distributed in the frequency range below 1.5 Hz. This frequency range should be paid special attention in the durability design for the vehicle structure. When the number of the failure pads is larger than 3, the pad failure in tram–track has significant influence on the system dynamic response. A cavity in subgrade has a limited effect on high frequency vibrations (above 100 Hz) of the rail, while the low frequency vibrations (below 75 Hz) of the rail can be obviously increased by cavities in subgrade. The model can be used in the optimization of suspension parameters and the tram vehicle–track coupled vibration analysis.

Evaluation of a multibody kinematics optimization method for three-dimensional canine pelvic limb gait analysis

BackgroundSkin marker-based three-dimensional kinematic gait analysis were commonly used to assess the functional performance and movement biomechanics of the pelvic limb in dogs. Unfortunately, soft tissue artefact would compromise the accuracy of the reproduced pelvic limb kinematics. Multibody kinematics optimization framework was often employed to compensate the soft tissue artefact for a more accurate description of human joint kinematics, but its performance on the determination of canine pelvic limb skeletal kinematics has never been evaluated. This study aimed to evaluate a multibody kinematics optimization framework used for the determination of canine pelvic limb kinematics during gait by comparing its results to those obtained using computed tomography model-based fluoroscopy analysis.ResultsEight clinically normal dogs were enrolled in the study. Fluoroscopy videos of the stifle joint and skin marker trajectories were acquired when the dogs walked on a treadmill. The pelvic limb kinematics were reconstructed through marker-based multibody kinematics optimization and single-body optimization. The reference kinematics data were derived via a model-based fluoroscopy analysis. The use of multibody kinematics optimization yielded a significantly more accurate estimation of flexion/extension of the hip and stifle joints than the use of single-body optimization. The accuracy of the joint model parameters and the weightings to individual markers both influenced the soft tissue artefact compensation capability.ConclusionsMultibody kinematics optimization designated for soft tissue artefact compensation was established and evaluated for its performance on canine gait analysis, which provided a further step in more accurately describing sagittal plane kinematics of the hip and stifle joints.

Hyper Dual Quaternions representation of rigid bodies kinematics

Hyper-Dual Quaternions, HDQ, are first introduced in this paper. Utilizing the Hyper-Dual Numbers, HDN, Dual Quaternions, DQ, and hyper-dual angle, the general expression of HDQ is obtained. Rigid single- and multi-body kinematics such as in a serial robot kinematics, are then expressed in HDQ form. Taking advantage of the dual numbers’ “automatic differentiation” feature, HDQ encompasses both body pose (translational and rotational) and body velocities in a compact form with no need for further pose differentiation.

Electrical Performance Design for Circuit Breakers Based on Multi-domain Sequential Coupling

This paper presents an electrical performance design method of mechatronic circuit breakers (CB) based on multi-domain sequential coupling (MSC). Firstly, the attraction force of electromagnetic trip mechanism is obtained by Maxwell formula and Ampere’s circuital law. The multi-body kinematics and dynamics model of CB are built by recursive Euler–Lagrange partial differential equations using generalized coordinates. The electrical performance optimization model of CB is built to obtain the optimal opening angle, clearance and over-travel of the contact. The MSC piecewisely combines one field with another field according to the variation and sensitivity of the unstable field to perform multiphysics simulation such as magnetohydro-dynamics (MHD). The physical experiment of rated short-circuit capacity is carried out to verify the proposed method using infrared thermogram. The peak voltage, Joule integral and on–off time of the CB are optimized and shortened with maximum change of ratio 8.13% which proves that the CB has better reliability with longer mean time between failures.

Structural synthesis of two-dof differential screw mechanism by the multi-body kinematics

Structural synthesis of two-dof differential screw mechanism by the multi-body kinematics

Research on the dynamical responses of H-type floating VAWT considering the rigid-flexible coupling effect

Offshore floating wind turbines are classified into floating horizontal axis wind turbines (HAWTs) and floating vertical axis wind turbines (VAWTs) according to the orientation of rotating shaft. Compared with the traditional floating HAWTs, main advantages of floating VAWTs are the independence of wind direction and the lower position of power generating system, which reduce the installation and maintenance costs. Dynamical characteristics of floating VAWTs were widely studied in the preceding researches by tackling the wind turbine as a rigid body. However, the increasing size of wind turbine is beneficial to achieve higher cost performance. The elastic deformations of slender structures including blades and tower should be considered when the dynamical characteristics of the floating wind turbine are studied. In this paper, rigid-flexible coupling equations were established to investigate the dynamic behavior of H-type floating VAWT based on multi-body kinematics and dynamics. Natural motion performances of the wind turbine structures were presented and the phenomenon of “dynamic stiffening” was analyzed. Motions of the floater and vibrations of the tower and blades were computed under complex environmental loads. Time domain and frequency domain simulations were carried out to study the dynamic response of floater, tower and blades, respectively. Besides, the effect of aerodynamic loads and wave loads on the floating VAWT was researched. Load transfer performance through rigid and flexible structures was investigated.

On the Influence of the Shoulder Kinematic Chain on Joint Kinematics and Musculotendon Lengths During Wheelchair Propulsion Estimated From Multibody Kinematics Optimization.

Multibody kinematic optimization is frequently used to assess shoulder kinematics during manual wheelchair (MWC) propulsion, but multiple kinematics chains are available. It is hypothesized that these different kinematic chains affect marker tracking, shoulder kinematics, and resulting musculotendon (MT) lengths. In this study, shoulder kinematics and MT lengths obtained from four shoulder kinematic chains (open-loop thorax-clavicle-scapula-humerus (M1), closed-loop with contact ellipsoid (M2), scapula rhythm from regression equations (M3), and a single ball-and- socket joint between the thorax and the humerus (M4) were compared. Right-side shoulder kinematics from seven subjects were obtained with 34 reflective markers and a scapula locator using an optoelectronic motion capture system while propelling on a MWC simulator. Data were processed based on the four models. The results showed the impact of shoulder kinematic chains on all studied variables. Marker reconstruction errors were found to be similar between M1 and M2 and lower than for M3 and M4. Few degrees-of-freedom (DoF) were noticeably different between M1 and M2, but all shoulder DoFs were significantly affected between M1 and M4. As a consequence of differences in joint kinematics, MT lengths were affected by the kinematic chain definition. The contact ellipsoid (M2) was found as a good trade-off between marker tracking and penetration avoidance of the scapula. The regression-based model (M3) was less efficient due to limited humerus elevation during MWC propulsion, as well as the ball-and-socket model (M4) which appeared not suitable for upper limbs activities, including MWC propulsion.

A Design Method of Two DOF Joint at the Base of Heavy-load Manipulator Based on Linear Driving

In this paper, we propose a two DOF joint mechanical design scheme for heavy-load manipulator based on linear driving, the key structural parameters that directly influencing on the linear driving force is determined. Based on the multi-body kinematics and the principle of virtual work, we derive the relationship between the torque of joint space at the base of the heavy-load manipulator and the force of linear driving, then by analyzing the relationship, we obtain the design method of key structural parameters. Finally, using simulation analysis we validate this design method.

A screening method to analyse the sensitivity of a lower limb multibody kinematic model

The study presents a screening method used to identify the influential parameters of a lower limb model including ligaments, at low numerical cost. Concerning multibody kinematics optimisation, the ligament parameters (isometric length) were found the most influential ones in a previous study. The screening method tested if they remain influential with minimised length variations. The most important parameters for tibiofemoral kinematics were the skin markers, segment lengths and joint parameters, including two ligaments. This was confirmed by a quantitative sensitivity analysis. The screening method has the potential to be used as a stand-alone procedure for a sensitivity analysis.

Validation of a coupled model of discrete element method with multibody kinematics to simulate the screening process of a swing-bar sieve

The swing-bar sieve is a separation machine that is widely used in grain grading and cleaning as well as seed processing. The motion of the screen deck is a complex planar motion. In this paper, the LA-LK laboratory scale swing-bar sieve and soybean particles are taken as the research objects. The real-virtual boundary method is proposed to build the geometrical model of the screen deck. The motion of the screen deck is modelled using the planar multibody kinematics. The flowing and passing of soybean particles on the screen deck are simulated by the coupled model of the discrete element method (DEM) with multibody kinematics (MBK). In addition, experiments using the LA-LK swing-bar sieve are conducted. The simulated results are in good agreement with those obtained experimentally in terms of the distributions of passing percentage for different size ranges of soybean particles along the screen deck. This verifies the real-virtual boundary method and the coupled model of DEM with MBK we proposed in this paper. This work provides a reference for the design optimization of the swing-bar sieve and the related research.

Functional estimation of bony segment lengths using magneto-inertial sensing: Application to the humerus.

Inertial sensor technology has assumed an increasingly important role in the field of human motion analysis. However, the reliability of the kinematic estimates could still be critical for specific applications in the field of functional evaluation and motor rehabilitation. Within this context, the definition of subject-specific multi-body kinematic models is crucial since it affects the accuracy and repeatability of movement reconstruction. A key step for kinematic model calibration is the determination of bony segment lengths. This study proposes a functional approach for the in vivo estimation of the humerus length using a single magneto-inertial measurement unit (MIMU) positioned on the right distal posterior forearm. The humerus length was estimated as the distance between the shoulder elevation axis and the elbow flexion–extension axis. The calibration exercise involved five shoulder elevations in the sagittal plane with the elbow completely extended and five elbow flexion–extensions with the upper arm rigidly aligned to the trunk. Validation of the method was conducted on five healthy subjects using the humerus length computed from magnetic resonance imaging as the gold standard. The method showed mean absolute errors of 12 ± 9 mm, which were in the estimate of the humerus length. When using magneto-inertial technology, the proposed functional method represents a promising alternative to the regressive methods or manual measurements for performing kinematic model calibrations. Although the proposed methodology was validated for the estimation of the humerus length, the same approach can be potentially extended to other body segments.

Characterizing Spring Durability for Automotive Ride Using Artificial Neural Network Analysis

This paper presents the establishment of a relationship between coil spring fatigue life and automotive vertical vibration using neural network. During an automotive suspension design process, the suspension components are designed with the consideration of structure strength and fatigue life as well as the effects toward automotive ride. Hence, it is important to have a functional mathematical model to predict the fatigue life and automotive life simultaneously. To build the mathematical model, a multibody kinematic quarter model of suspension system was constructed to simulate force and acceleration time histories from the suspension system and the sprung mass of the vehicle model. The force time histories were used to predict the fatigue life of the coil spring while the acceleration time histories were converted into ISO vertical vibration index. A neural network model was created and used to fit the spring fatigue life and vehicle vertical vibration into a mathematical function. The neural network with 1 hidden layer and 2 neurons has shown a good fitting of the data with coefficient of determination as high as 0.88, 0.98, 0.96 for training, validation and testing, respectively. This constructed neural network serves to predict the vehicle vertical vibration using the spring fatigue life and suspension natural frequencies as input, and hence reduce the automotive suspension design process.

The inner-cone angle measurement of aero-engine nozzle based on conoscopic holography

The geometry of aero-engine nozzle has a significant impact on its working performance. In this work, the conoscopic holography is employed to measure the inner-cone angle of aero-engine nozzle in a noncontact way. For such purpose, a five-axis coordinate measuring machine, the experimental platform, is built. Its measuring mathematic model is established afterwards according to multi-body kinematics. The objective function of least square fitting on conic surface is defined in terms of parameterized vector of cone, and Levenberg-Marquardt algorithm is used for solving its unknown geometric parameters. Finally, the experimental results demonstrate that the adopted method in this work is feasible and high-precision. The measuring repetitive error of conic angle is within 0.0019°.