A collision between two bodies is a usual phenomenon in many engineering applications. The most important problem with the collision analysis is determining the hysteresis damping factor or the hysteresis damping ratio. The hysteresis damping ratio is related to the coefficient of restitution. In this paper, an explicit expression is determined for this relation. For this reason, a parametric expression is considered for the relation between the deformation and its velocity of the contact process. This expression consists of two unknown constants. Using the energy balance, a new explicit parametric expression between the hysteresis damping factor and the coefficient of restitution is derived. For determining the unknown constants, the root mean square (RMS) of the hysteresis damping ratio of this new expression with respect to the numerical model is minimized. This new model is completely suitable for the whole range of the coefficient of restitution. So, the new model can be used in the hard and soft impact problems. Finally, three numerical examples of two colliding bodies, the classic bouncing ball problem, the resilient impact damper, and a planar slider–crank mechanism, are presented and analyzed.

Much of the previous research on modeling and simulation of cycling has focused on seated pedaling, modeling the crank load with an effective resistive torque and inertia. This study focuses on modeling standing starts, a component of certain track cycling events in which the cyclist starts from rest and attempts to accelerate to top speed as quickly as possible. A ten degree-of-freedom, two-legged cyclist and bicycle model was developed and utilized for predictive dynamic simulations of standing starts. Experimental data including crank torque, cadence, and joint kinematics were collected for a member of the Canadian Olympic team performing standing starts on the track. Using direct collocation optimal control to maximize the simulated distance traveled, the predictive simulations aligned well with the experiments and replicated key aspects of the standing start technique such as the drive and reset. The model’s use in “What if?” scenarios presents interesting possibilities for investigating optimal techniques and equipment in cycling.

Friction phenomena exist in almost every mechanical device. Due to its complicated nature and influence on the system performance, extensive dynamic simulations are often required in the early system design stage. In this work, a novel approach for eliminating the numerical discontinuity in the classical Coulomb law and its extension is developed. Specifically, the method improves the computation process instead of modifying the Coulomb friction model. The estimated error of this procedure is derived under a simple and idealized model with an externally applied sinusoidal force. Two application examples of a single-body system are used to verify the proposed method, namely, 1-DOF mass-spring system with a moving belt and static ground. Results indicate that the proposed approach reveals the characteristics of the classical Coulomb friction law and its development and eliminates oscillations in the simulated friction force. Furthermore, a 3-DOF multi-body system is simulated to investigate the difference between the LuGre model and the proposed approach.

The development of wheel–rail contact models is an active topic of railway research with the dual objective of improving the accuracy of multibody simulations and reducing its computational effort. This paper extends the online Hertzian contact model, proposed by Pombo et al. (Veh. Syst. Dyn. 45: 165–189, 2007) to propose a non-Hertzian contact model. The new methodology presented here includes the following steps: (i) search of the points of contact; (ii) identification of the undeformed distance function; (iii) evaluation of the contact patch; (iv) calculation of the normal and tangential contact forces; (v) application of the contact forces in the multibody vehicle model. Among several contact models available in the literature, this non-Hertzian contact approach uses the Kik–Piotrowski model for the normal contact force, while the tangential forces are obtained from the interpolation of the available Kalker Book of Tables for non-Hertzian (KBTNH) contact. With the purpose to demonstrate the proper implementation and selection of parameters that define this new model, several contact analysis and dynamic simulations are performed in which the wheel S1002 and the rail UIC50 are considered. First, the contact analyses that determine the contact condition of different wheel–rail interactions serve to assess the accuracy of the Hertzian and non-Hertzian models with respect to the software of reference CONTACT. Second, the Hertzian and non-Hertzian models are utilised to perform dynamic simulations of a wheelset, a bogie and a vehicle running in tangent and curved tracks. In short, this work provides, not only a complete description of the implementation of a non-Hertzian contact model in a multibody code, but also suggests for the proper selection of the parameters that promote better accuracy and optimal computational efficiency.

This paper proposes a method for analyzing comprehensive theoretical digging performance of an excavator based on the convex polytope. The convex polytope is generated by using Newton–Euler’s equations to establish dynamic relationships between the digging capability of the bucket and the driving capability of hydraulic cylinders with the consideration of the excavator tipping and slipping constraints, and is used to identify the excavator’s output capability for digging forces and moments in the bucket force space. A set of indices for theoretically quantifying the digging capability, digging efficiency, as well as the matchability between the manipulator mechanism and the driving capability of hydraulic cylinders are proposed based on the polytope, and they are used to assess the digging trajectory characteristics and the dynamic digging performance of the entire excavator workspace. Two case studies for the excavator’s digging performance assessment and optimal digging trajectory generation are conducted to test and validate this method. The proposed method contributes to comprehensively and deeply understand the design principles of an excavator, and shows the promising application prospect for guiding the design and development of new excavators.

In this paper, a new way of computing the constraint transfer matrix for the inverse dynamic and joint force analysis of multibody systems is developed. The method is based on the Newton–Euler method and the screw theory notations. This method is first developed in (Taghvaeipour et al. in Multibody Syst. Dyn. 29(2):139–168, 2013), however, in this study, it is efficiently modified by incorporating a unified constraint transfer matrix for all types of joints. This change makes both the derivation of the equations and the computations less time consuming. Moreover, in the foregoing procedure, the constraint wrenches of a system are obtained in one reference frame, namely, the global reference frame. As a case study, the proposed method is carried out on the agile wrist which is a three-legged spherical parallel robot with three degrees of freedom. At the end, the results obtained by the modified method are verified with the ones calculated by the original procedure and a software package.

This paper represents an explicit analytical solution for attitude dynamics of spacecraft combination during on-orbit refueling. Due to the fuel transfer from the servicer to the client, the inertia tensor of the spacecraft combination varies in time, which evidently leads to an inner disturbance torque on the attitude motion. Firstly, the variation of the inertia tensor matrix is formulated in terms of fuel transfer rate, and the refueling disturbance torque associated with the variation of inertia tensor is analyzed. Secondly, with an additional consideration of the effect from gravity gradient, the behavior of attitude dynamics during and after fuel transfer is investigated. Finally, different scenarios are simulated to demonstrate the efficiency of the proposed model. The result in this work is important and allows for evaluations on the attitude disturbance and stability for an on-orbit refueling mission.

The creep and wear of ultra-high-weight polyethylene hip prostheses under physiological conditions are studied in the present research work. A fully integrated contact-coupled dynamic model based upon multibody dynamics methodology is developed, allowing the evaluation of not only sliding distance, but also contact mechanics as well as cross-shear effects and both average pressure and in-service duration associated with the creep phenomenon. In vivo forces and motions of hip joint are used as input for the dynamic simulation, which result in more realistic contact point trajectory and contact pressure, and consequently wear and creep, compared to simplified inputs. The analysis also takes into account inertia forces due to hip motion, tribological properties of bearing bodies, and energy loss owing to contact-impact events. The principal molecular orientation (PMO) of the polyethylene cup is determined through an iterative algorithm and dynamic outcomes. Archard’s wear law is also integrated into the multibody dynamics model for wear prediction in hip implants. Creep, besides wear, is attributed to polyethylene damage, which is investigated by implementing a creep model extracted from experimental data. The model is validated using clinical data and numerical results available from previously published studies. It is shown that creep plays a significant role in hip damage along with wear, both of which can be influenced by hip parameters, e.g., hip and clearance sizes. Moreover, the creep mechanism according to creep experiment is discussed, and contributing factors to the wear phenomenon are analyzed throughout this study.

The standard approach to railway vehicle dynamic analysis includes running the vehicle multibody models in rigid railway tracks. The wheel–rail contact, independently of the rolling contact model used, is either handled online or via lookup tables. This traditional approach disregards the coupling effects between the railway vehicle dynamics and the railway track flexibility. In this work the assumption of rigidity of the railway track is relaxed and a finite element model of the complete track, i.e. rails, pads, sleepers, ballast and infrastructure, is used to represent the track geometry and flexibility. A rail–wheel contact model that evaluates the contact conditions and forces is used online. The dynamics of the railway vehicle is described using a multibody methodology while the track structure is described using a finite element approach. Due to the fact that not only the multibody and the finite element dynamic analysis use different integration algorithms but also because the vehicle and track models are simulated in different, codes a co-simulation procedure is proposed and demonstrated to address the coupled dynamics of the system. This approach allows us to analyze the vehicle dynamics in a flexible track with a general geometry modeled with finite elements, i.e. including curvature, cant, vertical slopes and irregularities, which is another novel contribution. The methodology proposed in this work is demonstrated in an application, in which the railway vehicle–track interaction shows the influence of the vehicle dynamics on the track dynamics and vice versa.

We consider the dynamics of an absolutely rigid body moving along a rough horizontal plane. We assume that the plane deforms during the motion so that the contact patch is non-planar and has non-zero, but comparatively small area. In the contact patch, the vertical reactions are proportional to the vertical deformations and their rates, that is, we consider Kelvin–Voigt model. The tangent forces are assumed to be classic Coulomb dry friction in sliding regime (no stiction in contact patch). Due to the viscous part of Kelvin–Voigt law, the contact patch, the plane’s normal reaction, friction force and torque depend on the position, orientation, velocity of the center of mass and the angular velocity of the body. The model does not involve any additional dynamic parameter and gives the friction force and torque directly for any given state of the body. To show the advances of the model, we recall the analytical solution of Cauchy’s initial problem with general initial conditions of ODE governing the dynamics of the homogeneous sphere on a horizontal plane (results of Zobova and Treschev in Proc. Steklov Inst. Math. 281:91–118, 2013). Here we generalize the model for arbitrary convex bodies and study its main properties. The model is compared to the continuous velocity-base friction model for pure sliding (Brown and McPhee in ASME J. Comput. Nonlinear Dyn. 11(5):054502, 2016) and to the combined dry friction (Awrejcewicz and Kudra in Multibody Syst. Dyn., 2018, https://doi.org/10.1007/s11044-018-9624-9 ) in case of sliding with spinning. We illustrate the model considering the results of numerical integration of the Cauchy problem for a controlled differential-drive vehicle on a horizontal plane.