Pure Rolling Motion Research Articles

Jump effect of an eccentric cylinder rolling on an inclined plane

This work addresses the intriguing phenomenon of the jump effect exhibited by an eccentric cylinder rolling on an inclined plane. Our main objective is to determine the region of the parameter space where the cylinder can undergo a jump after pure rolling motion. In previous works, it was assumed that slipping always precedes a jump, leading to the belief that slip is necessary. In contrast, our study challenges this prevailing notion by demonstrating the existence of situations where a jump can occur after pure rolling motion. We present a detailed theoretical description of the jump effect, investigating the dependence of the jump behavior on the initial conditions, the forces involved, and the parameter values. Through rigorous analysis, we determine the restricted region in the parameter space that allows for jumps to occur without slipping. Our findings contribute to the ongoing debate surrounding the jump effect in eccentric cylinder dynamics.

Kinematic Analysis of a New 3-DOF Parallel Wrist-Gripper Assembly with a Large Singularity-Free Workspace

This paper introduces a novel dexterous 3-DOF parallel wrist-gripper assembly with a large singularity-free range of motion. It consists of a zero-torsion 2-DOF parallel wrist and a 1-DOF parallel gripper. The wrist produces a 2-DOF sphere-on-sphere pure rolling motion. This large singularity-free 2-DOF sphere-on-sphere pure rolling motion of the wrist allows for smooth and precise manipulation of objects in various orientations, making it suitable for applications such as assembly, pick-and-place, and inspection tasks. Using a geometrical approach, analytical solutions for the inverse and forward kinematics problems of the wrist and gripper are derived. From the inverse kinematic equations, the Jacobian matrices are derived and it is shown that the whole workspace is free of type I and type II singularities. It is shown that with a proper choice of design variables, a large singularity-free range of motion can be obtained. The absence of singularities in the whole workspace of the wrist-gripper assembly is an important feature that enhances its reliability. Finally, the correctness of the derived equations for the wrist inverse and forward kinematics are verified using MSC Adams. These results confirm the feasibility and effectiveness of the proposed parallel wrist-gripper assembly. Overall, the novel parallel wrist-gripper assembly presented in this paper demonstrates great potential for improving the efficiency and flexibility of robotic manipulators in a variety of industrial and research applications.

Shear and flexural deformations in flextegrity segmental beams inspired by Leonardo’s triangular masonry construction

In Tabula XCI verso of Codex Atlanticus, Leonardo da Vinci presents an ingenious masonry structure composed of segments in the shape of inverted triangles. These are assembled by contact in a chain to obtain a lintel or jack arch, where they are pressed together by the thrust of the end constraints. Drawing inspiration from Leonardo’s sketches, we show that, by connecting the segments in pair through elastic tendons, this system represents a new type of flextegrity beam. In a classical flextegrity, the contact surfaces of the segments are curved conjugate profiles, imposing a pure rolling motion along properly designed pitch lines: the consequent elongation of the tendon dictates the constitutive response as a function of the relative rotation of the segments. Here, the contact is through plane surfaces, so that the kinematics, besides the relative rotation, is characterized by segmental shearing. This system is theoretically analysed and a continuum model is derived as the length of the segments becomes small. Comparisons with experiments on three-dimensional-printed prototypes confirm the theoretical findings and highlight the possible competition between rotational and sliding types of deformation. Apart from the historical value, this type of construction can be used in innovative structures or metamaterials.

Independent friction-restitution description of billiard ball collisions

The oblique impact of a cue ball moving on a horizontal surface with an arbitrary spin on an object ball at rest is described using the independent friction-restitution modeling of impact. The model yields theoretical expressions for the post-collision linear and angular velocities in terms of ‘constant’ coefficients of normal restitution, tangential restitution, and friction for both stick and slip regimes of impact. The model also predicts the post-impact velocities reached by the balls when, as a result of friction with the supporting surface, the pure rolling motion is established. Theoretical predictions are in satisfactory agreement with experimental data for collisions between regulation billiard balls, steel, brass, and rubber spheres.

Flextegrity simple cubic lattices

Flextegrity lattices are spatial grids composed of stiff segments kept in contact by compliant pre-tensioned tendons. The kinematic skeleton is sensible to the orientation of the segments, since their relative rotation produces the straining of the tendons to an amount that depends upon the angle of rotation and the shape of the pitch surfaces of the contact joints: these dictate the constitutive properties of the lattice in response to external actions. Two- and three-dimensional lattices are investigated, in which the contact pitch surfaces, obtained with axial-symmetric toothed conjugate profiles, mimic the kinematics of spheres, centred at the nodes of a simple cubic lattice, in pure rolling motion. The allowed mechanisms are discussed under infinitesimal deformation, to recognize possible eigenstress states in the lattice. The response under finite deformations is worked out for two-dimensional lattices under symmetric and asymmetric loading. The theoretical predictions are compared with experimental results on 3D-printed physical models. Possible extensions are discussed for lattices with segments of varying size, different arrangements and multi-stable contact joints. The flextegrity microstructure can represent a mesoscopic model for homogeneous crystals composed of non-pointwise molecules, but it could actually be manufactured in metamaterials with peculiar properties.

Evolution of grease lubrication regimes and surface damage during reciprocation-oscillation transformation

The responses of two kinds of lithium greases during the transformation from reciprocating motion to oscillation were firstly studied on a ball-on-disk test rig using optical interferometric technique. Although in pure rolling motion, after a long run a thin film lubrication (TFL) state is formed on the track, in simple sliding motion an interior boundary lubrication (BL) region is quickly developed in the contact after only tens of working cycles and the region increases with the increase of the radius stroke ratio. Microstructure of the thickener fiber makes a difference in the formation of the inside BL region. By an SRV tester, grease lubricated wear tests were carried out using samples with smooth surfaces, textured surfaces and textured + diamond like carbon (DLC) coated surfaces in simple sliding reciprocating and oscillating motion. It is seen that lubrication using grease with thinner and evenly distributed thickener fibers produces less severe surface damage. The smooth or textured surface is soon worn out, causing severe surface damage. The application of DLC coating onto the textured surface can protect the surface well but increase the friction coefficient a little bit.

Kinematic analysis of a new 2-DOF parallel wrist with a large singularity-free rotational workspace

This paper introduces a novel dexterous overconstrained 2-DOF parallel wrist with a large singularity-free range of motion. This mechanism produces a 2-DOF sphere on sphere pure rolling motion. The mechanism is compact, lightweight, stiff and fast. These properties make this robot a good candidate for different types of applications, namely, arm wrist, tracking , gimbals, pointing mechanisms and others.Using a geometrical approach, the compact parametric closed-form inverse and forward kinematic models of the mechanism and the Jacobian matrices are derived and it is shown that the mechanism is singularity-free throughout the whole range of motion. It is shown that, with a proper choice of design parameters, a large rotational and translational workspace can be obtained. The correctness of the derived inverse and forward kinematics models is verified by comparing with the results that are obtained using MSC Adams software. Finally, A contact interference analysis is performed in the CAD software and the practical workspace of the proposed mechanism is extracted and compared to that of the Omni-Wrist III with the same dimensions.

Validation of Nonlinear Dependence of Rolling Friction Moment on the Normal Force for Elastic Materials.

Analogous to the Amonton–Coulomb relation, which states the linear dependency between the dynamic sliding friction and the normal reaction, the rolling friction moment is commonly accepted as proportional to the normal reaction in a concentrated point contact. This hypothesis persists since it gives simple dynamic models and also due to difficulties met in experimental estimations of the rolling friction torques. Recent theoretical studies proved that this dependency is nonlinear even for elastic materials. A special rotor is designed, with an adjustable position for the center of mass but with constant mass and constant axial inertia moment. The pure rolling motion of the rotor on an inclined controlled small slope is studied. The angular acceleration of motion is theoretically deduced, assuming that the rolling friction torque is proportional to the normal force raised at a certain power. The deduced theoretical dynamic model evidences the influence of the eccentricity of the rotor upon the acceleration. For the particular case of linear dependency—the exponent of the power equal to one, the law of motion is independent of the configuration of the rotor. Experimental tests were made using the rotor constructed according to the theoretical model. For two positions of the center of mass, the experimental law of motion on the inclined plane is established by a non-contact method and the two different laws obtained to validate the nonlinear dependence rolling friction torque-normal force. The paper validates in an experimental manner the considered nonlinear assumption. The experimental tests concerning the microtopography of the contacting surfaces reveal that the hypothesis required by Hertzian theory, namely smooth contacting surfaces, is not satisfied. Thus, the distribution of pressure on the contact area does not obey the Hertzian semi-ellipsoidal distribution and further experimental tests are required for quantitative findings on the rolling friction torque-normal force relationship.

Experimental Study of the Lubrication Mechanism of Micro-Spherical Solid Particles between Flat Surfaces

In this study, a novel apparatus was designed and constructed to perform micro-sliding friction experiments while simultaneously observing the motion of micro-sized spheres using a visual inspection technique. The apparatus comprises a precision elevation stage that is used to elevate a flat mica disk, with the microspheres on top of it, to bring it into contact with a stationary surface and apply low loads on the contact. During micro-sliding experiments, it was found that the velocity of the center of the microsphere was half the velocity of the mica disk; in addition, friction force measurements revealed a very low coefficient of friction (about 0.03), indicating the rolling motion of the microspheres. The main outcome of our study was the verification of the hypothesis that spherical particles can be used to avoid direct contact among flat surfaces and can also introduce rolling motion within the system. The pure rolling motion of the microspheres sandwiched between a stationary and a moving flat surface supports the idea of adding rigid spherical particles to oil lubricants to further reduce friction and wear in the system by performing as micro and nanoscale ball bearings.

Minimum‐series twist distributions for yawing‐moment control during pure roll*

AbstractThe main wings of most aircraft produce adverse yaw during roll. In order to control the lateral direction of the aircraft during the roll, the rudder is often mixed with the aileron. Lifting‐line theory is used here to develop spanwise lift distributions that require the minimum number of terms in the Fourier‐series solution for controlling the yawing moment during pure rolling motion using only the main wing. It is shown that the yawing moment can be controlled for arbitrary rolling moments and/or rolling rates by adding symmetric twist in the main wing. The induced‐drag penalty for using this method to control the yawing moment is significant and discussed in detail. For example, it is shown that if zero yawing moment is prescribed, the induced drag can increase by 108% for a prescribed rolling moment or by 300% during a steady rolling rate relative to the induced drag in steady level flight. Because this is the minimum‐series solution, it does not represent the solution for yaw control with minimum induced drag, since more terms could be used in the Fourier series describing the lift distribution to control yaw with less induced drag. However, the solutions presented here can be useful for aircraft with continuous trailing‐edge technologies that are limited in spanwise deflection gradients, and provide a theoretical upper bound on the minimum induced‐drag that can be expected if the main wing is used for yawing‐moment control during pure roll.

On the Efficiency of a Conical Underplatform Damper for Turbines

Abstract Underplatform dampers (UPDs) are commonly used in aircraft engines to limit the risk of high-cycle fatigue of turbine blades. The latter is located in a groove between two consecutive blades. The dry friction contact interface between the damper and the blades dissipates energy and so reduces the vibration amplitudes. Two common geometries of dampers are used nowadays, namely wedge and cylindrical dampers, but their efficiency is limited when the blades have an in-phase motion (or a motion close to it), since the damper tends to have a pure rolling motion. The objective of this study is to analyze a new damper geometry, based on a conical shape, which prevents from this pure rolling motion of the damper and ensures a high kinematic slip. The objective of this study is to demonstrate the damping efficiency of this geometry. Hence, in a first part, the kinematic slip is approximated with analytical considerations. Then, a nonlinear dynamic analysis is performed, and the damping efficiency of this new geometry is compared to the wedge and the cylindrical geometries. The results demonstrate that the conical damper has a high damping capacity and is more efficient and more robust than the two others.

Analytic and computational analysis of wing twist to minimize induced drag during roll

Geometric and/or aerodynamic wing twist can be used to produce a lift distribution that results in a rolling moment. A decomposed Fourier-series solution to Prandtl’s lifting-line theory is used to develop analytic spanwise antisymmetric twist distributions for roll control that minimize induced drag on wings of arbitrary planform in pure rolling motion. Roll initiation, steady rolling rate, and the transition between the two are each considered. It is shown that if these antisymmetric twist distributions are used, the induced drag is proportional to the square of the rolling moment, and the induced drag during a steady rolling rate is equal to that on the wing at the same lift coefficient with no rolling rate or antisymmetric twist distribution. Results also show that if these antisymmetric twist distributions are used on straight, tapered wings without symmetric twist, any rolling maneuver for which the rolling rate and rolling moment have the same sign will always produce a yawing moment in the opposite direction. Computational results are also included, which were obtained using a gradient-based optimization algorithm in combination with a modern numerical lifting-line algorithm to find the optimum twist solutions. The resulting twist, induced drag, and yawing moment solutions compare favorably with the analytic solutions developed in the text. The solutions presented here can be used to inform the design of morphing aircraft.

The inverse kinematics of rolling contact of timelike curves lying on timelike surfaces

Rolling contact between two surfaces plays an important role in robotics and engineering such as spherical robots, single wheel robots, and multi-fingered robotic hands to drive a moving surface on a fixed surface. The rolling contact pairs have one, two, or three degrees of freedom (DOFs) consisting of angular velocity components. Rolling contact motion can be divided into two categories: spin-rolling motion and pure-rolling motion. Spin-rolling motion has three (DOFs), and pure-rolling motion has two (DOFs). Further, it is well known that the contact kinematics can be divided into two categories: forward kinematics and inverse kinematics. In this paper, we investigate the inverse kinematics of spin-rolling motion without sliding of one timelike surface on another timelike surface in the direction of timelike unit tangent vectors of their timelike trajectory curves by determining the desired motion and the coordinates of the contact point on each surface. We get three nonlinear algebraic equations as inputs by using curvature theory in Lorentzian geometry. These equations can be reduced as a univariate polynomial of degree six by applying the Darboux frame method. This polynomial enables us to obtain rapid and accurate numerical root approximations and to analyze the rolling rate as an output. Moreover, we obtain another outputs: the rolling direction and the compensatory spin rate.

Influence of the roughness on surface geometry of rolling contacts

The topography of the active surfaces in rolling contact depends on the surface roughness obtained by different manufacturing process technology (turning, grinding, polishing, lapping, etc.). The aim of this paper work is to evidence the influence of the surface roughness on surface geometry of rolling contacts. The experimental tests were carried out on the AMSLER machine and an experimental setup for pure rolling motion. The surfaces of the rolling samples were analyzed with SEM (scanning electron microscopy) and EDS (energy dispersive X-ray spectroscopy) techniques for structural and chemical analysis and measured with the Taylor Hobson profilometer before and after the experimental tests for surface topography.

Study on the Rolling‐Type Microvibration Isolation Mechanisms Based on Completely Elastic Contact

The previous models of rolling‐type mechanisms were built based on rigid contact and pure rolling motion, but when applied to ground microvibration isolation, a large error in the natural frequency was sometimes observed in the experiments. A new model of a common mechanism based on completely elastic contact is developed, and the expression of the natural frequency is provided under a microvibration condition. The experiments and analysis show that the proposed model is more accurate than the previous model, and the natural frequency is independent of the payload. The analysis shows that the proposed model is only suitable in the range of completely elastic contact, and the load range is provided after comparing the experimental results with existing theory.

A rolling ball magic trick

This paper describes a simple and effective trick with a ball on a flat surface. The trick does not require any skills, is surprising and can provide an attention-grabbing, fun introduction for high school students into the topic of pure rolling motion versus rolling with slipping.

A method for the determination of the coefficient of rolling friction using cycloidal pendulum

The paper presents a method for experimental finding of coefficient of rolling friction appropriate for biomedical applications based on the theory of cycloidal pendulum. When a mobile circle rolls over a fixed straight line, the points from the circle describe trajectories called normal cycloids. To materialize this model, it is sufficient that a small region from boundary surfaces of a moving rigid body is spherical. Assuming pure rolling motion, the equation of motion of the cycloidal pendulum is obtained - an ordinary nonlinear differential equation. The experimental device is composed by two interconnected balls rolling over the material to be studied. The inertial characteristics of the pendulum can be adjusted via weights placed on a rod. A laser spot oscillates together to the pendulum and provides the amplitude of oscillations. After finding the experimental parameters necessary in differential equation of motion, it can be integrated using the Runge-Kutta of fourth order method. The equation was integrated for several materials and found values of rolling friction coefficients. Two main conclusions are drawn: the coefficient of rolling friction influenced significantly the amplitude of oscillation but the effect upon the period of oscillation is practically imperceptible. A methodology is proposed for finding the rolling friction coefficient and the pure rolling condition is verified.

Study of adhered particle’s secondary migration on the slider air bearing surface

An entrapped particle on the slider’s air bearing damages the surface of the slider or the disk. The study of particle movement on and the particle adhesion mechanism onto the slider surface is critical to reduce entrapped particle-induced damage. In this paper, we proposed a dynamical model of the adhesive particle’s secondary migration on the slider surface. The model predicts whether the adhered particle will remain static by the action of the aerodynamic and adhesion forces. There are three migration movement styles which are rolling, sliding and lifting away from the original adhered location. Further, particle rolling migration behaviors on the slider air bearing surface (ABS) are analyzed considering the effects of flow shear rate, particle diameter and properties. Finally, the particle migration trajectory and velocity with time on the investigated slider are presented. It was found that most particles that adhere to the slider surface remain static for the investigated slider; pure rolling motion on the slider ABS is the main migration styles. The particle with a larger diameter and air shear rate speeds up to a higher velocity, and it takes more time to speed up to the constant velocity. A particle’s secondary migration motion can be observed for the particle that adheres to the slider recession region and trailing pad. Then the particle enters airflow blowing out of or rolls away from the head-disk interface.

Kinematics and trajectory of both-sides cylindrical lapping process in planetary motion type

The both-sides lapping process in planetary motion type is proposed in this paper to lap and polish the cylindrical surface of bearing roller. The rolling speed of roller is the key kinematical parameter that affects the generation of cylindrical surface of roller. Through analysis of friction forces and pure rolling motion, it was discovered that the rolling speed of roller only depends on the rotation speed of lower plate rather than upper plate. Based on the above result, the geometry and kinematics of workpiece in this method is described, and the functions are proved valid by an experiment in which the rolling speed of roller is observed in video. By theoretical tests under different speed conditions, it is indicated that the roller's rolling speed varies with respect to time along a nonstandard cosine curve with an offset, its amplitude depends on the speeds of lower plate rotation and carrier circulation, and its offset depends on the speeds of lower plate rotation and carrier rotation. Based on geometry and kinematics, the trajectories on the cylindrical surface of roller and on the flat surface of plate are both described and simulated. The standard deviation and the range of path curve length distribution density are applied to numerically evaluate and analyze the trajectory distribution. The effect of speed parameters on the trajectory distribution, and the generation of trajectory with respect to time are investigated.

Video analysis of rolling cylinders

In this work, we studied the rolling motion of solid and hollow cylinders down aninclined plane at different angles. The motions were captured on video at 300 frames s − 1, and the videos were analyzed frame by frame using video analysis software. Data from thereal motion were compared with the theory of rolling down an inclined plane withoutslipping. From the experiment, the acceleration does not depend on the cylinder mass asindicated from the theory. For the wood–steel surface, we found that the coefficient ofstatic friction was equal to 0.131 and the critical angle for the solid cylinder was21.45°. The critical angle for the hollow cylinder depends on the inner and outer radius of thecylinder. Motion paths of a point on the hollow cylinder at small and large angles wereshown to elucidate the pure rolling condition. Finally, we demonstrated that totalmechanical energy was conserved during the pure rolling motion. This confirms that workdone by the friction force is zero. We will use these results to design an interactive lecturedemonstration on rolling without slipping.