Experimental Study of the Motion Modes of a Planar Mechanical System with Multi-Clearance Revolute Joints

Clearances in joints of a mechanical multibody system can induce impulsive forces, leading to vibrations that compromise the system’s reliability, stability, and lifespan. Through dynamic analysis, designers can investigate the effects of the clearances on the dynamics of the multibody system. A revolute joint with clearance exhibits three motions which are;free-flight, impact and continuous contact motion modes. Therefore, a multibody system with n-number of revolute clearance joints will exhibit 3n motion modes which are a combination of the three motions in each joint. This study investigates experimentally the nine motion modes in a mechanical system with two revolute clearance joints. A slider crank mechanism has been used as the demonstrative example. We observed that the experimental curve exhibits a greater impact compared to the simulation curve. In conclusion, this experimental investigation offers valuable insights into the dynamics of planar mechanical systems with multiple clearance revolute joints. Utilizing a slider-crank mechanism for data acquisition, the study successfully confirmed seven out of nine motion modes previously identified in numerical research. The missing modes are attributed to inherent complexities in real-world systems, such as journal-bearing misalignment.

Three-dimensional analysis of relationship between relative orientation and motion modes

Target motion modes have a close relationship with the relative orientation of missile-totarget in three-dimensional highly maneuvering target interception. From the perspective of relationship between the sensor coordinate system and the target body coordinate system, a basic model of sensor is stated and the definition of relative angular velocity between the two coordinate systems is introduced firstly. Then, the three-dimensional analytic expressions of relative angular velocity for different motion modes are derived and simplified by analyzing the influences of target centroid motion, rotation around centroid and relative motion. Finally, the relationships of the relative angular velocity directions and values with motion modes are discussed. Simulation results validate the rationality of the theoretical analysis. It is demonstrated that there are significant differences of the relative orientation in different motion modes which include luxuriant information about motion modes. The conclusions are significant for the research of motion mode identification,maneuver detection, maneuvering target tracking and interception using target signatures.

Numerical Simulation on Oscillation-Sliding-Uplift Rock Coupled Motion of Caisson Breakwater Under Wave Excitation

Corresponding to the sliding and the overturning failure,the elementary motion modes of caisson breakwater include the horizontal-rotational oscillation coupled motion,the horizontal sliding-rotational oscillation coupled motion,the horizontal vibrating-uplift rocking coupled motion,and the horizontal sliding-uplift rocking coupled motion.The motion mode of a caisson will transform from one to another depending on the wave forces and the motion behaviors of the caisson.The numerical models of four motion modes of caisson are developed,and the numerical simulation procedure for joint motion process of various modes of caisson breakwater under wave excitation is presented and tested by a physical model experiment.It is concluded that the simulation procedure is reliable and can be applied to the dynamic stability analysis of caisson breakwaters.

Dynamic flight stability of a hovering model insect:lateral motion

The lateral dynamic flight stability of a hovering model insect （dronefly） was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The main results are as following. （i） Three natural modes of motion were identified： one unstable slow divergence mode （mode 1）, one stable slow oscillatory mode （mode 2）, and one stable fast subsidence mode （mode 3）. Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis （x-axis） and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. （ii） Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. （iii） For the unstable divergence mode, td, the time for initial disturbances to double, is about 9 times the wingbeat period （the longitudinal motion of the model insect was shown to be also unstable and td of the longitudinal unstable mode is about 14 times the wingbeat period）. Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.

An Integrated Dynamic Model of Ocean Mining System and Fast Simulation of Its Longitudinal Reciprocating Motion

An integrated dynamic model of China＇s deep ocean mining system is developed and the fast simulation analysis of its longitudinal reciprocating motion operation processes is achieved. The seafloor tracked miner is built as a three-dimensional single-body model with six-degree-of-freedom. The track-terrain interaction is modeled by partitioning the track-terrain interface into a certain number of mesh elements with three mutually perpendicular forces, including the normal force, the longitudinal shear force and the lateral shear force, acting on the center point of each mesh element. The hydrodynamic force of the miner is considered and applied. By considering the operational safety and collection efficiency, two new mining paths for the miner on the seafloor are proposed, which can be simulated with the established single-body dynamic model of the miner. The pipeline subsystem is built as a three-dimensional multi-body discrete element model, which is divided into rigid elements linked by flexible connectors. The flexible connector without mass is represented by six spring-damper elements. The external hydrodynamic forces of the ocean current from the longitudinal and lateral directions are both considered and modeled based on the Morison formula and applied to the mass center of each corresponding discrete rigid element. The mining ship is simplified and represented by a general kinematic point, whose heave motion induced by the ocean waves and the longitudinal and lateral towing motions are considered and applied. By integrating the single-body dynamic model of the miner and the multi-body discrete element dynamic model of the pipeline, and defining the kinematic equations of the mining ship, the integrated dynamic model of the total deep ocean mining system is formed. The longitudinal reciprocating motion operation modes of the total mining system, which combine the active straight-line and turning motions of the miner and the ship, and the passive towed motions of the pipeline, are proposed and simulated with the developed 3D dynamic model. Some critical simulation results are obtained and analyzed, such as the motion trajectories of key subsystems, the velocities of the buoyancy modules and the interaction forces between subsystems, which in a way can provide important theoretical basis and useful technical reference for the practical deep ocean mining system analysis, operation and control.

Scholte wave dispersion and particle motion mode in ocean and ocean crust

The dispersion equation of the Scholte wave was reviewed using the homogeneous elastic half-space covered by a liquid layer,and the range of the Scholte wave propagation velocity was examined using the dispersion equation.The displacement expressions of the Scholte waves in liquid and solid were derived.Additionally,the mode of motion of Scholte waves in liquid and solid and their variation with depth was studied.The following results were obtained:The dispersion equation shows that the propagation velocity of the fundamental Scholte wave was greater than the P-wave in liquid and less than that of the Scholte wave in homogeneous elastic half-space.In contrast,the velocity of higher-order Scholte waves was greater than that of P waves in liquid and S-waves in solid.Only the fundamental Scholte wave has no cutoff frequency.The Scholte wave at the liquid surface moved only vertically,while the particles inside the liquid medium moved elliptically.The amplitude variation with depth in the solid medium caused the particle motion to change from a retrograde ellipse to a prograde ellipse.The above results imply the study of Scholte waves in the ocean and oceanic crust and help estimate ocean depths.

Improvement of the prediction accuracy of polar motion using empirical mode decomposition

Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode decomposition （EMD）, which is increasingly popular and has advantages over classical wavelet decomposition, can be used to remove short period variations from observed time series of pole co- ordinates. A hybrid model combing EMD and extreme learning machine （ELM）, where high frequency signals are removed and processed time series is then modeled and predicted, is summarized in this paper. The prediction performance of the hybrid model is compared with that of the ELM-only method created from original time series. The results show that the proposed hybrid model outperforms the pure ELM method for both short-term and long-term prediction of pole coordinates. The improvement of prediction accuracy up to 360 days in the future is found to be 24.91% and 26.79% on average in terms of mean absolute error （MAE） for the xp and yp components of pole coordinates, respectively.

Dynamic flight stability of hovering insects

The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the ＂rigid body＂ assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of four insects （hoverfly, cranefly, dronefly and hawkmoth） in hovering flight is studied （the mass of the insects ranging from 11 to 1,648 mg and wingbeat frequency from 26 to 157Hz）. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. The validity of the ＂rigid body＂ assumption is tested and how differences in size and wing kinematics influence the applicability of the ＂rigid body＂ assumption is investigated. The primary findings are： （1） For insects considered in the present study and those with relatively high wingbeat frequency （hoverfly, drone fly and bumblebee）, the ＂rigid body＂ assumption is reasonable, and for those with relatively low wingbeat frequency （cranefly and howkmoth）, the applicability of the ＂rigid body＂ assumption is questionable. （2） The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e., one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. （3） Approximate analytical expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived. The expressions identify the speed derivative Mu （pitching moment produced by unit horizontal speed） as the primary source of the unstable oscillatory mode and the stable fast subsidence mode and Zw （vertical force produced by unit vertical speed） as the primary source of the stable slow subsidence mode.

Dynamic flight stability of a bumblebee in forward flight

The longitudinal dynamic flight stability of a bumblebee in forward flight is studied. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion. The primary findings are as the following. The forward flight of the bumblebee is not dynamically stable due to the existence of one （or two） unstable or approximately neutrally stable natural modes of motion. At hovering to medium flight speed [flight speed Ue = （0-3.5）m s^-1; advance ratio J = 0-0.44], the flight is weakly unstable or approximately neutrally stable; at high speed （Ue = 4.5 m s^-1; J = 0.57）, the flight becomes strongly unstable （initial disturbance double its value in only 3.5 wingbeats）.

Dynamic flight stability of a model dronefly in vertical flight

The dynamic flight stability of a model dronefly in hovering and upward flight is studied.The method of computational fluid dynamics is used to compute the stability derivatives and the techniques of eigenvalue and eigenvector used to solve the equations of motion.The major finding is as following.Hovering flight of the model dronefly is unstable because of the existence of an unstable longitudinal and an unstable lateral natural mode of motion.Upward flight of the insect is also unstable,and the instability increases as the upward flight speed increases.Inertial force generated by the upward flight velocity coupled with the disturbance in pitching angular velocity is responsible for the enhancement of the instability.

Dynamic modeling and simulation for the flexible spacecraft with dynamic stiffening

A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.

A Computational Study on Lateral Flight Stability of the Cranefly in Hover

The dynamic flight stability of hovering insects includes the longitudinal and lateral motion.Research results have shown that for the majority of hovering insects the same longitudinal natural modes are identified and the hovering flight in longitudinal is unstable.However,in lateral,the modal structure for hovering insects could be different and the stability property of lateral disturbance motion is not as robust as that of longitudinal motion.The cranefly possesses larger aspect ratio and lower Reynolds number,and such differences in morphology and kinematics may make the lateral dynamic stability different.In this paper,the lateral flight stability of the cranefly in hover is investigated by numerical simulation.Firstly,the stability derivatives are acquired by solving the incompressible Navier–Stokes equations.Subsequently,the dynamic stability characteristics are checked by analyzing the eigenvalues and eigenvectors of the linearized system.Computational results indicate that the lateral dynamic modal structure of cranefly is different from most other insects,consisting of three natural modes,and the weakly oscillatory mode illustrates the hovering lateral flight is nearly neutral.This neutral stability is mainly caused by the negative derivative of roll-moment vs.sideslip-velocity,which can be attributed to the weaker‘changingLEV-axial-velocity’effect.These results suggest that insects in nature may exhibit different dynamic stabilities with different morphological and kinematic parameters,which should be considered in the designs of flapping wing air vehicles.

Analysis of Motion in Longitudinal Plane of Negative Buoyancy Vehicle Flying Fish Ⅱ

This article describes an experimental prototype flying fish II and builds a dynamic model that is a novel type of autonomous underwater vehicle(AUV)under the condition of negative buoyancy vehicle(NBV) without large buoyancy mechanism.Compared with the AUV Remus 100,the flying fish II can cruise with double speeds within the same range and dimensions.The static stability and motion modes of flying fish II in the longitudinal plane are analyzed through the linear system theory.The flying fish II has static stability in the longitudinal plane and the motion mode is related to metacentric height.

Research on parafoil stability using a rapid estimate model

With the consideration of rotation between canopy and payload of parafoil system, a four-degree-of-freedom（4-DOF） longitudinal static model was used to solve parafoil state variables in straight steady flight. The aerodynamic solution of parafoil system was a combination of vortex lattice method（VLM） and engineering estimation method. Based on small disturbance assumption,a 6-DOF linear model that considers canopy additional mass was established with benchmark state calculated by 4-DOF static model. Modal analysis of a dynamic model was used to calculate the stability parameters. This method, which is based on a small disturbance linear model and modal analysis, is high-efficiency to the study of parafoil stability. It is well suited for rapid stability analysis in the preliminary stage of parafoil design. Using this method, this paper shows that longitudinal and lateral stability will both decrease when a steady climbing angle increases. This explains the wavy track of the parafoil observed during climbing.

Dynamic Flight Stability of a Model Hoverfly in Inclined-Stroke-Plane Hovering

Most hovering insects flap their wings in a horizontal plane, called ＇normal hovering＇. But some of the best hoverers, e.g. true hoverflies, hover with an inclined stroke plane. In the present paper, the longitudinal dynamic flight stability of a model hoverfly in inclined-stroke-plane hovering was studied. Computational fluid dynamics was used to compute the aerodynamic derivatives and the eigenvalue and eigenvector analysis was used to solve the equations of motion. The primary findings are as follows. （1） For inclined-stroke-plane hovering, the same three natural modes of motion as those for normal hovering were identified： one unstable oscillatory mode, one stable fast subsidence mode, and one stable slow subsidence mode. The unstable oscillatory mode and the fast subsidence mode mainly have horizontal translation and pitch rotation, and the slow subsidence mode mainly has vertical translation. （2） Because of the existence of the unstable oscillatory mode, inclined-stroke-plane hov- ering flight is not stable. （3） Although there are large differences in stroke plane and body orientations between the in- clined-stroke-plane hovering and normal hovering, the relative position between the mean center of pressure and center of mass for these two cases is not very different, resulting in similar stability derivatives, hence similar dynamic stability properties for these two types of hovering.

Numerical analysis of dynamic stability of falling maple samaras

Due to autorotation,samaras can fly efficiently and stably to be dispersed over a great distance under various weather conditions.Here,we provide a quantitative analysis of the dynamic stability of free-falling maple samara(Acer grosseri Pax)and verify whether they are dynamically stable as observed.Morphological and kinematic parameters were obtained based on the existing experimental data of the maple seed.Then the linearized equations of motion were derived,and the stability derivatives were calculated by a computational fluid dynamics method.The techniques of eigenvalue and eigenvector analysis were also used to examine the stability characteristics.It is found that there are five natural modes of motion of the maple seed:one stable oscillatory mode,one fast subsidence mode,one slow subsidence mode,and two neutral stable modes.The two neutral modes are manifested as the seed moving horizontally at a low speed under disturbance.Results show that the maple seed has dynamic stability in sustaining the steady autorotation and descent,exhibiting a minor horizontal motion when disturbed.These findings can beapplied to biomimetic aircraft.

Nodal structure of the wave function for a two-dimensionalhydrogen molecular ion

Under the Born-Oppenheimer approximation, the exact solution of the Schrodinger equation for a two-dimensional hydrogen molecular ion is obtained through separation of variables. The inter-quantum numbers and the modes of internal motion are determined by analysing the nodal structure of the wavefunction. The eigenstates are classified and the classical periodic orbits corresponding to the modes of internal motion are found.