General Planar Motion Research Articles

The synthesis method of series-based bistable compliant mechanisms for rigid-body guidance problem based on geometrical similarity transformation of pole maps

Abstract Designing guidance mechanisms using bistable mechanisms with two stable positions is a common low-power solution for maintaining the guidance position without continuous external energy input. However, the coupling between kinematics and statics in compliant bistable mechanisms poses a challenge for their application in mechanism synthesis. To address this issue, this paper introduces the pole similarity transformation theory into the synthesis of compliant mechanisms and proposes a general synthesis method for planar serial-based compliant bistable mechanisms. This method models the compliant mechanism using the strain energy method and analyzes the bistable characteristics of the mechanism within its motion plane using the saddle point searching method. By doing so, the proposed method can identify stable positions without predetermined motion trajectories, making it more suitable for designing compliant bistable mechanisms with general planar motion. Additionally, this method utilizes the pole map to describe the stable positions of the rigid components in the compliant mechanism and establishes an information database for compliant bistable mechanisms. Through leveraging the pole similarity transformation, the pole maps of the mechanisms in the information database are matched with the pole map of the motion task, thus achieving the synthesis of planar serial-based compliant bistable mechanisms for the rigid-body guidance problem. The paper provides a detailed explanation of the mechanism synthesis process and demonstrates its application through a case study.

Boulder Transportation on the Flat Bed by Dam Break

Large coral boulders are usually deposited in coastal regions due to high-energy inundation events, such as tsunamis or storms. The study on physical mechanisms is an important issue in hydrodynamics and sedimentology. In this study, the dam break induced the transportation, and the initial movements of a boulder are simulated on a flatbed in a laboratory experiment using a microelectromechanical system (MEMS) and image analysis. The scaled-down modeled boulder made the three-dimensional reconstruction rebuild the shape and surface texture of a realistic boulder. The MEMS integrated with the modeled boulder autonomously measures the signals and numerically calculates corresponding postures and transportation in three submerged conditions of the modeled boulder in the hydrodynamic experiment. Experimental results show that the boulder transportation process is a typical two-dimensional general planar motion, which includes sliding along the transported direction and swaying around the [Formula: see text]-axis. Rolling and saltation are not dominant modes in the experiment. The results show that a complete transportation includes a variable speed movement in the initial motion, acceleration–deceleration to the uniform motion, and boulder stopping in the destination. The transported velocities of the modeled boulder are smaller than wave celerities. The maximum/minimum velocities and displacements occur in the partially and fully submerged conditions, respectively. The adjustment of the boulder’s posture is completed in the initial motion, and then the boulder almost keeps the same posture to move forward to the end. Moreover, the boulder is not driven when the nondimensional water depth is close to the critical condition.

Globally-Optimal Inlier Maximization for Relative Pose Estimation Under Planar Motion.

Planar motion constraint occurs in visual odometry (VO) and SLAM for Automated Guided Vehicles (AGVs) or mobile robots in general. Conventionally, two-point solvers can be nested to RANdom SAmple Consensus to reject outliers in real data, but the performance descends when the ratio of outliers goes high. This study proposes a globally-optimal Branch-and-Bound (BnB) solver for relative pose estimation under general planar motion, which aims to figure out the globally-optimal solution even under a quite noisy environment. Through reasonable modification of the motion equation, we decouple the relative pose into relative rotation and translation so that a simplified bounding strategy can be applied. It enhances the efficiency of the BnB technique. Experimental results support the global optimality and demonstrate that the proposed method performs more robustly than existing approaches. In addition, the proposed algorithm outperforms state-of-art methods in global optimality under the varying level of outliers.

General planar motion modeling and control of a smart rigid-flexible satellite considering large deflections

General planar motion modeling and control of a smart rigid-flexible satellite considering large deflections

Adaptive nonsingular fast terminal sliding mode controller design for a smart flexible satellite in general planar motion

In this research, a new mathematical modeling is obtained for a smart satellite with flexible appendages in general planar motion by considering two control thrust forces, a control torque and piezoelectric actuators and sensors. The satellite consists of a central rigid body and two flexible appendages modeled as Euler-Bernoulli beams. It has ability to translate and rotate in the plane of motion. Moreover, its flexible appendages can arbitrarily vibrate in the satellite's moving plane. The Lagrange method based on the Rayleigh-Ritz method is employed to derive the governing equations of motion and the sensors equations. The nonlinearity of the satellite's motion equations is the result of considering large angle rotation. Continuous terminal sliding mode and adaptive nonsingular fast terminal sliding mode controllers are designed to control the smart flexible satellite's position and attitude and suppress vibrations of the flexible appendages in the presence of uncertainties and external disturbances simultaneously. Finally, numerical simulations are presented in order to validate the proposed dynamic model and demonstrate the performance of the proposed controllers.

Coefficient of friction random field modelling and analysis in planar sliding

In this paper, we investigate inherent mesoscale spatial fluctuations of the coefficient of friction (COF) in dry frictional phenomena by modelling it as a random field. The statistical properties of the resulting global random forces and torque are derived for three types of interface motion: pure translation, pure rotation and general planar motion. Closed-form formulas are derived for the case where the interface has a square geometry and a numerical simulation method is developed for more complex shapes. The analysis of these results shows that the statistical properties of the global forces and torque are functions of the ratio of the correlation length of the random field to the characteristic length of the interface, which enables limit analyses to be performed with respect to this ratio. These analyses provide guidance regarding whether the coefficient of friction should be modelled as a random field, a random variable or a deterministic variable. The concepts developed in this paper are illustrated through a simple crank-slider model for which the statistics of energy dissipated (because of the friction) are analysed concerning the value of the ratio of the correlation length to the sliding surface size.

An Application of Yaglom's Geometric Algebra to Kinematic Synthesis of Linkages for Prescribed Planar Motion of Oriented Lines

Planar motion coordination of an unoriented line passing through a point or tangent to a conic is a well-known problem in kinematics. In Yaglom's algebraic geometry, oriented lines in a plane are represented with dual numbers. In the present paper, such algebraic geometry is applied in the kinematic synthesis of an inverted slider–crank for prescribed three and four finitely separated positions of the coupler. No previous application of Yaglom's algebraic geometry in the area of linkage kinematic synthesis is recorded. To describe the planar finite displacement of an oriented line about a given rotation pole, new dual operators are initially obtained. Then, the loci of moving oriented lines whose three and four homologous planar positions are tangent to a circle are deduced. The paper proposes the application of findings to the mentioned kinematic synthesis of the inverted slider–crank. Numerical examples show the reliability of the proposed approach. Finally, it is also demonstrated that, for a general planar motion, there is not any line whose five finitely separated positions share the same concurrency point. For the case of planar infinitesimal displacements, the same property was established in a paper authored by Soni et al. (1978, “Higher Order, Planar Tangent-Line Envelope Curvature Theory,” ASME J. Mech. Des., 101(4), pp. 563–568.)

Advanced Computational Analysis of Connecting Rod of an Aircraft Engine

Development of internal combustion engine’s components is based on the use of advanced computational models in order to compare and verify the individual design proposals. Connecting rod, which performs a general planar motion, is exposed to the gas pressure forces, inertia, contacts, and hydrodynamic pressure during the engine operation cycle. To incorporate all these aspects, Finite Element Method (FEM) is extended by Finite Difference Method (FDM) simulating a slide bearing of connecting rod’s end. It includes different properties of lubricating oil (pressure and temperature dependent viscosity and density) and elastic deformations, so the pressure distribution in an oil film can be evaluated. The computational process concludes with an estimation of the endurance safety factor of the connecting rod. The four-cylinder inverted aircraft engine is used as an example.

Quadratic modeling of wheeled moving platforms on planes

Planar motion of wheeled moving platforms, on which a camera is installed to capture videos, is common in real‐world scenarios. For a general planar motion, Scaramuzza et al. proposed a linear one‐point model to recover motions from a video under a potential assumption that the camera needs to be placed somewhere between the rear wheels of a moving platform. However, the assumption is too restricted for researchers and manufacturers, because the camera is generally fixed either on the front top of vehicles for a broad view or near the left/right mirrors because of the requirement of mechanical design. In this paper, we focus on motion modeling of wheeled moving platforms without the restriction of cameras' location on a vehicle, and propose a quadratic motion model to circumvent the limitation. Newton's iterative method and bounded quadratic least squares are used to solve the quadratic optimization problem. We test our model on both the synthetic data and the real data, and conclude that the tradeoff between model error and computational error and that between performance and computational cost are the main concerns in the practice of visual odometry. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Research on the General Second Mechanisms Synthesis Task of Disc Cam Mechanisms with Roller Follower Moving in General Planar Motion

To cam mechanisms with roller follower moving in general planar motion,the concepts of "special and general type II mechanisms synthesis tasks" are put forward,and the scientific and exact description is brought.Via establishment of coordinate system,introduction of "floating coordinate system" and division of front and rear work travel,especially the introductions of new concepts of "instantaneous choice area" and "whole choice area",the new graphic fundamental for solving "instantaneous choice area" of roller-center as well as deep analysis of boundary are brought out.The concepts of "most commercial search belt-area" and important thinking of eqisdistance-dispersion are given.Dimensionality-drop rapid solving algorithm is given,which satisfactorily solves "general type II mechanisms synthesis task".

Second Mechanisms Synthesis Task of Positive-drive Disc Cam Mechanisms with Roller Follower Moving in General Planar Motion

Positive-drive cam mechanisms are used in a great variety of applications and are of complexity and speciality in synthesis theory and methods.Based on the concepts "floating axis","instantaneous and whole nested interval" and introducing the new concepts "go and return travel","radius-marking line",It deeply and systematically researches the second mechanisms task of conjugate-cam,groove-cam and yoke radial cam with roller follower.Research results is as follow: not being simple combination and summation of force-drive cam mechanisms,the synthesis of positive-drive cam mechanisms is of complicated,deep,special and original research cultivation.Regarding the yoke radial cam with roller follower as sample,a series of research thought,research method and research conclusions are obtained.A mechanism synthesis example is displayed.

Physical characteristics of dynamic vertical–horizontal-rocking response of surface foundations on cohesionless soils

A fundamental experimental research programme on the dynamic behaviour of surface foundations on sand in general planar motion and the use of centrifuge modelling in soil–structure interaction studies is presented. Pursued with the dual purpose of extending the conventional formulation of dynamic test programmes as well as generating a physical database with sufficient parametric variations of the key aspects, an extensive experimental study to explore the dynamic soil–structure interaction problem in the small-amplitude regime is described. Through a comparison of the generated data with those from sequential vertical-centric and horizontal load tests, a novel hybrid-mode test concept by way of eccentric excitations is substantiated in terms of its economy and efficiency in capturing the force–response characteristics of the system. Synthesised in the frequency domain for direct qualitative and quantitative insights, multiple forced-response records of the foundation models on sand subjected to random vertical, horizontal and rocking excitations are summarised. As an illustration of the engineering relevance of the experimental database, a critical evaluation of the commonly used homogeneous half-space dynamic foundation solution pertaining to cohesionless soils is also provided.

Instant Center Based Kinematic Formulation for Planar Wheeled Platforms

For a general J wheeled mobile platform capable of up to three-degrees-of-freedom planar motion, there are up to two J independent input parameters yet the output of the platform is completely represented by three independent variables. This leads to an input parameter resolution problem based on operational criteria, which are in development just as they have been developed for n input manipulator systems. To resolve these inputs into a meaningful decision structure means that all motions at the wheel attachment points must have clear physical meaning. To this effect, we propose a methodology for kinematic modeling of multiwheeled mobile platforms using instant centers to efficiently describe the motion of all system points up to the nth order using a generalized algebraic formulation. This is achieved by using a series of instant centers (velocity, acceleration, jerk, and jerk derivative), where each point in the system has a motion property with its magnitude proportional to the radial distance of the point from the associated instant center and at a constant angle relative to that radius. The method of instant center provides a straightforward and physically intuitive way to synthesize a general order planar motion of mobile platforms. It is shown that a general order motion property of any point on a rigid body follows two properties, namely, directionality and proportionality, with respect to the corresponding instant center. The formulation presents a concise expression for a general order motion property of a general point on the rigid body with the magnitude and direction separated and identified. The results are summarized for up to the fifth order motion in the summary table. Based on the initial formulation, we propose the development of operational criteria using higher order properties to efficiently synthesize the motion of a J wheeled mobile platform.

Analysis and Experimental Verification for Dynamic Modeling of A Skid-Steered Wheeled Vehicle

Skid-steered vehicles are often used as outdoor mobile robots due to their robust mechanical structure and high maneuverability. Sliding, along with rolling, is inherent to general curvilinear motion, which makes both kinematic and dynamic modeling difficult. For the purpose of motion planning, this paper develops and experimentally verifies dynamic models of a skid-steered wheeled vehicle for general planar (2-D) motion and for linear 3-D motion. These models are characterized by the coefficient of rolling resistance, the coefficient of friction, and the shear deformation modulus, which have terrain-dependent values. The dynamic models also include motor saturation and motor power limitations, which enable correct prediction of vehicle velocities when traversing on hills. It is shown that the closed-loop system that results from inclusion of the dynamics of the [proportional--integral--derivative (PID)] speed controllers for each set of wheels does a much better job than the open-loop model of predicting the vehicle linear and angular velocities. For a vehicle turning with small linear and angular accelerations, the model provides accurate predictions of velocities and reasonable predictions of torques. Hence, the closed-loop model is recommended for motion planning.

Experimental Response of Piles in Sand under Compound Motion

This paper describes a fundamental experimental study on the vertical, horizontal, and rocking dynamic behavior of single pile foundations in granular soils. Aimed at generating an extensive experimental database with sufficient parametric variations to clarify a number of issues, multiple series of canonical small-strain forced-vibration centrifuge tests were performed on two model piles using the technique of random vibration and impact loading. Correlated well with vertical- and horizontal-centric dynamic tests within the experimental program, a novel hybrid-mode test method by means of eccentric excitation is validated and employed for the characterization of the foundation responses in general planar motion. A large set of experimental data for different length scales were generated and synthesized in the frequency domain in the form of directional force-response transfer functions. By virtue of the physical measurements, the validity and limitations of two fundamental elastodynamic pile solutions pertaining to the physical dynamic soil-foundation problem are also evaluated.

Planar Accelerometer Configurations

Numerous accelerometer configurations have been proposed and implemented by previous researches to determine parameters of the motion of the body to which the accelerometers are attached. To date, there has been no study of the geometric requirements of such configurations. This paper presents the requirements for minimal configurations for the case of general planar motion.

A new method and device for motion accuracy measurement of NC machine tools. Part 2: device error identification and trajectory measurement of general planar motions

This paper describes in two parts a new method and device for measuring motion accuracy of NC machine tools. In the first part, the measurement principle and the characteristics of the prototype device have been presented and discussed. In the second part, an efficient and practical approach to identifying the errors of the proposed device after assembly is developed and evaluated. The approach ensures realising the aim of the investigation, i.e. to measure the most items of the motion accuracy, especially, to measure and assess the trajectory accuracy of a general planar motion of NC machine tools. The result of the identification experiment by using the prototype device on a machining centre for the prototype device is presented and it well verifies the validity and practicality of the approach. Some measurement results for the general planar motions of the machining centre are also shown, which sufficiently demonstrate the desirable capability of the proposed method and device.

Interaction between Rotating Elliptic Cylinder and Fixed Circular Cylinder

The general planar motion of an elliptic cylinder through an inviscid and incompressible fluid in the vicinity of a fixed circular cylinder is investigated analytically. The velocity potential is derived by using the successive-image method and the perturbation method, and it is used to determine the hydrodynamic interactions between them. In a relative coordinate system moving with the uniform flow, the kinetic energy of the fluid is expressed as a function of 15 generalized added masses due to the motion of these two cylinders. The generalized added masses are then employed to determine the translational and rotational motion of the elliptic cylinder based on the dynamic equations of motion that are obtained from Lagrange's equations of motion. Numerical results show that the initial configuration of the elliptic cylinder greatly affects its subsequent motions.

Frequency domain analysis of general planar rigid motion with finite duration

We present the frequency domain analysis of the most general model of planar rigid motion, i.e., motion under the joint effects of translations and rotations with polynomial-type time dependence. We show that in the frequency domain the contribution of the object’s shape and texture is separate from that of the motion parameters in this general framework. Special attention is devoted to the case of translations and rotations with constant velocity and constant acceleration, which are the most likely candidates for modeling motion in practical contexts. This work also focuses on the distinction between the effects of the motion parameters and those of time duration, a distinction that is necessary for a clear assessment of the effects of acceleration in the frequency domain. The results presented belong to the field of signal theory and may serve as a theoretical basis in the various applications of motion models in the frequency domain, which include pattern recognition, television, image registration, image sequence analysis, and classification and neural modeling of motion perception.

The limitations of the instantaneous centre of rotation in joint research

The limitations on the use of the instantaneous centre of rotation (ICR), as calculated from discrete displacement data, are often not fully appreciated. As a consequence, the concept of the ICR has been improperly applied in some instances. In this paper, the procedures used to compute the ICR are developed in detail, and the factors that affect the computed results are identified. With an example, it is shown that in addition to being path dependent, ICR location is also sampling increment size dependent. Therefore, it is not appropriate to consider the ICR as a rotation centre if the body is undergoing general planar (combined translation and rotation) motion because it does not uniquely characterize the movement.