Kinematic Geometry Research Articles

Assembly accuracy prediction method of planetary gear train considering bolt-bearing-shaft-gear coupling effects

Planetary gear train (PGT) is a complex transmission system composed of gears, shafts, bearings and bolted joints, of which the assembly accuracy affects the transmission accuracy and dynamic behavior. In this paper, a new assembly accuracy prediction method is proposed for PGT considering gear-shaft-bearing-bolt coupling effects. The new method is formulated by establishing three models for bolt assembly, shaft error motion and assembly accuracy (transmission error) of PGT. The model for bolt assembly is an original FE-analytical model to analyze the bolt assembly effect on elastic deformation of bearing cap, which is developed by finite element (FE) method and analytical method for addressing the elastic effect of bearing cap and elastic interaction between bolts. The models for shaft error motion and assembly accuracy are performed by the three-dimensional contact analysis with errors and preload of bearing cap based on analytical method and kinematic geometry relationship. Combining the three models, the assembly accuracy can be predicted by simulations. The simulations indicate that the proper bolt assembly parameters can alleviate the influence of manufacturing errors on assembly accuracy. The assembly accuracy tests of PGT are conducted. The results well agree with the simulations’, and the assembly accuracy is improved by the proper bolt assembly parameters.

Updating structural synthesis methodology of mechanisms: from kinematic geometry to kinematic geometry accompanied with statics

Mechanism is a device to transmit and convert motion, force, and energy. However, for a long time, the structural synthesis methodology using the instantaneity and continuity based methods with a total of 11 variants actually just discusses the kinematic geometry significance and losses the mechanic concern. It neglects to extract the force and energy characteristics from task's requirements, and may produce low-payload, weak-stiffness, or low-efficiency mechanisms. How to take full consideration of motion, force, and energy in structural synthesis has become a tough challenge for strongly-interactive and physically-intelligent applications in the new-generation robot community. Therefore, this study proposes a new structural synthesis methodology unifying kinematic geometry and statics, integrating continuity and instantaneity by developing the finite and instantaneous screw theory, and taking motion, force, and energy characteristics simultaneously to design moving platform, limb, and joint respectively. As an example, the 2R1T mechanism exerted by 1F1M loads is designed with good payload, interaction and transmission work efficiencies. By utilizing this methodology, the feasible topologies designed are actually very fewer than those obtained by kinematic geometry based methodology, which may behave weak payload and work efficiency during strong interaction.

An Automatic Method Framework for Personalized Knee Prosthetic Modeling Based on Kinematic Geometry.

The shape of a knee prosthesis has an important impact on the effect of total knee arthroplasty. Comparing to a standard common prosthesis, the personalized prosthesis has inherent advantages. However, how to construct a personalized knee prosthesis has not been studied deeply. In this paper, we present an automatic method framework of modeling personalized knee prostheses based on shape statistics and kinematic geometry. Firstly, the average healthy knee model is established through an unsupervised process. Secondly, the sTEA (Surgical Transecpicondylar Axis) is calculated, and the average healthy knee model is resized according to it. Thirdly, the resized model is used to simulate the knee's motion in a healthy state. Fourthly, according to the target patient's condition, an excising operation is simulated on both patient's knee model and the resized model to generate an initial knee prosthesis model. Finally, the initial prosthesis model is adjusted according to the simulated motion results. The average maximum error between the resized healthy knee model and the patient's own knee model is less than 2 mm, and the average maximum error between the motion simulation results and actual motion results is less than 3 mm. This framework can generate personalized knee prosthesis models according to the patient's different conditions, which makes up for the deficiencies of standard common prostheses.

Kinematic Geometry of a Timelike Line Trajectory in Hyperbolic Locomotions

This study utilizes the axodes invariants to derive novel hyperbolic proofs of the Euler–Savary and Disteli formulae. The inflection circle, which is widely recognized, is situated on the hyperbolic dual unit sphere, in accordance with the principles of the kinematic theory of spherical locomotions. Subsequently, a timelike line congruence is defined and its spatial equivalence is thoroughly studied. The formulated assertions degenerate into a quadratic form, which facilitates a comprehensive understanding of the geometric features of the inflection line congruence.

One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode

In this paper, based on the E. Study map, direct appearances were sophisticated for one-parameter hyperbolic dual spherical locomotions and invariants of the axodes. With the suggested technique, the Disteli formulae for the axodes were acquired and the correlations through kinematic geometry of a timelike line trajectory were provided. Then, a ruled analogy of the curvature circle of a curve in planar locomotions was expanded into generic spatial locomotions. Lastly, we present new hyperbolic proofs for the Euler–Savary and Disteli formulae.

Structural synthesis of the reconfigurable legged mobile lander for strong geometry-physical interaction with extraterrestrial environment

To design the engineering prototype of reconfigurable legged mobile lander (ReLML) for strong geometry-physical interaction with extraterrestrial environment, this paper proposes a tailored structural synthesis methodology unifying kinematic geometry and statics. Compared with our preceding works, three inbuilt operation modes are first integrated: adjusting mode is a totally new mode defined as three rotations (3R) with a strong geometrical adaptation to hostile terrain; landing mode is redefined as two rotations one translation (2R1T), inherits Chang'E lander to survive from strong impact interaction; roving mode turns into the other 2R1T motion for good motion/force interactivity. The interaction characteristics (motion, force, energy) between ReLML and environment are extracted to derive output finite motions and instantaneous wrenches of leg end-effector, following the principles of optimal force system equilibrium and work efficiency. The motion and force synergistic syntheses of metamorphic limb and joint are implemented to design and assemble mechanical generators. The ReLML can serve the alien base construction and adjustable launch bracket. The unified structural synthesis methodology of kinematic geometry and statics is universal and effective for designing parallel mechanisms and reconfigurable mechanisms, especially for strong physical interaction scenarios.

Alpine structural evolution of the Internal Piedmont Zone in the Upper Viù Valley (Lanzo Valleys Ophiolite, Western Alps)

New structural data have been collected in the high-pressure meta-ophiolites exposed in the Lanzo Valleys (i.e., the Lanzo Valleys Ophiolite, LVO) and tectonically overlying the continental crust of the Dora-Maira and Gran Paradiso massifs in the Western Alps. Detailed geological mapping and structural analysis carried out in the south-western sector of the LVO (i.e., the Upper Viù Valley) allow to distinguish four ductile deformation phases, corresponding to the subduction-related D1 phase, the early exhumation-related D2-phase and the late exhumation-related D3 and D4 phases. The geometry of structures and kinematics have been reconstructed, and their regional tectonic meaning is discussed in the frame of the Alpine tectonic evolution of the Internal Piedmont Zone (i.e., the remnants of the Alpine Tethyan oceanic lithosphere) in the Western Alps.

Timelike Ruled Surfaces with Stationary Disteli-Axis

This paper derives the declarations for timelike ruled surfaces with stationary timelike Disteli-axis by the E. Study map. This prepares the ability to determine a set of Lorentzian invariants which explain the local shape of timelike ruled surfaces. As a result, the Hamilton and Mannhiem formulae of surfaces theory are attained at Lorentzian line space and their geometrical explanations are examined. Then, we define and explicate the kinematic geometry of a timelike Plűcker conoid created by the timelike Disteli-axis. Additionally, we provide the relationships through timelike ruled surface and the order of contact with its timelike Disteli-axis.

Kinematic geometry of spatial RSSR mechanisms

Two different novel methods to derive the input–output (IO) equation of arbitrary RSSR linkages are described. Both methods share some common elements, i.e., they use the standard Denavit–Hartenberg notation to first describe the linkage as an open kinematic chain, and Study’s kinematic mapping to describe the displacement of the coordinate frame attached to the end-effector of the chain with respect to the relatively non-moving base frame. The kinematic closure equation is obtained in the seven-dimensional projective kinematic mapping image space by equating the eight Study soma coordinates to the identity array. Then two methods are successfully applied to eliminate the intermediate joint angle parameters leading to the degree four biquadratic implicit algebraic IO equation: (a) the linear implicitisation algorithm, which can be applied after rearranging the closure equation such that the linkage can be viewed as two serial RS chains, and (b) numerical elimination theory using pseudowitness sets. Both approaches lead to the same IO equation. The utility of this algebraic form of the IO equation is illustrated with three detailed application examples.

One-parameter Lorentzian spatial kinematics and Disteli's formulae

<abstract><p>In this paper, based on the E. Study map, clear terms are offered for the differential equations of one-parameter Lorentzian spatial kinematics that are coordinate system-independent. This cancels the request of demanding coordinate transformations that are typically required in the determination of the canonical systems. With the suggested technique, new proofs of the Disteli formulae of a spacelike line trajectory are instantly gained and their spatial equivalents are studied in detail. As a consequence, we address the kinematic geometry of a point trajectory for the one-parameter Lorentzian spherical and planar movements.</p></abstract>

Kinematic Geometry of Timelike Ruled Surfaces in Minkowski 3-Space E13

Symmetry is a frequently recurring theme in mathematics, nature, science, etc. In mathematics, its most familiar manifestation appears in geometry, most notably line geometry, and in other closely related areas. In this study, we take advantage of the symmetry properties of both dual space and original space in order to transfer problems in original space to dual space. We use E. Study Mappingas a direct method for analyzing the kinematic geometry of timelike ruled and developable surfaces. Then, the invariants for a spacelike line trajectory are studied and the well-known formulae of Hamilton and Mannheim on the theory of surfaces are provenfor the line space. Meanwhile, a timelike Plücker conoid generated by the Disteli-axis is derived and its kinematic geometry is discussed. Finally, some equations for particular timelike ruled surfaces, such as the general timelike helicoid, the Lorentzian sphere, and the timelike cone, are derived and plotted.

An analytical framework of the kinematic geometry for general point-contact gears from contact path

Based on the idea that the relative curvature relationships along total contact path will better reflect the contact characteristics of gears, this study attempts to develop an analytical framework for the kinematic geometry of point-contact gears from the contact paths. First, a general method for obtaining the contact path of a gear from a pinion is proposed. Second, a normal curvature and geodesic torsion calculation method in the contact path direction is developed. Then, based on the linearly dependent condition of the tangent vectors of the two contact paths, two relative normal curvature analysis methods are proposed by applying the fundamental form theory. Finally, a sample case is presented to show the application and complete the verification of the kinematic geometry methods. The sample case agrees with the analytical model.

Time-like Ruled Surface in One-Parameter Hyperbolic Dual Spherical Motions

In this work, we introduce a time-like ruled surface in one-parameter hyperbolic dual spherical motions. This provides the ability to derive some formulae of surface theory into line spaces. Then, a time-like Plücker conoid associated with the motion has been obtained, and its kinematic geometry is researched in detail. Consequently, a characterization for a time-like ruled surface to be a constant Disteli-axis is derived and investigated in detail. At last, we have discussed some special cases which lead to some special time-like ruled surfaces such as the time-like helicoids, Lorentzian sphere, and time-like cone.

Kinematic Geometry of Spatial Rssr Mechanisms

Kinematic Geometry of Spatial Rssr Mechanisms

Study of quality criteria for two-phase iron-based composite coatings formed by plasma spraying

The increasing relevance in the field of repair and restoration of machines and mechanisms is acquiring gas-thermal methods of applying functional coatings to the working surfaces of parts of machine assemblies. The purpose of gas-thermal coating methods is to provide and obtain special physical and mechanical properties of the surface of the part, as well as to restore worn-out components and mechanisms after their long-term and intensive operation. Plasma spraying of composite coatings is an effective method of gas-thermal treatment of the surface of a part. In this paper, a study was conducted on the optimal selection of material for plasma spraying of a part, taking into account its operational features and types of wear of working surfaces. In particular, the operating conditions of the screw of the conveying conveyor are analyzed. The technological features of the application of composite materials by plasma spraying technology are considered. The theoretical selection of a two-phase dispersed-filled composite for application to the working surfaces of the screw in order to restore and harden it has been carried out. Studies and analysis of one of the main indicators of the quality of the formed coating after plasma spraying – the magnitude of the resulting residual stresses (stretching and compression) have been carried out. Taking as a basis the kinematic modes and geometry features of the working surfaces of the screw, as well as the criteria for the formation of the thickness of the sprayed layer, the calculation equations for determining the residual stresses arising on the screw and cylindrical surfaces of the screw of the conveying conveyor are obtained. It is concluded that in order to achieve the required physical and mechanical properties of the coating, the volume fraction of the filler in the matrix of the PG-SR4 composite powder should be in the range of 20–25%. Therefore, it is possible to use in practice a particulate-filled composite of the NiСrВSiFе type with 20–25% reinforcing TiC filler particles in order to restore parts of machines and mechanisms.

Visual perception of apparent motion abides by minimization principles of geometry.

Apparent motion is a robust perceptual phenomenon in which observers perceive a stimulus traversing the vacant visual space between two flashed stimuli. Although it is known that the "filling-in" of apparent motion favors the simplest and most economical path, the interpolative computations remain poorly understood. Here, we tested whether the perception of apparent motion is best characterized by Newtonian physics or kinematic geometry. Participants completed a target detection task while Pacmen-shaped objects were presented in succession to create the perception of apparent motion. We found that target detection was impaired when apparent motion, as predicted by kinematic geometry, not Newtonian physics, obstructed the target's location. Our findings shed light on the computations employed by the visual system, suggesting specifically that the "filling-in" perception of apparent motion may be dominated by kinematic geometry, not Newtonian physics. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Kinematic sensitivity, parameter identification and calibration of a non-fully symmetric parallel Delta robot

In this paper, the sensitivity analysis and kinematic calibration of a modified parallel Delta robot are presented. The influence of the variations related to the manipulator components and geometric parameters onto the motion accuracy, including the parallelogram, is studied by means of the variational method. The sensitivity analysis shows that the robot under study is slightly less sensitive to the geometric variations compared to its original counterpart. The developed error model was further used in the kinematic calibration of the robot as the parameter identification model, allowing more parameters and variations to be identified compared to the differential kinematic geometry based error models, which was confirmed through simulated calibrations. The calibration process was carried out along with a laser tracker to measure the end-effector positions, to identify the parameters by making use of the least square minimization method to minimize the square residuals between the predicted and measured positions. After calibration, the positioning error of the robot end-effector is significantly enhanced, with the absolute accuracy improved from 1.4mm to 0.1–0.13mm. The presented calibration process can be applicable to other parallel robots.

Protein secondary structure motifs: A kinematic construction.

The kinematic geometry of protein backbone structures, constrained by either single or multiple hydrogen bonds (H-bonds), possibly in a periodic array, is discussed. These structures include regular secondary structure elements α-helices and β-sheets but also include other short H-bond stabilized irregular structural elements like β-turns. The work here shows that the variations observed in such structures have simple geometrical correlations consistent with constrained motion kinematics. A new classification of the ideal helices is given, in terms of the parameter α, the angle at a Cα atom to its two neighboring Cα 's along the helix, and shown how it can be generalized to include nonideal helices. Specifically, we derive an analytical expression of the backbone dihedrals, (ϕ, ψ), in terms of the parameter α subject to the constraint that the peptide planes are parallel to the helical axis. Helices constructed in this way exhibit near-vertical alignment of the C = O and N - H units and are the canonical objects of this study. These expressions are easily modifiable to include perturbations of parameters relevant to nonplanar peptide units and noncanonical angles. The addition of a second parameter, ε0 , inclination of successive peptide planes along a helix with respect to the helical axis leads to a generalization of the previous expression and provides an efficient parametrization of such structures in terms of coordinates consistent with H-bond parameters. An analogs parametrization of β-turns, using inverse kinematic methods, is also given. Besides offering a unifying viewpoint, our results may find useful applications to protein and peptide design.

A comprehensive study of analyzing powers in the proton\u2013deuteron break-up channel at 135 MeV

A measurement of the analyzing powers for the ^2hbox {H}(vec {p},pp)n break-up reaction was carried out at KVI exploiting a polarized-proton beam at an energy of 135,hbox {MeV}. The scattering angles and energies of the final-state protons were measured using the Big Instrument for Nuclear-polarization Analysis (BINA) with a nearly 4pi geometrical acceptance. In this work, we analyzed a large number of kinematical geometries including forward–forward configurations in which both the final-state particles scatter to small polar angles and backward–forward configurations in which one of the final-state particles scatters to large polar angles. The results are compared with Faddeev calculations based on modern nucleon–nucleon (NN) and three-nucleon (3N) potentials. Discrepancies between polarization data and theoretical predictions are observed for configurations corresponding to small relative azimuthal angles between the two final-state protons. These configurations show a large sensitivity to 3N force effects.

Analytical synthesis of the kinematic geometry of spiral bevel gears of pure-rolling contact

This work attempts to improve the kinematic geometry model of pure-rolling contact spiral bevel gears (PCSBGs). A systematic report on the analytical design and analysis methods for PCSBGs is presented herein. The tooth surface model of PCSBGs are extended, and a direct relationship between the normal vector and normal pressure angle of PCSBGs is derived, which contributes to building a bridge between the basic geometric parameters and contact characteristics of PCSBGs. The curvature relationships between the tooth surfaces of PCSBGs are derived, and simple equations related to the relative normal curvatures of PCSBGs are obtained from tensor analysis. A logarithmic spiral bevel gear is used as a sample case to demonstrate the application of the kinematic geometry model of PCSBGs and to verify the analytical expressions. The numerical analysis results of the logarithmic spiral bevel gears agree with the analytical model.