A Comparative Study on Kinematic Calibration for a 3-DOF Parallel Manipulator Using the Complete-Minimal,Inverse-Kinematic and Geometric-Constraint Error Models

Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.

Compliance Modeling and Analysis of a 3-RPS Parallel Kinematic Machine Module

The compliance modeling and rigidity performance evaluation for the lower mobility parallel manipulators are still to be remained as two overwhelming challenges in the stage of conceptual design due to their geometric complexities. By using the screw theory, this paper explores the compliance modeling and eigencompliance evaluation of a newly patented 1T2R spindle head whose topological architecture is a 3-RPS parallel mechanism. The kinematic definitions and inverse position analysis are briefly addressed in the first place to provide necessary information for compliance modeling. By considering the 3-RPS parallel kinematic machine（PKM） as a typical compliant parallel device, whose three limb assemblages have bending, extending and torsional deflections, an analytical compliance model for the spindle head is established with screw theory and the analytical stiffness matrix of the platform is formulated. Based on the eigenscrew decomposition, the eigencompliance and corresponding eigenscrews are analyzed and the platform＇s compliance properties are physically interpreted as the suspension of six screw springs. The distributions of stiffness constants of the six screw springs throughout the workspace are predicted in a quick manner with a piece-by-piece calculation algorithm. The numerical simulation reveals a strong dependency of platform＇s compliance on its configuration in that they are axially symmetric due to structural features. At the last stage, the effects of some design variables such as structural, configurational and dimensional parameters on system rigidity characteristics are investigated with the purpose of providing useful information for the structural design and performance improvement of the PKM. Compared with previous efforts in compliance analysis of PKMs, the present methodology is more intuitive and universal thus can be easily applied to evaluate the overall rigidity performance of other PKMs with high efficiency.

Magnetostrictive and Kinematic Model Considering the Dynamic Hysteresis and Energy Loss for GMA

Due to the influence of magnetic hysteresis and energy loss inherent in giant magnetostrictive materials （GMM）, output displacement accuracy of giant magnetostrictive actuator （GMA） can not meet the precision and ultra precision machining. Using a GMM rod as the core driving element, a GMA which may be used in the field of precision and ultra precision drive engineering is designed through modular design method. Based on the Armstrong theory and elastic Gibbs free energy theory, a nonlinear magnetostriction model which considers magnetic hysteresis and energy loss characteristics is established. Moreover, the mechanical system differential equation model for GMA is established by utilizing D＇Alembert＇s principle. Experimental results show that the model can preferably predict magnetization property, magnetic potential orientation, energy loss for GMM. It is also able to describe magnetostrictive elongation and output displacement of GMA. Research results will provide a theoretical basis for solving the dynamic magnetic hysteresis, energy loss and working precision for GMA fundamentally.

Improved Stiffness Modeling for An Exechon‑Like Parallel Kinematic Machine(PKM)and Its Application

Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy,stiffness and workspace of machining equipment.Therefore,a 5-DOF(degrees of freedom)parallel kinematic machine(PKM)with redundant constraints is proposed.Based on the kinematics analysis of the parallel mechanism using intermediate variables,the kinematics problems of the PKM are solved through equivalent kinematics model.The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM,where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis.And the stiffness model of the parallel mechanism is improved by correction coefficient matrix,each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism.The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively.The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism.To enhance the machining accuracy of the PKM,the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece.A plate workpiece taken as example is examined in the case study section,which demonstrates the effectiveness of optimization method.

A Kinematic Thermal Model for Descending Slabs with Velocity Boundary Layers:A Case Study for the Tonga Subducting Slab

For the purpose of investigating the influence of metastable olivine（MO） phase transformations on both deep seismicity and stagnation of slabs,we constructed a 2-dimensional finite element thermal model for a 120 Ma-old 50°dipping oceanic lithosphere descending at 10 cm/yr with velocity boundary layers,which would mitigate the interference of constant velocity field for the slab. The resulting temperatures show that most of intermediate and deep earthquakes occurring within the Tonga slab are occurring inside the 800℃and 1200℃isotherm,respectively.The elevation of olivine transformation near～410 km and respective persistence of metastable olivine and spinel within the transition zone and beneath 660 km would thus result in bimodal positive,zonal,negative density anomalies,respectively.These results together with the resulting pressure anomalies may reflect the stress pattern of the Tonga slab：（i） slab pull force exerts above a depth of～230 km;（ii） MO existence changes the buoyancy force within the transition zone and facilitates slab stagnation at a depth of 660 km;（iii） as the subducting materials accumulated over 660 km,deepest earthquakes occur due to MO transformation;（iv） a flattened‘slab’ may penetrate into the lower mantle due to the density increment of Sp transformation.

Preliminary results on kinematic model of tectonic blocks derived from high precision GPS observations in Southwest China

In the paper, the kinematic model of tectonic blocks in southwest China is studied based on the precision GPS observations carried out under the major subject of 'Studies on Current Crustal Movement and Geodynamics' which belongs to the State Climbing Project. It is believed that at present, the data of high precision GPS observation may provide convincing information related to the horizontal movement of tectonic blocks in the Chinese mainland. The preliminary results obtained from the kinematic model have given some direct evidences for the research of dynamic mechanism of crustal deformation in the Chinese mainland and on the basis of which, the kinematic characteristics and their relations to the seismicity and seismic risk in the reobserved region are analysed. The preliminary observation results are encouraging.

Anomaly detection method based on kinematics model and nonholonomic constraint of vehicle

A method used to detect anomaly and estimate the state of vehicle in driving was proposed.The kinematics model of the vehicle was constructed and nonholonomic constraint conditions were added,which refer to that once the vehicle encounters the faults that could not be controlled,the constraint conditions are violated.Estimation equations of the velocity errors of the vehicle were given out to estimate the velocity errors of side and forward.So the stability of the whole vehicle could be judged by the velocity errors of the vehicle.Conclusions were validated through the vehicle experiment.This method is based on GPS/INS integrated navigation system,and can provide foundation for fault detections in unmanned autonomous vehicles.

Neural Network Based Multi-level Fuzzy Evaluation Model for Mechanical Kinematic Scheme

To implement a quantificational evaluation for mechanical kinematic scheme more effectively,a multi-level and multi-objective evaluation model is presented using neural network and fuzzy theory. Firstly,the structure of evaluation model is constructed according to evaluation indicator system. Then evaluation samples are generated and provided to train this model. Thus it can reflect the relation between attributive value and evaluation result,as well as the weight of evaluation indicator. Once evaluation indicators of each candidate are fuzzily quantified and fed into the trained network model,the corresponding evaluation result is outputted and the best alternative can be selected. Under this model,expert knowledge can be effectively acquired and expressed,and the quantificational evaluation can be implemented for kinematic scheme with multi-level evaluation indicator system. Several key problems on this model are discussed and an illustration has demonstrated that this model is feasible and can be regarded as a new idea for solving kinematic scheme evaluation.

Vehicle kinematics modeling and design of vehicle trajectory generator system

A trajectory generator based on vehicle kinematics model was presented and an integrated navigation simulation system was designed.Considering that the tight relation between vehicle motion and topography,a new trajectory generator for vehicle was proposed for more actual simulation.Firstly,a vehicle kinematics model was built based on conversion of attitude vector in different coordinate systems.Then,the principle of common trajectory generators was analyzed.Besides,combining the vehicle kinematics model with the principle of dead reckoning,a new vehicle trajectory generator was presented,which can provide process parameters of carrier anytime and achieve simulation of typical actions of running vehicle.Moreover,IMU(inertial measurement unit) elements were simulated,including accelerometer and gyroscope.After setting up the simulation conditions,the integrated navigation simulation system was verified by final performance test.The result proves the validity and flexibility of this design.

Kinematic error modeling and error compensation of desktop 3D printer

Desktop 3D printers have revolutionized how designers and makers prototype and manufacture certain products.Highly popular fuse deposition modeling(FDM)desktop printers have enabled a shift to low-cost consumer goods markets,through reduced capital equipment investment and consumable material costs.However,with this drive to reduce costs,the computer numerical control(CNC)systems implemented in FDM printers are often compromised by poor accuracy and contouring errors.This condition is most critical as users begin to use 3D-printed components in load-bearing applications or to perform mechanical functions.Improved methods of low-cost 3D printer calibration are needed before their open-design potential can be realized in applications,including 3D-printed orthotics and prosthetics.This paper applies methodologies associated with high-precision CNC machining systems,namely,kinematic error modeling and compensation coupled with standardized test methods from ISO230-4,such as the ballbar for kinematic and dynamic error measurements,to examine the influence and feasibility for use on low-cost CNC/3D printing platforms.Recently,the U.S.Food and Drug Administration's"Technical considerations for additive manufactured medical devices"highlighted the need to develop standards specific to additive manufacturing in regulated manufacturing environments.This paper shows the benefits of the methods described within ISO230-4 for error assessment,alongside applying kinematic error modeling and compensation to the popular kinematic configuration of an Ultimaker 3D printer.A Renishaw ballbar QC10 is used to quantify the Ultimaker's errors and thereby populate the error model.This method quantifies machine errors and populates these in a mathematical model of the CNC system.Then,a post-processor can be used to compensate the printing code.Subsequently,the ballbar is used to demonstrate the dramatic impact of the error compensation model on the accuracy and contouring of the Ultimaker printer with 58%reduction in overall circularity error and 90%reduction in squareness error.

A Kinematic Thermal Model for Descending Slabs with Velocity Boundary Layers

Kinematic models compute the temperature distribution by prescribing a constant convergent velocity for the subducting slab,resulting in an artificial velocity discontinuity,which may accelerate the heating of subducting slabs.For the purpose to moderate the influence of such artificial discontinuity, we construct a 2D thermal model for subduction zones with a velocity boundary layer,within which the velocities decrease linearly with the distance from the interfaces of slabs.Temperatures are calculated

A Generic Kinematic Model for Three Main Types of Five-axis Machine Tools

Material removal is one of the most used processes in manufacturing. Five-axis CNC machines are believed to be the best tools in sculptured surface machining. In this study, a generic and unified kinematic model was developed as a viable alternative to the particular solutions that are only applicable to individual machine configurations. This versatile model is then used to verify the feasibility of the two rotational joints within the kinematic chain of three main types of a five-axis machine-tool. This versatile model is very useful applied to the design of five-axis machine tools.

KINEMATIC WAVE PROPERTIES OF ANISOTROPIC DYNAMICS MODEL FOR TRAFFIC FLOW

The analyses of kinematic wave properties of a new dynamics model for traffic flow are carried out. The model does not exhibit the problem that one characteristic speed is always greater than macroscopic traffic speed, and therefore satisfies the requirement that traffic flow is anisotropic. Linear stability analysis shows that the model is stable under certain condition and the condition is obtained. The analyses also indicate that the model has a hierarchy of first- and second-order waves and allows the existence of both smooth traveling wave and shock wave. However, the model has a distinctive criterion of shock wave compared with other dynamics models, and the distinction makes the model more realistic in dealing with some traffic problems such as wrong-way travel analysis.

Kinematics modeling of a 6-PSS parallel mechanism with wide-range flexure hinges

A novel 6-PSS flexible parallel mechanism was presented,which employed wide-range flexure hinges as passive joints.The proposed mechanism features micron level positioning accuracy over cubic centimeter scale workspace.A three-layer back-propagation(BP) neural network was utilized to the kinematics analysis,in which learning samples containing 1 280 groups of data based on stiffness-matrix method were used to train the BP model.The kinematics performance was accurately calculated by using the constructed BP model with 19 hidden nodes.Compared with the stiffness model,the simulation and numerical results validate that BP model can achieve millisecond level computation time and micron level calculation accuracy.The concept and approach outlined can be extended to a variety of applications.

Modeling and Kinematics Simulation of Hydro-mechanical Split Path Steering Device of Tracked Vehicle Based on CATIA

Based on the working principle of hydro-mechanical split path of tracked vehicle, a operating gear was developed which was controlled by steering wheel and match with transmission case. Then CATIA software was used to build the three-dimensional model and carry out dynamic simulation of the mechanism. The result indicates that the design of the mechanism fulfills the request.

Kinematic source model for simulation of near-fault ground motion field using explicit finite element method

This paper briefly reviews the characteristics and major processes of the explicit finite element method in modeling the near-fault ground motion field. The emphasis is on the finite element-related problems in the finite fault source modeling. A modified kinematic source model is presented, in which vibration with some high frequency components is introduced into the traditional slip time function to ensure that the source and ground motion include sufficient high frequency components. The model presented is verified through a simple modeling example. It is shown that the predicted near-fault ground motion field exhibits similar characteristics to those observed in strong motion records, such as the hanging wall effect, vertical effect, fling step effect and velocity pulse effect, etc.

Analysis of Runoff in Ungauged Mountain Watersheds in Sichuan,China using Kinematic-wave-based GIUH Model

Floods are one of the most common natural hazards occurring all around the world.However,the knowledge of the origins of a food and its possible magnitude in a given region remains unclear yet.This lack of understanding is particularly acute in mountainous regions with large degrees in Sichuan Province,China,where runoff is seldom measured.The nature of streamflow in a region is related to the time and spatial distribution of rainfall quantity and watershed geomorphology.The geomorphologic characteristics are the channel network and surrounding landscape which transform the rainfall input into an output hydrograph at the outlet of the watershed.With the given geomorphologic properties of the watershed,theoretically the hydrological response function can be determined hydraulically without using any recorded data of past rainfall or runoff events.In this study,a kinematic-wave-based geomorphologic instantaneous unit hydrograph (KW-GIUH) model was adopted and verified to estimate runoff in ungauged areas.Two mountain watersheds,the Yingjing River watershed and Tianquan River watershed in Sichuan were selected as study sites.The geomorphologic factors of the two watersheds were obtained by using a digital elevation model (DEM) based on the topographic database obtained from the Shuttle Radar Topography Mission of US's NASA.The tests of the model on the two watersheds were performed both at gauged and ungauged sites.Comparison between the simulated and observed hydrographs for a number of rainstorms at the gauged sites indicated the potential of the KW-GIUH model as a useful tool for runoff analysis in these regions.Moreover,to simulate possible concentrated rainstorms that could result in serious flooding in these areas,synthetic rainfall hyetographs were adopted as input to the KW-GIUH model to obtain the flow hydrographs at two ungauged sites for different return period conditions.Hydroeconomic analysis can be performed in the future to select the optimum design return period for determining the flood control work.

A kinematics-uplift model for the HimalayanTibetan region

The Lhasa-Gangdise Terrane is taken as a representative mobile terrane during the Himalayan orogeny of the India- Eurasia continental collision, for which a corresponding kinematics-uplift model is set up. The parameterization of the model is ultimately constrained by the uplift history outlined by synthesized paleogeoglaphic studies with consideration of the following factors: (1 ) kinematic features of india-Eurasia plate convergence; (2) 3-D mass conservation during terrane deformations incorporating shortening, thickening, extension, uplift and ero sion; and (3) instantaneous vertical movement of lithospheric material under the control of isostasy. The model study involves the following four groups of uplift-relevant parameters: ① plate converging velocity and its variations with time; ② extent of lateral mass transfer; ③ crustal structure: and ④) surface erosion mode. The results of calculation of 144 models of different Parameter combinations have indicated the non-uniqueness of solution. Nevertheless, it is also proved that for a fixed kinematic mode of plate convergence there exists a unique best-fitting model which may reproduce the observed uplift history, implying the uniqueness of dynamic environment of two converging plates. Therefore, the uplift of the Himalayan-Tibetan region is mainly controlled by plate dynamics-kinematics and is a complicated geological process of far-reaching implications.

A Method for Automatically Establishing a Mathematical Model of Kinematic Analysis to a Planar Mechanism with a Multiple Joint and Prismatic Pair

A method for automatically establishing a mathematical model of kinematic analysis to a planar mechanism with multiple joint and prismatic pair is presented. The breadth （ or depth ） first search spanning tree can be obtained based on an adjacency matrix of the mechanism. Then the kinematic chain （or mechanism）＇s basic loops can be obtained. On the basis of these basic loops, a mathematical model of kinematic analysis can be established and solved automatically. In the sense of a calculative mechanism, structural analysis of the kinematic chain relates to the kinematic analysis of a mechanism. Thus, an effective way is supplied to the given mechanism＇s kinematic analysis for automatic modeling and solving, and a method is supplied to the structural type to optimize kinematic synthesis.

Kinematic modeling and analysis of novel eight-wheel lunar rover

A new kind of eight-wheel lunar rover is developed, which is a complex closed-chain system and has good capabilities of climbing slope, surmounting obstacles and adapting to uneven terrain. In this paper, the mechanical structure of the novel eight-wheel lunar rover is introduced, forward and inverse kinematic models of the rover are established according to the closed-chain coordinate transformation and instantaneous coincidence coordinate. Based on structural characteristics, its kinetic characteristics are analyzed. Wheel slippages are separated and calculated, and a method for closed-loop control modification using wheel slip estimation during the model establishment is proposed. The results can be applied to the motion control of lunar rover.