(cache)Journal articles: 'Kinematic geometry'

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Heil, D. P., and Robert Pickels. "The Influence of Bicycle Geometry on Time-Trial Positioning Kinematics and Markers of Performance." International Journal of Physical Education, Fitness and Sports 8, no. 1 (January 20, 2019): 11–24. http://dx.doi.org/10.26524/ijpefs1912.

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Studies have previously documented how changes in cycling body kinematics are related to submaximal energetics and power output, as well as cycling performance, but few have focused specifically on how body kinematics will vary with changes in bicycle geometry. This study sought to describe kinematic changes resulting from the systematic change of several bicycle geometry variables: Trunk angle (“low” and “high” positions), seat-tube angle (76° and 80°), saddle tilt angle (0° to -10°), saddle sitting position (middle or nose), as well as two types of saddles. Methods: Well-trained cyclists were kinematically evaluated across specific combinations of geometry variables using a modified cycle ergometer at a standard relative power. Standard two dimensional sagittal-view kinematics from the left side were used to summarize a collection of kinematic variables: Trunk angle, hip angle (HA), knee angle, pelvic tilt angle, and two “composite” angles called body position and pelvic position (PP). Finally, each trial was also evaluated for frontal area (FA; m2) from stationary digital photography. Data were evaluated using repeated measures ANOVA (a=0.05) to evaluate change in kinematics between trials, as well as regression analysis to determine predictability of performance markers (HA and FA) from the collection of geometry and kinematic variables. Results: Changing trunk angle had the greatest impact on other kinematic variables, while saddle type had no influence. Regression showed that geometry variables could explain 75-85% of the variability in either HA or FA, while 78-79% of the variation in HA and 83- 84% of FA was explained by PP alone. Conclusions: The composite kinematic measure PP was generally a better predictor of both HA and FA than any combination of geometry variables. These results can serve as a starting point for understanding the interactions between bicycle geometry and body kinematics, both of which are important determinants of power generation and aerodynamic drag.

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Wang, Michael Yu, Tong Liu, and Diana M. Pelinescu. "Fixture Kinematic Analysis Based on the Full Contact Model of Rigid Bodies." Journal of Manufacturing Science and Engineering 125, no. 2 (April 15, 2003): 316–24. http://dx.doi.org/10.1115/1.1557293.

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The conventional point-kinematic model of fixtures has only treated point geometry of the contacts between locators and workpiece. However, this model, which ignores the underlying surface properties of the locators-plus-workpiece system, is inherently incapable of capturing the effects of the geometric properties important to accurate positioning of the workpiece. In this paper, we present a fixture kinematic analysis based on the full kinematics of locator-workpiece contact. This model incorporates a “virtual” kinematic chain with meshing parameters of contact kinematics in a velocity formulation. Conditions of a deterministic fixture are derived. It is shown that the workpiece position and orientation are completely characterized by the kinematic properties of the locator contacts with the workpiece, including not only the arbitrary locator location errors but also the surface properties at nonprismatic locator-workpiece contacts. This is illustrated with numerical examples. The fixture kinematic analysis developed here has a strong implication for designing fixtures with high locating precision requirements.

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Gonçalves, Fernando, Tiago Ribeiro, António Fernando Ribeiro, Gil Lopes, and Paulo Flores. "A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles." Robotics 11, no. 1 (January 14, 2022): 15. http://dx.doi.org/10.3390/robotics11010015.

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Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

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Hanuschik, R. W. "FeII line widths as tracers for the geometry of Be star envelopes." Symposium - International Astronomical Union 162 (1994): 265–66. http://dx.doi.org/10.1017/s0074180900215015.

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The geometry of Be star envelopes is not directly observable, apart from those very few cases where interferometry has been successful. This is even more true for the kinematical conditions in these envelopes. An indirect measure of kinematics, density law and geometry can be achieved by comparing line widths of photospheric absorption lines (⇔ v* sin i) and circumstellar emission lines (⇔ v(r) sin i). Hitherto existing determinations of line widths have been, however, quite unsatisfactory. The reason is that in these studies Balmer line parameters were used [see Hanuschik (1989) and references therein] which are strongly broadened by radiative transfer and Thomson scattering in addition to kinematic broadening. Because the question of geometry and kinematics is of crucial importance for understanding the Be phenomenon, I have started a new study, using measurements of the Fe ii λ5317 line. This line shows almost optically thin emission and is broadened primarily by kinematics.

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Abadjieva, Emilia. "Kinematic Theory of Spatial Rack Drives." Applied Mechanics and Materials 851 (August 2016): 265–72. http://dx.doi.org/10.4028/www.scientific.net/amm.851.265.

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On the basis of performed vector analysis of spatial motion transformation of type rotation into translation is created a kinematic theory of this transformation type. Using the kinematic theory the basic kinematic-geometric characteristics of spatial rack mechanisms, applicable to their analysis and synthesis are initiated. These characteristics: kinematic cylinder of level, kinematic relative helicoids, and kinematic pitch surfaces are elements of kinematic geometry of the spatial rack drives

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Todorovič, Dejan. "Is kinematic geometry an internalized regularity?" Behavioral and Brain Sciences 24, no. 4 (August 2001): 641–51. http://dx.doi.org/10.1017/s0140525x01000073.

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A general framework for the explanation of perceptual phenomena as internalizations of external regularities was developed by R. N. Shepard. A particular example of this framework is his account of perceived curvilinear apparent motions. This paper contains a brief summary of the relevant psychophysical data, some basic kinematical considerations and examples, and several criticisms of Shepard's account. The criticisms concern the feasibility of internalization of critical motion types, the roles of simplicity and uniqueness, the contrast between classical physics and kinematic geometry, the import of perceived path curvilinearity, and the relation of perceptual and scientific knowledge.

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Li, Shutian, and Q. J. Ge. "Rational Be´zier Line-Symmetric Motions." Journal of Mechanical Design 127, no. 2 (March 1, 2005): 222–26. http://dx.doi.org/10.1115/1.1798251.

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This paper brings together line geometry, kinematic geometry of line-symmetric motions, and computer aided geometric design to develop a method for geometric design of rational Be´zier line-symmetric motions. By taking advantage of the kinematic geometry of a line-symmetric motion, the problem of synthesizing a rational Be´zier line-symmetric motion is reduced to that of designing a rational Be´zier ruled surface. In this way, a recently developed de Casteljau algorithm for line-geometric design of ruled surfaces can be applied. An example is presented in which the Bennet motion is represented as a rational Be´zier line-symmetric motion whose basic surface is a hyperboloid.

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Alluhaibi, Nadia, and Rashad A. Abdel-Baky. "Kinematic-geometry of lines with special trajectories in spatial kinematics." AIMS Mathematics 8, no. 5 (2023): 10887–904. http://dx.doi.org/10.3934/math.2023552.

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<abstract><p>This paper derives the expressions for kinematic-geometry of lines with special trajectories in spatial kinematics by means of the E. Study map. A particular assurance goes to the 2nd order movement characteristics for extracting a new proof of the Disteli formulae of the axodes. Meanwhile, a new height dual function is defined and utilized to investigate the geometrical properties of the Disteli-axis. Consequently, as an implementation, the spatial equivalent of the cubic of stationary curvature is established and researched. Finally, Disteli formulae of a line-trajectory are extracted and inspected in detail.</p></abstract>

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Xiong, Tao, Liping Chen, Jianwan Ding, Yizhong Wu, and Wenjie Hou. "Recognition of Kinematic Joints of 3D Assembly Models Based on Reciprocal Screw Theory." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/1761968.

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Reciprocal screw theory is used to recognize the kinematic joints of assemblies restricted by arbitrary combinations of geometry constraints. Kinematic analysis is common for reaching a satisfactory design. If a machine is large and the incidence of redesign frequent is high, then it becomes imperative to have fast analysis-redesign-reanalysis cycles. This work addresses this problem by providing recognition technology for converting a 3D assembly model into a kinematic joint model, which is represented by a graph of parts with kinematic joints among them. The three basic components of the geometric constraints are described in terms of wrench, and it is thus easy to model each common assembly constraint. At the same time, several different types of kinematic joints in practice are presented in terms of twist. For the reciprocal product of a twist and wrench, which is equal to zero, the geometry constraints can be converted into the corresponding kinematic joints as a result. To eliminate completely the redundant components of different geometry constraints that act upon the same part, the specific operation of a matrix space is applied. This ability is useful in supporting the kinematic design of properly constrained assemblies in CAD systems.

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Schaaf, J. A., and An Tzu Yang. "Kinematic Geometry of Spherical Evolutes." Journal of Mechanical Design 114, no. 1 (March 1, 1992): 109–16. http://dx.doi.org/10.1115/1.2916903.

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In this paper, we define spherical evolutes corresponding to the trajectory of a point in spherical kinematics. We derive general expressions for the curvature properties of the nth spherical evolute in terms of the geodesic curvature and the derivative of the geodesic curvature for the (n-1)the spherical evolute. The results are illustrated by numerical examples for the motion of a circular cone rolling on a fixed circular cone, of a spherical turning-block linkage, and of a spherical four-bar linkage.

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Flores, Alfinio. "THE KINEMATIC METHOD IN GEOMETRY." PRIMUS 12, no. 4 (January 2002): 321–33. http://dx.doi.org/10.1080/10511970208984038.

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Manrique-Escobar, Camilo Andres, Carmine Maria Pappalardo, and Domenico Guida. "A Multibody System Approach for the Systematic Development of a Closed-Chain Kinematic Model for Two-Wheeled Vehicles." Machines 9, no. 11 (October 20, 2021): 245. http://dx.doi.org/10.3390/machines9110245.

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In this investigation, a closed-chain kinematic model for two-wheeled vehicles is devised. The kinematic model developed in this work is general and, therefore, it is suitable for describing the complex geometry of the motion of both bicycles and motorcycles. Since the proposed kinematic model is systematically developed in the paper by employing a sound multibody system approach, which is grounded on the use of a straightforward closed-chain kinematic description, it allows for readily evaluating the effectiveness of two alternative methods to formulate the wheel-road contact constraints. The methods employed for this purpose are a technique based on the geometry of the vector cross-product and a strategy based on a simple surface parameterization of the front wheel. To this end, considering a kinematically driven vehicle system, a comparative analysis is performed to analyze the geometry of the contact between the front wheel of the vehicle and the ground, which represents a fundamental problem in the study of the motion of two-wheeled vehicles in general. Subsequently, an exhaustive and extensive numerical analysis, based on the systematic multibody approach mentioned before, is carried out in this work to study the system kinematics in detail. Furthermore, the orientation of the front assembly, which includes the frontal fork, the handlebars, and the front wheel in a seamless subsystem, is implicitly formulated through the definition of three successive rotations, and this approach is used to propose an explicit formulation of its inherent set of Euler angles. In general, the numerical results developed in the present work compare favorably with those found in the literature about vehicle kinematics and contact geometry.

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Almoneef, Areej A., and Rashad A. Abdel-Baky. "Kinematic Differential Geometry of a Line Trajectory in Spatial Movement." Axioms 12, no. 5 (May 14, 2023): 472. http://dx.doi.org/10.3390/axioms12050472.

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This paper investigates the kinematic differential geometry of a line trajectory in spatial movement. Specifically, we provide a theoretical expression of inflection line congruence, which is the spatial equivalent of the inflection circle of planar kinematics. Additionally, we introduce new proofs for the Euler–Savary and Disteli formulae and thoroughly analyze their spatial equivalence.

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Wampler, Charles W., and Andrew J. Sommese. "Numerical algebraic geometry and algebraic kinematics." Acta Numerica 20 (April 28, 2011): 469–567. http://dx.doi.org/10.1017/s0962492911000067.

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In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.

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Han, Youcheng, Weizhong Guo, Changjie Zhao, Ziyue Li, Ze Fu, and Yinghui Li. "Updating structural synthesis methodology of mechanisms: from kinematic geometry to kinematic geometry accompanied with statics." Mechanism and Machine Theory 192 (February 2024): 105516. http://dx.doi.org/10.1016/j.mechmachtheory.2023.105516.

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Luo, Ji Man, Da Long Wang, Zhi Hui Xing, and Ngai Ming Kwok. "Multi-Objective Optimal Kinematic Design of 3-TPS/TP Parallel Robot Manipulator." Advanced Engineering Forum 2-3 (December 2011): 324–29. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.324.

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The purpose of this research work is to find the optimized kinematic structural parameters of the 3-TPS/TP parallel manipulator while taking into consideration the workspace, kinematic properties and other factors. The Ranked Pareto Particle Swarm Optimization (RP-PSO) approach is applied to solve the multi-objective optimization problems. Firstly, the structure of the parallel manipulator and its kinematic model are devised. Then, we set up the kinematical performance indices for the evaluation of manipulator working properties, including Local Condition Index (LCI), Global Condition Index (GCI) and Good Condition Workspace (GCW). The optimization is further carried out in a Parameter Design Space (PDS) with normalized geometry parameters. Then the geometry optimization problems are solved using a PDS based RP-PSO approach. Finally, the feasibility of this approach is supported by examples given this paper.

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Zhao, Guojuan, Shengcheng Jiang, Kai Dong, Quanwang Xu, Ziling Zhang, and Lei Lu. "Influence Analysis of Geometric Error and Compensation Method for Four-Axis Machining Tools with Two Rotary Axes." Machines 10, no. 7 (July 19, 2022): 586. http://dx.doi.org/10.3390/machines10070586.

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Four-axis machine tools with two rotary axes are widely used in the machining of complex parts. However, due to an irregular kinematic relationship and non-linear kinematic function with geometric error, it is difficult to analyze the influence the geometry error of each axis has and to compensate for such a geometry error. In this study, an influence analysis method of geometric error based on the homogeneous coordinate transformation matrix and a compensation method was developed, using the Newton iterative method. Geometric errors are characterized by a homogeneous coordinate transformation matrix in the proposed method, and an error matrix is integrated into the kinematic model of the four-axis machine tool as a means of studying the influence the geometric error of each axis has on the tool path. Based on the kinematic model of the four-axis machine tool considering the geometric error, a comprehensive geometric error compensation calculation model based on the Newton iteration was then constructed for calculating the tool path as a means of compensating for the geometric error. Ultimately, the four-axis machine tool with a curve tool path for an off-axis optical lens was chosen for verification of the proposed method. The results showed that the proposed method can significantly improve the machining accuracy.

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Koifman, K. G. "Reference shape of bodies with enhanced kinematics. Part II. Second gradient and microstructure." Vestnik of Samara University. Natural Science Series 29, no. 4 (December 26, 2023): 54–76. http://dx.doi.org/10.18287/2541-7525-2023-29-4-54-76.

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The work develops differential-geometric methods for modeling finite incompatible deformations of hyperelastic solids with enhanced kinematics. The response of such bodies, along with the standard kinematic field represented by the deformation gradient, is characterized by additional tensor fields. As such, the paper considers: 1) the second deformation gradient and 2) the tensor field of the second rank, modeling the microstructure of the body. For each of these two cases, compatibility conditions are obtained and their geometric interpretation is proposed. Geometry is synthesized on the material manifold representing a body with enhanced kinematics. The corresponding affine connection has non-zero torsion and curvature, which can be useful for modeling a body with dislocations and disclinations.

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Tian, Yingzhong, Mingxuan Luan, Xu Gao, Wenbin Wang, and Long Li. "Kinematic Analysis of Continuum Robot Consisted of Driven Flexible Rods." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/6984194.

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This paper presents the kinematic analysis of a continuum bionic robot with three flexible actuation rods. Since the motion of the end-effector is actuated by the deformation of the rods, the robot structure is with high elasticity and good compliance and the kinematic analysis of the robot requires special treatment. We propose a kinematic model based on the geometry with constant curvature. The analysis consists of two independent mappings: a general mapping for the kinematics of all robots and a specific mapping for this kind of robots. Both of those mappings are developed for the single section and for the multisections. We aim at providing a guide for kinematic analysis of the similar manipulators through this paper.

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Guo, Wentao, Weizhong Guo, Jeffrey Q. Ge, and Feng Gao. "A novel method to model the effect of environmental constraint of geometry in the mechanism design." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 20 (January 5, 2018): 3751–66. http://dx.doi.org/10.1177/0954406217742934.

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Few studies have considered the effect of environmental constraints throughout the entire design process of mechanical systems. Neglecting such effect might lead to misunderstanding the kinematic performance of the mechanical systems. In our work, an environment-based design concept was proposed by using passive limbs to model and analyze geometrical constraints in each step of the theoretical design process. Redesigning of a thrust system in a shield machine is taken as an example for better demonstration of this design approach. A new equivalent model of the thrust system was synthesized by using passive limbs to express environmental constraints of geometry based on the shield behavior. The uniform kinematic model was developed for the integrated equivalent mechanism of the thrust system. The effectiveness of the passive limbs in expressing environmental constraints was then evaluated by kinematical analysis. A singularity analysis was performed to assess the consistency between the equivalent model and a real thrust system. The reachable angular workspace was also analyzed to demonstrate the influence of the passive limbs as an example of environment-based parameter design. A motion simulation was performed to demonstrate the improvement of the forward kinematics by using the passive limbs to solve the singularity problem. A dexterity performance index based on the proposed model was conducted to demonstrate the kinematical property of the thrust system.

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Sreenivasan, S. V., and P. Nanua. "Kinematic Geometry of Wheeled Vehicle Systems." Journal of Mechanical Design 121, no. 1 (March 1, 1999): 50–56. http://dx.doi.org/10.1115/1.2829429.

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This paper utilizes a kinematic-geometric approach to study the first-order motion characteristics of wheeled vehicles on even and uneven terrain. The results obtained from first-order studies are compared to those obtained from second order kinematic analyses, and special situations where the first-order analysis is inadequate are discussed. This approach is particularly suited for studying actively actuated vehicles since their designs typically do not include intentional passive compliances. It is shown that if a vehicle-terrain combination satisfies certain geometric conditions, for instance when a wheeled vehicle operates on even terrain or on a spherical surface, the system possesses a singularity—it possesses finite range mobility that is higher than the one obtained using Kutzbach criterion. On general uneven terrain, the same vehicles require undesirable ‘kinematic slipping’ at the wheel-terrain contacts to attain the mobility that it possesses on these special surfaces. The kinematic effects of varying the vehicle and/or terrain geometric parameters from their nominal values are discussed. The design enhancements that are required in existing off-road vehicles to avoid kinematic slipping are presented for a class of vehicles that include two-wheel axles in their designs.

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Todorovic, Dejan. "Is kinematic geometry an internalized regularity?" Behavioral and Brain Sciences 24, no. 4 (June 1, 2001): 778. http://dx.doi.org/10.1017/s0140525x01790085.

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Martinez-Torres, L. M., R. Ramon-Lluch, and L. Eguiluz. "Tectonic wedges: geometry and kinematic interpretation." Journal of Structural Geology 16, no. 10 (October 1994): 1491–94. http://dx.doi.org/10.1016/0191-8141(94)90011-6.

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Rotzoll, Mirja, Margaret H. Regan, Manfred L. Husty, and M. John D. Hayes. "Kinematic geometry of spatial RSSR mechanisms." Mechanism and Machine Theory 185 (July 2023): 105335. http://dx.doi.org/10.1016/j.mechmachtheory.2023.105335.

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Ibaraki, Soichi, and Ibuki Yoshida. "A Five-Axis Machining Error Simulator for Rotary-Axis Geometric Errors Using Commercial Machining Simulation Software." International Journal of Automation Technology 11, no. 2 (March 1, 2017): 179–87. http://dx.doi.org/10.20965/ijat.2017.p0179.

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This paper presents a simulator that graphically presents the influence of rotary-axis geometric errors on the geometry of a finished workpiece. Commercial machining simulation software is employed for application to arbitrary five-axis tool paths. A five-axis kinematic model is implemented with the simulator to calculate the influence of rotary-axis geometric errors. The machining error simulation is demonstrated for 1) the cone frustum machining test described in ISO 10791-7:2015 [1], and 2) the pyramid-shaped machining test proposed by some of the authors in [2]. The influences of the possible geometric errors are simulated in advance. By comparing the measured geometry of the finished workpiece to the simulated profiles, major error causes are identified without numerical fitting to the machine’s kinematic model.

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Beldean, Calin, Ioan Vuşcan, Kalman Kacso, and Nicolae Panc. "The Geometry Equations for Multiple Kinematic Structures Using Direct Geometry." Applied Mechanics and Materials 808 (November 2015): 292–97. http://dx.doi.org/10.4028/www.scientific.net/amm.808.292.

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In this paper are presented two kinematic structures able to move/rotate along/around tree axis each simultaneous. These two structures are restricted on a common fix bed and have the possibility perform a translational motion first and then to rotate along or around each axis. The equation used to describe the position and orientation of the first structure in relation to the second are then presented. Furthermore a reduction of the general case is made to prove the general mathematical model on a structure similar to a five axis turning and milling machine.

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Yang, Qiang, Hongkun Ma, Jiaocheng Ma, Zhili Sun, and Cuiling Li. "Sensitivity Analysis of Reliability of Low-Mobility Parallel Mechanisms Based on a Response Surface Method." Applied Sciences 11, no. 19 (September 27, 2021): 9002. http://dx.doi.org/10.3390/app11199002.

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Kinematic accuracy is a crucial indicator for evaluating the performance of mechanisms. Low-mobility parallel mechanisms are examples of parallel robots that have been successfully employed in many industrial fields. Previous studies analyzing the kinematic accuracy analysis of parallel mechanisms typically ignore the randomness of each component of input error, leading to imprecise conclusions. In this paper, we use homogeneous transforms to develop the inverse kinematics models of an improved Delta parallel mechanism. Based on the inverse kinematics and the first-order Taylor approximation, a model is presented considering errors from the kinematic parameters describing the mechanism’s geometry, clearance errors associated with revolute joints and driving errors associated with actuators. The response surface method is employed to build an explicit limit state function for describing position errors of the end-effector in the combined direction. As a result, a mathematical model of kinematic reliability of the improved Delta mechanism is derived considering the randomness of every input error component. And then, reliability sensitivity of the improved Delta parallel mechanism is analyzed, and the influences of the randomness of each input error component on the kinematic reliability of the mechanism are quantitatively calculated. The kinematic reliability and proposed sensitivity analysis provide a theoretical reference for the synthesis and optimum design of parallel mechanisms for kinematic accuracy.

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Ouerfelli, M., and V. Kumar. "Optimization of a Spherical Five-Bar Parallel Drive Linkage." Journal of Mechanical Design 116, no. 1 (March 1, 1994): 166–73. http://dx.doi.org/10.1115/1.2919341.

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The spherical five bar parallel drive linkage is investigated for use as a spherical manipulator or as a pointing mechanism. The direct and inverse kinematics are derived for a general 5-R linkage. Kinematic and dynamic optimization yields a geometry in which all link lengths are equal to a right angle.

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Müller, Andreas. "On the terminology and geometric aspects of redundant parallel manipulators." Robotica 31, no. 1 (April 20, 2012): 137–47. http://dx.doi.org/10.1017/s0263574712000173.

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SUMMARYParallel kinematics machines (PKMs) can exhibit kinematics as well as actuation redundancy. While the meaning of kinematic redundancy has been already clarified for serial manipulators, actuation redundancy, which is only possible in PKMs, is differently classified in the literature. In this paper a consistent terminology for general redundant PKM is proposed. A kinematic model is introduced with the configuration space (c-space) as central part. The notion of kinematic redundancy is recalled for PKM. C-space, output, and input singularities are distinguished. The significance of the c-space geometry is emphasized, and it is pointed out geometrically that input singularities can be avoided by redundant actuation schemes. In order to distinguish different actuation schemes of PKM, a nonlinear control system is introduced whose dynamics evolves on c-space. The degree of actuation (DOA) is introduced as the number of independent control vector fields, and PKMs are classified as full-actuated and underactuated machines. Relating this DOA to degree of freedom allows to classify the actuation redundancy.

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Santolaria, Jorge, Javier Conte, Marcos Pueo, and Carlos Javierre. "ROTATION ERROR MODELING AND IDENTIFICATION FOR ROBOT KINEMATIC CALIBRATION BY CIRCLE POINT METHOD." Metrology and Measurement Systems 21, no. 1 (March 1, 2014): 85–98. http://dx.doi.org/10.2478/mms-2014-0009.

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Abstract Screw axis measurement methods obtain a precise identification of the physical reality of the industrial robots’ geometry. However, these methods are in a clear disadvantage compared to mathematical optimisation processes for kinematical parameters. That’s because mathematical processes obtain kinematical parameters which best reduce the robot errors, despite not necessarily representing the real geometry of the robot. This paper takes the next step at the identification of a robot’s movement from the identification of its real kinematical parameters for the later study of every articulation’s rotation. We then obtain a combination of real kinematic and dynamic parameters which describe the robot’s movement, improving its precision with a physical understanding of the errors.

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Jiao, Xiaodong, Jin Tao, Hao Sun, and Qinglin Sun. "Kinematic Modes Identification and Its Intelligent Control of Micro-Nano Particle Manipulated by Acoustic Signal." Mathematics 10, no. 21 (November 7, 2022): 4156. http://dx.doi.org/10.3390/math10214156.

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In this paper, the dynamics of a micro-nano particle on the micro-thin plate driven by an acoustic signal was investigated, including the particle kinematics mode, kinematics equation, and trajectory control. According to Newton’s kinematic theorem, analyzing the forces acting on the particle, the kinematic modes of the driven particle are distinguished with specific mathematical conditions, which are classified as slide, bounce, and stable modes strictly planned on a thin plate area. Based on the theory of kinematic modal analysis, the simulation results reveal the distribution rules of particle motion modes against the driving signal or plate geometry. The particle kinematics equation governing the sliding movement on the thin plate was then derived in light of the interaction between the particle and driving signal, based on which, the particle trajectory was drawn and analyzed in detail. For the purpose of controlling the particle trajectory, the control problem was designed in accordance with a linear active disturbance rejection controller (LADRC). Further, a guidance law was proposed, and the corresponding controller was designed to realize the linear trajectory following.

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Duffy, Joseph. "Kinematic Geometry of Mechanisms (K. H. Hunt)." SIAM Review 33, no. 4 (December 1991): 678–79. http://dx.doi.org/10.1137/1033163.

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Bałchanowski, J. "Some aspects of topology and kinematics of a 3DOF translational parallel mechanism." International Journal of Applied Mechanics and Engineering 19, no. 1 (February 1, 2014): 5–15. http://dx.doi.org/10.2478/ijame-2014-0001.

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Abstract The paper presents elements of the topology, geometry and the kinematic analysis of a translational parallel mechanism with three degrees of freedom. In such mechanisms the selection of a proper structure and geometry ensures that the driven link maintains a fixed orientation relative to the base. The method of determination of the configuration of mechanisms using contour vector notation was elaborated in the paper. The equations for the analysis of the direct and inverse kinematics task are determined. An analytical procedure for determining the system’s singular positions is presented and illustrated with examples

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Pllana, Gani, and Sadete Pllana. "Overview of Basic Terms of Technical Lexis of Mechanics in the Albanian Language." European Journal of Language and Literature 4, no. 4 (November 29, 2018): 66. http://dx.doi.org/10.26417/ejls.v4i4.p66-71.

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The subject of the study in this paper is the basic terms of the field of mechanics as a broad field, understanding with this concept not only nouns with nominal base, like pair and kinematic pair, but also other units that can be called terms if they are seen from a certain perspective when connected to the system by terms of nouns or when expressing the specifics of the field as kinematics (adj.) - kinematic (adv.) - shifting (v.), in Albanian kinematik-e (mb.) – kinematikisht (ndajf.) – zhvendoset (fol.). As it is well known in the compilation of terminology dictionaries, both criteria apply, although it can be said that there is no definite stance on this problem. By appearing as single word units, on their own, as well as in wider compounded units (word group), these units serve as compound elements of around 70-80% of the whole Mechanics vocabulary, as they are in Albanian and respectively in English: mekanizëm XE "mekanizëm – mechanism, makin XE "makinëë – machine, hallkë XE "hallkë – link, zinxhir – chain, zhvendosje XE "zhvendosje – displacement, lëvizje XE "lëvizje" – motion XE "motion" , rrotullim XE "rrotullim – rotation, rrotulloj – rotate, rrotullues-e – rotary, kinematik-e – kinematic, kinematikisht – kinametically etc. All of this base vocabulary appears mainly in the basic subfields of Mechanics, in the Theory of Mechanics and in the Applied Mechanics in Machines, in the special subfields, as well as in the subfield of Mechanical Technology of automobiles, of heat technology etc., but it connects also with the base fields of knowledge which stands at the foundation of Mechanics, as with mathematics, geometry, physics, chemistry etc.

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35

Kubovy, Michael, and William Epstein. "Internalization: A metaphor we can live without." Behavioral and Brain Sciences 24, no. 4 (August 2001): 618–25. http://dx.doi.org/10.1017/s0140525x01000048.

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Shepard has supposed that the mind is stocked with innate knowledge of the world and that this knowledge figures prominently in the way we see the world. According to him, this internal knowledge is the legacy of a process of internalization; a process of natural selection over the evolutionary history of the species. Shepard has developed his proposal most fully in his analysis of the relation between kinematic geometry and the shape of the motion path in apparent motion displays. We argue that Shepard has made a case for applying the principles of kinematic geometry to the perception of motion, but that he has not made the case for injecting these principles into the mind of the percipient. We offer a more modest interpretation of his important findings: that kinematic geometry may be a model of apparent motion. Inasmuch as our recommended interpretation does not lodge geometry in the mind of the percipient, the motivation of positing internalization, a process that moves kinematic geometry into the mind, is obviated. In our conclusion, we suggest that cognitive psychologists, in their embrace of internal mental universals and internalization may have been seduced by the siren call of metaphor.

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Zhang, Yan Hua, Xiu Ju Du, and Bai Yong Zhang. "Synthesis and Analysis of 4-DOF Parallel Manipulators of Computer Aided Geometry Approach." Advanced Materials Research 912-914 (April 2014): 1010–16. http://dx.doi.org/10.4028/www.scientific.net/amr.912-914.1010.

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A novel computer aided geometry approach for type synthesis and analysis of new spatial 4-DOF parallel manipulators is put forward, and create the computer simulation mechanisms of parallel manipulators using the geometric constraints and dimension driving techniques in CAD software, Based on the computer simulation mechanisms of parallel manipulators, several new spatial 4-DOF parallel manipulators are synthesized, the kinematic characteristics of the moving platforms are analyzed by computer simulation. The results of computer simulation prove that the computer aided geometric approach for solving type synthesis and kinematic analysis is not only fairly quick and straightforward, but also has the advantages of accuracy.

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Wang, Zhi, Huimin Dong, Shaoping Bai, and Delun Wang. "A new approach of kinematic geometry for error identification and compensation of industrial robots." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 5 (May 15, 2018): 1783–94. http://dx.doi.org/10.1177/0954406218772595.

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A new approach for kinematic calibration of industrial robots, including the kinematic pair errors and the link errors, is developed in this paper based on the kinematic invariants. In most methods of kinematic calibration, the geometric errors of the robots are considered in forms of variations of the link parameters, while the kinematic pairs are assumed ideal. Due to the errors of mating surfaces in kinematic pairs, the fixed and moving axes of revolute pairs, or the fixed and moving guidelines of prismatic pairs, are separated, which can be concisely identified as the kinematic pair errors and the link errors by means of the kinematic pair errors model, including the self-adaption fitting of a ruled surface, or the spherical image curve fitting and the striction curve fitting. The approach is applied to the kinematic calibration of a SCARA robot. The discrete motion of each kinematic pair in the robot is completely measured by a coordinate measuring machine. Based on the global kinematic properties of the measured motion, the fixed and moving axes, or guidelines, of the kinematic pairs are identified, which are invariants unrelated to the positions of the measured reference points. The kinematic model of the robot is set up using the identified axes and guidelines. The results validate the approach developed has good efficiency and accuracy.

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38

Ciobanu, Gabriel, and Dănuţ Rusu. "Kinematics of Mechanical Systems by Dynamic Geometry." Mathematics 10, no. 23 (November 25, 2022): 4457. http://dx.doi.org/10.3390/math10234457.

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The advancement of technology influenced the development of mechanical and mechatronic systems. This article presents the integration of new technologies into traditional mechanics. Specifically, it presents a flexible interactive software for dynamic plane geometry used for designing, simulating and analyzing the mechanical systems. The article presents this interactive software for dynamic geometry as a useful tool for the kinematic analysis of constrained linkages. The simulation and kinematic analysis of some mechanical systems are presented.

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Baran, Eray A., Ozhan Ozen, Dogacan Bilgili, and Asif Sabanovic. "Unified Kinematics of Prismatically Actuated Parallel Delta Robots." Robotica 37, no. 9 (February 15, 2019): 1513–32. http://dx.doi.org/10.1017/s0263574719000092.

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SummaryThis paper presents a unified formulation for the kinematics, singularity and workspace analyses of parallel delta robots with prismatic actuation. Unlike the existing studies, the derivations presented in this paper are made by assuming variable angles and variable link lengths. Thus, the presented scheme can be used for all of the possible linear delta robot configurations including the ones with asymmetric kinematic chains. Referring to a geometry-based derivation, the paper first formulates the position and the velocity kinematics of linear delta robots with non-iterative exact solutions. Then, all of the singular configurations are identified assuming a parametric content for the Jacobian matrix derived in the velocity kinematics section. Furthermore, a benchmark study is carried out to determine the linear delta robot configuration with the maximum cubic workspace among symmetric and semi-symmetric kinematic chains. In order to show the validity of the proposed approach, two sets of experiments are made, respectively, on the horizontal and the Keops type of linear delta robots. The experiment results for the confirmation of the presented kinematic analysis and the simulation results for the determination of the maximum cubic workspace illustrate the efficacy and the flexible applicability of the proposed framework.

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Płocica, Mieczysław, and Jadwiga Pisula. "The Influence of Changes in the Geometry of the Tooth Surface of the Pinion Bevel Gear on the Kinematic Accuracy of Pair Mesh." Acta Mechanica et Automatica 8, no. 2 (August 15, 2014): 95–98. http://dx.doi.org/10.2478/ama-2014-0017.

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Abstract The paper describes the possibilities of bevel gears kinematics design on the basis of the motion graph and improving modifications to cut the pinion teeth flanks. The result is the ability to increase the accuracy of the kinematic transmission. The issue of changing the geometry of the pinion gear is considered in respect of a gear intended for the use in aviation, which requires the cooperation of high quality meshing. The basic geometric features that have been modified include the profile angle, the angle of tooth line, crowning trans-verse and longitudinal and lateral surface twist angle of the tooth. The modification of each of the selected geometrical parameters has had a different effect on the chart of transmission. It has been shown that the effect of the intended changes in the geometry of the pinion may reduce the deviation of motion delays gear and an improve the gear transmission chart.

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41

Dooner, David B. "On the Three Laws of Gearing." Journal of Mechanical Design 124, no. 4 (November 26, 2002): 733–44. http://dx.doi.org/10.1115/1.1518501.

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Three laws of gearing are presented in terms of a three link 1-dof spatial direct contact mechanism. The first law of gearing defines the instantaneous relationship between an infinitesimal displacement of an output body to an infinitesimal angular displacement of an input body for a specified tooth contact normal. A system of cylindroidal coordinates are introduced to facilitate a universal methodology to parameterize the kinematic geometry of generalized motion transmission between skew axes. The second law of gearing establishes a relation between the instantaneous gear ratio and the apparent radii of the hyperboloidal pitch surface in contact as parameterized using a system of cylindroidal coordinates. The third law of gearing establishes an instantaneous relationship for the relative curvature of two conjugate surfaces in direct contact and shows that this relation is independent of the tooth profile geometry. These three laws of gearing along with the system of cylindroidal coordinates establish, in part, a generalized geometric theory comparable to the existing theory for planar kinematics.

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Mavroidis, C., F. B. Ouezdou, and P. Bidaud. "Inverse kinematics of six-degree of freedom “general” and “special” manipulators using symbolic computation." Robotica 12, no. 5 (September 1994): 421–30. http://dx.doi.org/10.1017/s0263574700017975.

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SUMMARYThis paper presents an algorithm that solves the inverse kinematics problem of all six degrees of freedom manipulators, “general” or “special”. A manipulator is represented by a chain of characters that symbolizes the position of prismatic and revolute joints in the manipulator and the special geometry that may exist between its joint axes. One form of the loop closure equation is chosen and the Raghavan and Roth method is used to obtain symbolically a square matrix. The determinant of this matrix yields the characteristic polynomial of the manipulator in one of the kinematic variables. As an example of the use of this algorithm we present the solution to the inverse kinematics problem of the GMF Arc Mate welding manipulator. In spite of its geometry, this industrial manipulator has a non-trivial solution to its inverse kinematics problem.

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Straume, Eldar. "On the geometry and behavior ofn-body motions." International Journal of Mathematics and Mathematical Sciences 28, no. 12 (2001): 689–732. http://dx.doi.org/10.1155/s016117120100669x.

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The kinematic separation of size, shape, and orientation ofn-body systems is investigated together with specific issues concerning the dynamics of classicaln-body motions. A central topic is the asymptotic behavior of general collisions, extending the early work of Siegel, Wintner, and more recently Saari. In particular, asymptotic formulas for the derivatives of any order of the basic kinematic quantities are included. The kinematic Riemannian metric on the congruence and shape moduli spaces are introduced viaO(3)-equivariant geometry. Forn=3, a classical geometrization procedure is explicitly carried out for planary 3-body motions, reducing them to solutions of a rather simple system of geodesic equations in the 3-dimensional congruence space. The paper is largely expository and various known results on classicaln-body motions are surveyed in our more geometrical setting.

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Kim, Jin Seob, and Gregory S. Chirikjian. "Inverse kinematic solutions of 6-D.O.F. biopolymer segments." Robotica 34, no. 8 (April 13, 2016): 1734–53. http://dx.doi.org/10.1017/s0263574716000138.

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SUMMARYWe present two methods to find all the possible conformations of short six degree-of-freedom segments of biopolymers which satisfy end constraints in position and orientation. One of our methods is motivated by inverse kinematic solution techniques which have been developed for “general” 6R serial robotic manipulators. However, conventional robot kinematics methods are not directly applicable to the geometry of polymers, which can be treated as a degenerate case where all the “link lengths” are zero. Here, we propose a method which extends the elimination method of Kohli and Osvatic. This method can be applied directly to the geometry of biopolymers. We also propose a heuristic method based on a Lie-group-theoretic description. In this method, we utilize inverse iterations of the Jacobian matrix to obtain all conformations which satisfy end constraints. This can be easily implemented for both the general 6R manipulator and polymers. Although the extended elimination method is computationally faster than the Jacobian method, in cases where some of the joint angles are 180° (i.e., where the elimination method fails), we combine these two methods effectively to obtain the full set of inverse kinematic solutions. We demonstrate our approach with several numerical examples.

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Ivers, D. J. "Kinematic dynamos in spheroidal geometries." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2206 (October 2017): 20170432. http://dx.doi.org/10.1098/rspa.2017.0432.

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The kinematic dynamo problem is solved numerically for a spheroidal conducting fluid of possibly large aspect ratio with an insulating exterior. The solution method uses solenoidal representations of the magnetic field and the velocity by spheroidal toroidal and poloidal fields in a non-orthogonal coordinate system. Scaling of coordinates and fields to a spherical geometry leads to a modified form of the kinematic dynamo problem with a geometric anisotropic diffusion and an anisotropic current-free condition in the exterior, which is solved explicitly. The scaling allows the use of well-developed spherical harmonic techniques in angle. Dynamo solutions are found for three axisymmetric flows in oblate spheroids with semi-axis ratios 1≤ a / c ≤25. For larger aspect ratios strong magnetic fields may occur in any region of the spheroid, depending on the flow, but the external fields for all three flows are weak and concentrated near the axis or periphery of the spheroid.

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DeVries, W. R., and Cheng-Jih Li. "Algorithms to Deconvolve Stylus Geometry From Surface Profile Measurements." Journal of Engineering for Industry 107, no. 2 (May 1, 1985): 167–74. http://dx.doi.org/10.1115/1.3185981.

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Stylus methods for measuring surface topography impose certain limits on resolving the true profile of a surface. These limits are primarily due to the finite geometric size of the stylus. In this paper, kinematic and geometric algorithms are developed to compensate for stylus geometry so as to present a better picture of the true surface profile. To demonstrate their effectiveness, these algorithms are applied to simulated deterministic and stochastic profile measurements.

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Панчук, K. Panchuk, Ляшков, A. Lyashkov, Варепо, and L. Varepo. "Kinematic Geometry of Curve and Its Application to Geometric Modeling Flat Gear." Geometry & Graphics 5, no. 2 (July 4, 2017): 25–31. http://dx.doi.org/10.12737/article_5953f2c5611703.02086017.

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The paper presents the results of investigations in the field of kinematic geometry of the spatial curve of a line. The basis of the research is the method of the movable trihedron of the curve. The components of the trihedron motion along the spatial curve are considered and it is shown that its resultant instantaneous motion is screw motion. This result differs from the representation of the motion of a trihedron known in geometry as a rotation described by the Darboux vector. An analytical description of the set of axes of instantaneous helical motions of a trihedron in a moving and fixed system of assigning a spatial curve is given. The possibility of applying the obtained general results to the investigation of a plane curve is shown. The paper proposes a flat tooth gearing model based on the geometric interpretation of the motions of a trihedron of a plane curve and known in the geometric theory of plane mechanisms of the construction of Bobillier. The geometric scheme of this construction is expanded due to the introduction of evolutes simulating instantaneous motions of trihedron of the corresponding construction curves. As a result, a geometric model is obtained, which is more complete in comparison with the known models of flat gearing. It allows to perform both direct and inverse tasks of profiling the teeth of the wheels while simultaneously obtaining the curvature of the desired profiles in the absence of such. The proposed model can be used as the basis for the development of gears with a planar gearing scheme by the condition of achieving the necessary transmission performance due to the geometric shape of the teeth of the wheels.

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Rong, Xuewen, Rui Song, Hui Chai, and Xiaolin Ma. "Mechanical Design and Kinematics Analysis of a Hydraulically Actuated Manipulator." Open Mechanical Engineering Journal 8, no. 1 (December 12, 2014): 457–61. http://dx.doi.org/10.2174/1874155x01408010457.

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This paper gives a mechanism design of a six DOF hydraulically actuated manipulator firstly. Then its DH frames and link parameters are given. Next, its forward kinematic equations are derived according to homogeneous transformation method. Fourthly, the analytical solutions of its inverse kinematics are solved by given the position and posture of the end-effector simultaneously. The posture of the end-effector is given with three z-y-z Euler angles for they have obvious geometry meanings and are easy to be measured. In addition, the correctness of the inverse kinematic equations is verified in Simulink by comparing many sets of randomly produced joint variables in workspace and their corresponding inverse solutions.

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HSIANG, WU-YI. "ON THE KINEMATIC GEOMETRY OF MANY BODY SYSTEMS." Chinese Annals of Mathematics 20, no. 01 (January 1999): 11–28. http://dx.doi.org/10.1142/s0252959999000047.

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Au, C. K., and Tony C. Woo. "Geometry of inhibition and activation in kinematic waves." Computer-Aided Design 36, no. 12 (October 2004): 1253–61. http://dx.doi.org/10.1016/j.cad.2004.01.010.

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Journal articles on the topic 'Kinematic geometry'

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