Motion synthesis of mechanisms using constraint manifolds in image space

Kinematic mappings, quaternion algebra, and constraint manifolds in the algebraic image space are applied to the problems of the dimensional synthesis of mechanisms. Dimensions of a mechanism are determined such that a tracer frame fixed on the coupler will pass through or at least as close as possible to the desired positions and orientations in the physical space as the input link rotates about its fixed joint. First, using kinematic mappings, the desired positions and orientations of the tracer frame of the mechanism can be mapped onto points in a hyperspace in which the motion of the tracer frame can be represented by a curve. Second, using quaternion algebra, the structure equations representing the transformations from the reference frame to the tracer frame via each leg, each crank-coupler dyad of the mechanism, form the constraint manifolds of the mechanism. Finally, the problem of dimensional synthesis thus becomes one of finding a curve, generated by the intersection of constraint manifolds and fulfilling the constraint equations of kinematic mappings, which passes through or near the desired image points. The dimensions of the mechanism are found by using total least square algorithms to minimize the normal distance between all the desired image points and image curve of the tracer frame. Using this approach, the synthesis problems of all three types of mechanisms, planar, spherical, and spatial, can be formulated similarly. It provides a straightforward tool for general motion synthesis problems. The theory is illustrated by numerical examples of planar and spherical mechanisms

A Foundation for Analysis of Spherical System Linkages Inspired by Origami and Kinematic Paper Art

Origami and its related fields of paper art are known to map to mechanisms, permitting kinematic analysis. Many origami folds have been studied in the context of engineering applications, but a sufficient foundation of principles of the underlying class of mechanism has not been developed. In this work, the mechanisms underlying paper art are identified as “spherical system linkages” and are studied in the context of generic mobility analysis with the goal of establishing a foundation upon which future work can develop.Spherical systems consist of coupled spherical and planar loops, and they motivate a reclassification of mechanisms based on the Chebyshev-Grübler-Kutzbach framework. Spherical systems are capable of complex, closed-loop motion in 3D space despite the mobility calculation treating the links as constrained to a single 2D surface. This property permits generalization of some multi-loop planar mechanisms, such as the Watt mechanism, to a generalized 3D form with equal mobility. A minimal connectivity graph representation of spherical systems is developed, and generic mobility equations are identified. Spherical system linkages are generalized further into spherical/spatial hybrid mechanisms which may have any combination of spherical, planar, and spatial loops. These are represented and analyzed with a polyhedron model. The connectivity graph is modified for this case and appropriate generic mobility equations are identified and adapted.The generic analyses developed for spherical system linkages are sufficient to inform an exhaustive type synthesis process. Generation of all configurations of a paper art inspired mechanism subject to constraints is discussed, and a case study generates all configurations of a spatial chain using specified link types. This design process is enabled by the developed notation and analyses, which are used to identify, depict, and classify kinematic paper art inspired mechanisms

A new insight into the coupler curves of the RCCC four-bar linkage

The final publication is available at link.springer.comBased on the condition for four points to lie on the unit sphere, derived using Distance Geometry, a new mathematical formulation for the coupler curves of the RCCC linkage is presented. The relevance of this formulation is not only its simplicity, but the elegant way in which we can obtain the derivative of any variable with respect to any other, and the simple way in which intervals of monotonicity can be detected. All these results are compactly expressed in terms of Gramians and, as a consequence, they have a direct geometric meaning contrarily to what happens with previous approaches based on kinematic loop equations.Peer ReviewedPostprint (author's final draft

Galaxy Masses

Galaxy masses play a fundamental role in our understanding of structure formation models. This review addresses the variety and reliability of mass estimators that pertain to stars, gas, and dark matter. The different sections on masses from stellar populations, dynamical masses of gas-rich and gas-poor galaxies, with some attention paid to our Milky Way, and masses from weak and strong lensing methods, all provide review material on galaxy masses in a self-consistent manner.Comment: 145 pages, 28 figures, to appear in Reviews of Modern Physics. Figure 22 is missing here, and Figs. 15, 26-28 are at low resolution. This version has a slightly different title and some typos fixed in Chapter 5. For the full review with figures, please consult: http://www.astro.queensu.ca/~courteau/GalaxyMasses_28apr2014.pd

Task based synthesis of serial manipulators

Computing the optimal geometric structure of manipulators is one of the most intricate problems in contemporary robot kinematics. Robotic manipulators are designed and built to perform certain predetermined tasks. There is a very close relationship between the structure of the manipulator and its kinematic performance. It is therefore important to incorporate such task requirements during the design and synthesis of the robotic manipulators. Such task requirements and performance constraints can be specified in terms of the required end-effector positions, orientations and velocities along the task trajectory. In this work, we present a comprehensive method to develop the optimal geometric structure (DH parameters) of a non-redundant six degree of freedom serial manipulator from task descriptions. In this work we define, develop and test a methodology to design optimal manipulator configurations based on task descriptions. This methodology is devised to investigate all possible manipulator configurations that can satisfy the task performance requirements under imposed joint constraints. Out of all the possible structures, the structures that can reach all the task points with the required orientations are selected. Next, these candidate structures are tested to see whether they can attain end-effector velocities in arbitrary directions within the user defined joint constraints, so that they can deliver the best kinematic performance. Additionally least power consuming configurations are also identified

Robotization of hand woven carpet technology process

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2008Includes bibliographical references (leaves: 85-91)Text in English; Abstract: Turkish and Englishxi, 96 leavesThis thesis covers a study on the structural design of new overconstrained mechanisms and manipulators and their application to the robotization of hand woven carpet technology process.Moreover, recurrent vector equations are investigated for the synthesis of linkages, and used for the design of new mechanisms with linear-angular conditions in the subspace with general constraint one. These conditions are generalized for defining the structural groups of subspace ..5 and these structural groups are used both for the creation of new parallel manipulators and new serial-parallel platform manipulators.After investigating hand woven carpets, the knowledge gained during the structural design of mechanisms is applied to the robotization of hand woven carpet technology process. Finally, design of carpet weaving robot is introduced

Kinematic Modeling and Optimization of a New Reconfigurable Parallel Mechanism

This paper investigates a new reconfigurable parallel mechanism consisting of three SvPS kinematic limbs. Induced by phase changes of a metamorphic spherical variable-axis joint (Sv), the SvPS limb is capable of changing to two typical configurations, of which one exerts no constraint and the other exerts a constraint force to the moving platform. Reconfiguration of the three limbs enables the 3-SvPS parallel mechanism to have four distinct configurations with degrees of freedom (DOF) varying from 3 to 6. Analytical model of position and workspace analysis of the reconfigurable parallel mechanism are first investigated. In terms of the screw theory, a unified Jacobian matrix covering all the mobility configurations is established and utilized for analyzing singularity of the parallel mechanism in different configurations. Further, performance analysis and optimization are explored using the motion/force transmission method. The 3-SvPS parallel mechanism can be used as structure of reconfigurable robotic machine center with adaptability to changing task requirements

Kinematics and Robot Design I, KaRD2018

This volume collects the papers published on the Special Issue “Kinematics and Robot Design I, KaRD2018” (https://www.mdpi.com/journal/robotics/special_issues/KARD), which is the first issue of the KaRD Special Issue series, hosted by the open access journal “MDPI Robotics”. The KaRD series aims at creating an open environment where researchers can present their works and discuss all the topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems. Kinematics is so intimately related to the design of robotic/automatic systems that the admitted topics of the KaRD series practically cover all the subjects normally present in well-established international conferences on “mechanisms and robotics”. KaRD2018 received 22 papers and, after the peer-review process, accepted only 14 papers. The accepted papers cover some theoretical and many design/applicative aspects

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

"Available online 19 December 2017"A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review. Both dry and lubricated clearance joints are addressed here, and an effort is made to include a large number of research works in this particular field, which have been published since the 1960′s. First, the most frequently utilized methods for modeling planar and spatial multibody mechanical systems with clearance joints are analyzed, and compared. Other important phenomena commonly associated with clearance joint models, such as wear, non-smooth behavior, optimization and control, chaos, and uncertainty and links’ flexibility, are then discussed. The main assumptions procedures and conclusions for the different methodologies are also examined and compared. Finally, future developments and new applications of clearance joint modeling and analysis are highlighted.This research was supported in part by the China 111 Project (B16003) and the National Natural Science Foundation of China under Grants 11290151, 11472042 and 11221202. The work was also supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio