Replacement in a Plane Geared Linkage of High Kinematic Pairs with Lower Pairs

The analysis of constraints in plane mechanisms is an urgent problem in the theory of machines and mechanisms. Although kinematic pairs’ classification has been known for a long time, the issue of the conjugation of links, being at the heart of the analysis and synthesis of mechanisms and machines, is of considerable theoretical and practical interest and continues to attract scientists. One of the tasks that are solved in the process of analysis and synthesis of the structures of mechanisms is the re-placement of higher kinematic pairs by lower ones. As a rule, such a replacement is made to identify kinematic chains of zero mobility, Assur's structural groups, in a mechanism. The replacement may also aim at obtaining the necessary kinematic relations. That is because specific computational difficulties hamper the kinematic analysis of chains with higher kinematic pairs due to the relative sliding and shape irregularity of mating surfaces. Yet, the use of replacements to obtain kinematic and transmission functions is difficult due to nonisomorphism of the equivalent mechanism. Simultaneously, for mixed-type mechanisms, which include geared linkages, the equivalent replacement will allow unifying the kinematic analysis methods. The paper suggests the technology of replacing higher kinematic pairs with links with lower pairs as applied to a plane geared linkage. The technology is based on the properties of the involute of a circumference. The paper proved the structural and kinematic equivalence of such a replacement. The isomorphism of the equivalent linkage will enhance the kinematic analysis, make it possible using kinematic functions, and applying methods based on the instantaneous relative rotations of links, in particular, the Aronhold-Kennedy theorem. Another application of the replacement method presented in the paper will be the expansion of opportunities for identifying idle constraints in the mechanism.

Rigid Foldability of Generalized Triangle Twist Origami Pattern and Its Derived 6R Linkages

Rigid origami is a restrictive form of origami that permits continuous motion between folded and unfolded states along the predetermined creases without stretching or bending of the facets. It has great potential in engineering applications, such as foldable structures that consist of rigid materials. The rigid foldability is an important characteristic of an origami pattern, which is determined by both the geometrical parameters and the mountain-valley crease (M-V) assignments. In this paper, we present a systematic method to analyze the rigid foldability and motion of the generalized triangle twist origami pattern using the kinematic equivalence between the rigid origami and the spherical linkages. All schemes of M-V assignment are derived based on the flat-foldable conditions among which rigidly foldable ones are identified. Moreover, a new type of overconstrained 6R linkage and a variation of doubly collapsible octahedral Bricard are developed by applying kirigami technique to the rigidly foldable pattern without changing its degree-of-freedom. The proposed method opens up a new way to generate spatial overconstrained linkages from the network of spherical linkages. It can be readily extended to other types of origami patterns.

Kinematic equivalence between models driven by DBI field with constant γ and exotic holographic quintessence cosmological models

We show the kinematic equivalence between cosmological models driven by Dirac–Born–Infeld (DBI) fields [Formula: see text] with constant proper velocity of the brane and exponential potential [Formula: see text], and interactive cosmological systems with modified holographic Ricci type fluids as dark energy (DE) in flat Friedmann–Robertson–Walker (FRW) cosmologies.

Reconfiguration Modules Based Displacement Group Propagation

This paper investigates a metamorphic mechanism that can be decomposed and expressed by group chain corresponding to the kinematic equivalence leading to equivalent kinematic function but with different configurations. The metamorphic process is implemented through metamorphic module combinations and corresponding reconfiguration operations. However, metamorphic module is a constitution of a group using intrinsic geometrical entities instead of frame-dependent motion matrices and considering the available kinematic pair structures, which has potential ability to degenerate as inherent components. Moreover, the kinematic sequencing can set up a model for metamorphic configuration characteristics and the topology variation can be operated by metamorphic module variation with the displacement group transformation and propagation. A metamorphic mechanism can be converted into various topological configurations with respect to kinematic metamorphosis of joints and links in terms of metamorphic modules based on set theoretic.

Developing a Kinematic Estimation Model for a Climbing Mobile Robotic Welding System

Skid steer tracked-based robots are popular due to their mechanical simplicity, zero-turning radius and greater traction. This architecture also has several advantages when employed by mobile platforms designed to climb and navigate ferrous surfaces, such as increased magnet density and low profile (center of gravity). However, creating a kinematic model for localization and motion control of this architecture is complicated due to the fact that tracks necessarily slip and do not roll. Such a model could be based on a heuristic representation, an experimentally-based characterization or a probabilistic form. This paper will extend an experimentally-based kinematic equivalence model to a climbing, track-based robot platform. The model will be adapted to account for the unique mobility characteristics associated with climbing. The accuracy of the model will be evaluated in several representative tasks. Application of this model to a climbing mobile robotic welding system (MRWS) is presented.

Numerical Simulation of Vortex-Induced Vibrations on a Flexible Riser in Uniform Currents

A numerical model in a quasi-three-dimensional fashion is developed in this paper to simulate vortex-induced vibration of a flexible riser (the aspect ratio = 250, mass ratio, m* = 2.9, damping ratio, ζ = 0.01) in uniform current U∞ = [0.06, 0.80] m/s, (Reynolds number, Re = [0.01, 1.28]×104). Finite element method are and Finite volume method are applied in the structural and fluid domains respectively. Effects of fluid-structure interaction (FSI) are reckoned in by making use of kinematic equivalence of the relative flow between fluid and the body in inertial and non-inertial frames of reference. It is found transeverse motion and streamwise motion are strongly coupled, they have same changing trend at the same reduced velocity range, the upper branch appears in the range Vrn = U∞/fnD ≈ 5–7 for the generated nth mode, whilst the lock-in remains in the range Vrn ≈ 3–10, the phase angles decrease from about 90° in the initial branch to less than 45° in the lower branch. The RMS and envelop values of cross-flow displacements are 4∼6 times those of in-line, maximum amplitudes of about 1.2 diameters at cross-flow and 0.25 diameters at in-line have been observed. Standing wave response was observed as Vr1 = 6, the in-line response even contains the first and the second modes at the same time. The strouhal number, St is about 0.17 in the present cases.

Autonomous target capturing of free-floating space robot: Theory and experiments

SUMMARYSpace robotic systems are expected to play an increasingly important role in the future. Unlike on the earth, space operations require the ability to work in the unstructured environment. Some autonomous behaviors are necessary to perform complex and difficult tasks in space. This level of autonomy relies not only on vision, force, torque, and tactile sensors, but also the advanced planning and decision capabilities. In this paper, the authors study the autonomous target capturing from the issues of theory and experiments. Firstly, we deduce the kinematic and dynamic equations of space robotic system. Secondly, the visual measurement model of hand–eye camera is created, and the image processing algorithms to extract the target features are introduced. Thirdly, we propose an autonomous trajectory planning method, directly using the 2D image features. The method predicts the target motion, plans the end-effector's velocities and solves the inverse kinematic equations using practical approach to avoid the dynamic singularities. At last, numeric simulation and experiment results are given. The ground experiment system is set up based on the concept of dynamic simulation and kinematic equivalence. With the system, the experiments of autonomous capturing a target by a free-floating space robot, composed of a 6-DOF manipulator and a satellite as its base, are conducted, and the results validate the proposed algorithm.

Mapping a Space Manipulator to a Dynamically Equivalent Manipulator

In this paper, we discuss the problem of how a free-floating space manipulator can be mapped to a conventional, fixed-base manipulator which preserves both its dynamic and kinematic properties. This manipulator is called Dynamically Equivalent Manipulator (DEM). The DEM concept not only allows us to model a free-floating space manipulator system with simple, well-understood methods, but also to build a conventional manipulator system to experimentally study the dynamic performance and task execution of a space manipulator system, without having to resort to complicated experimental set-ups to simulate the space environment. This paper presents the theoretical development of the DEM concept, demonstrates the dynamic and kinematic equivalence, and presents simulation results to illustrate the equivalence under open-loop and closed-loop control strategies.