A practical implementation of a continuous isotropic spherical omnidirectional drive

This paper presents a continuous isotropic spherical omnidirectional drive mechanism that is efficient in its mechanical simplicity and use of volume. Spherical omnidirectional mechanisms allow isotropic motion, although many are limited from achieving true isotropic motion by practical mechanical design considerations. The mechanism presented in this paper uses a single motor to drive a point on the great circle of the sphere parallel to the ground plane, and does not require a gearbox. Three mechanisms located 120 degrees apart provide a stable drive platform for a mobile robot. Results show the omnidirectional ability of the robot and demonstrate the performance of the spherical mechanism compared to a popular commercial omnidirectional wheel over edges of varying heights and gaps of varying widths.

Type Synthesis of 3-DOF Multi-Mode Translational/Spherical Parallel Mechanisms with Lockable Joints

A 3-DOF (degrees-of-freedom) multi-mode translational/spherical PM (parallel mechanism) with lockable joints is a novel reconfigurable PM. It has both 3-DOF spatial translational operation mode and 3-DOF spherical operation mode. This paper presents an approach to the type synthesis of translational/spherical PMs with lockable joints. Using the proposed approach, several 3-DOF translational/spherical PMs are obtained. It is found that these translational/spherical PMs do not encounter constraint singular configurations and self-motion of sub-chain of a leg during reconfiguration. The approach can also be used for synthesizing other classes of multi-mode PMs with lockable joints, multi-mode PMs with variable kinematic joints, partially decoupled PMs, and reconfigurable PMs with a reconfigurable platform.

Design and Characterization of Curved and Spherical Flexure Hinges for Planar and Spatial Compliant Mechanisms

A flexure hinge is a flexible connector that can provide a limited rotational motion between two rigid parts by means of material deformation. These connectors can be used to substitute traditional kinematic pairs (like bearing couplings) in rigid-body mechanisms. When compared to their rigid-body counterpart, flexure hinges are characterized by reduced weight, absence of backlash and friction, part-count reduction, but restricted range of motion. There are several types of flexure hinges in the literature that have been studied and characterized for different applications. In our study, we have introduced new types of flexures with curved structures i.e. circularly curved-beam flexures and spherical flexures. These flexures have been utilized for both planar applications (e.g. articulated robotic fingers) and spatial applications (e.g. spherical compliant mechanisms). We have derived closed-form compliance equations for both circularly curved-beam flexures and spherical flexures. Each element of the spatial compliance matrix is analytically computed as a function of hinge dimensions and employed material. The theoretical model is then validated by comparing analytical data with the results obtained through Finite Element Analysis. A case study is also presented for each class of flexures, concerning the potential applications in the optimal design of planar and spatial compliant mechanisms. Each case study is followed by comparing the performance of these novel flexures with the performance of commonly used geometries in terms of principle compliance factors, parasitic motions and maximum stress demands. Furthermore, we have extended our study to the design and analysis of serial and parallel compliant mechanisms, where the proposed flexures have been employed to achieve spatial motions e.g. compliant spherical joints.

Depth of focus and visual acuity with primary and secondary spherical aberration

It is known that the depth of focus (DOF) of the human eye can be affected by the higher order aberrations. We estimated the optimal combinations of primary and secondary Zernike spherical aberration to expand the DOF and evaluated their efficiency in real eyes using an adaptive optics system. The ratio between increased DOF and loss of visual acuity was used as the performance indicator. The results indicate that primary or secondary spherical aberration alone shows similar effectiveness in extending the DOF. However, combinations of primary and secondary spherical aberration with different signs provide better efficiency for expanding the DOF. This finding suggests that the optimal combinations of primary and secondary spherical aberration may be useful in the design of optical presbyopic corrections. © 2011 Elsevier Ltd. All rights reserved.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Long-term experiments with an adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In this work, we introduce a method to update the reference views in a hybrid metrictopological map so that a mobile robot can continue to localize itself in a changing environment. The updating mechanism, based on the multi-store model of human memory, incorporates a spherical metric representation of the observed visual features for each node in the map, which enables the robot to estimate its heading and navigate using multi-view geometry, as well as representing the local 3D geometry of the environment. A series of experiments demonstrate the persistence performance of the proposed system in real changing environments, including analysis of the long-term stability.

Behavior of spherical particles at low Reynolds numbers in a fluctuating translational flow

The behavior of spheres in non-steady translational flow has been studied experimentally for values of Reynolds number from 0.2 to 3000. The aim of the work was to improve our qualitative understanding of particle transport in turbulent gaseous media, a process of extreme importance in power plants and energy transfer mechanisms.

Particles, subjected to sinusoidal oscillations parallel to the direction of steady translation, were found to have changes in average drag coefficient depending upon their translational Reynolds number, the density ratio, and the dimensionless frequency and amplitude of the oscillations. When the Reynolds number based on sphere diameter was less than 200, the oscillation had negligible effect on the average particle drag.

For Reynolds numbers exceeding 300, the coefficient of the mean drag was increased significantly in a particular frequency range. For example, at a Reynolds number of 3000, a 25 per cent increase in drag coefficient can be produced with an amplitude of oscillation of only 2 per cent of the sphere diameter, providing the frequency is near the frequency at which vortices would be shed in a steady flow at the mean speed. Flow visualization shows that over a wide range of frequencies, the vortex shedding frequency locks in to the oscillation frequency. Maximum effect at the natural frequency and lock-in show that a non-linear interaction between wake vortex shedding and the oscillation is responsible for the increase in drag.

Mechanisms of projectile penetration in Dyneema® encapsulated aluminum structures

Polymer composites comprising ultra-high molecular weight polyethylene (UHWMPE) fibers in a compliant matrix are now widely used in ballistic applications with varying levels of success. This is primarily due to a poor understanding of the mechanics of penetration of these composites in ballistic protection systems. In this study, we report experimental observations of the penetration mechanisms in four model systems impacted by a 12.7 mm diameter spherical steel projectile. The four model targets designed to highlight different penetration mechanisms in Dyneema® UHWMPE composites were: (i) a bare aluminum plate; (ii) the same plate fully encased in a 5.9 mm thick casing of Dyneema®; (iii) the fully encased plate with a portion of the Dyneema® removed from the front face so that the projectile impacts directly the Al plate; and (iv) the fully encased plate with a portion of the Dyneema® removed from the rear face so that the projectile can exit the Al plate without again interacting with the Dyneema®. A combination of synchronized high speed photography with three cameras, together with post-test examination of the targets via X-ray tomography and optical microscopy was used to elucidate the deformation and perforation mechanisms. The measurements show that the ballistic resistance of these targets increases in the order: bare Al plate, rear face cutout target, fully encased target and front face cutout target. These findings are explained based on the following key findings: (a) the ballistic performance of Dyneema® plates supported on a foundation is inferior to Dyneema® plates supported along their edges; (b) the apparent ballistic resistance of Dyneema® plates increases if the plates are given an initial velocity prior to the impact by the projectile, thereby reducing the relative velocity between the Dyneema® plate and projectile; and (c) when the projectile is fragmented prior to impact, the spatially and temporally distributed loading enhances the ballistic resistance of the Dyneema®. The simple model targets designed here have elucidated mechanisms by which Dyneema® functions in multi-material structures. © 2014 Elsevier Ltd.

Complex aggregates of spherical colloids via modified micromolding in capillaries

This paper describes a simple approach to fabricate aggregates composed of monodispersed silica microspheres by modified micromolding in capillaries (MIMIC). Two different kinds of contact modes, namely, conformal contact and non-conformal contact, between the poly(dimethylsiloxane) (PDMS) mold and the underlying prepatterned substrate, can be controlled during the micromolding, which result in the formation of different aggregates under the influence of template confinement and capillary forces. These aggregates, including woodpile structure, discoid, conoid and rectangular clusters, possess well-controlled sizes and orientation. The possible mechanisms for the formation of different aggregates are discussed in detail.

Spatial mechanisms for modelling the human ankle passive motion

Knowledge on how ligaments and articular surfaces guide passive motion at the human ankle joint complex is fundamental for the design of relevant surgical treatments. The dissertation presents a possible improvement of this knowledge by a new kinematic model of the tibiotalar articulation. In this dissertation two one-DOF spatial equivalent mechanisms are presented for the simulation of the passive motion of the human ankle joint: the 5-5 fully parallel mechanism and the fully parallel spherical wrist mechanism. These mechanisms are based on the main anatomical structures of the ankle joint, namely the talus/calcaneus and the tibio/fibula bones at their interface, and the TiCaL and CaFiL ligaments. In order to show the accuracy of the models and the efficiency of the proposed procedure, these mechanisms are synthesized from experimental data and the results are compared with those obtained both during experimental sessions and with data published in the literature. Experimental results proved the efficiency of the proposed new mechanisms to simulate the ankle passive motion and, at the same time, the potentiality of the mechanism to replicate the ankle’s main anatomical structures quite well. The new mechanisms represent a powerful tool for both pre-operation planning and new prosthesis design.

Methods for Clearance Influence Analysis in Planar and Spatial Mechanisms

This doctoral dissertation presents a new method to asses the influence of clearancein the kinematic pairs on the configuration of planar and spatial mechanisms. The subject has been widely investigated in both past and present scientific literature, and is approached in different ways: a static/kinetostatic way, which looks for the clearance take-up due to the external loads on the mechanism; a probabilistic way, which expresses clearance-due displacements using probability density functions; a dynamic way, which evaluates dynamic effects like the actual forces in the pairs caused by impacts, or the consequent vibrations. This dissertation presents a new method to approach the problem of clearance. The problem is studied from a purely kinematic perspective. With reference to a given mechanism configuration, the pose (position and orientation) error of the mechanism link of interest is expressed as a vector function of the degrees of freedom introduced in each pair by clearance: the presence of clearance in a kinematic pair, in facts, causes the actual pair to have more degrees of freedom than the theoretical clearance-free one. The clearance-due degrees of freedom are bounded by the pair geometry. A proper modelling of clearance-affected pairs allows expressing such bounding through analytical functions. It is then possible to study the problem as a maximization problem, where a continuous function (the pose error of the link of interest) subject to some constraints (the analytical functions bounding clearance- due degrees of freedom) has to be maximize. Revolute, prismatic, cylindrical, and spherical clearance-affected pairs have been analytically modelled; with reference to mechanisms involving such pairs, the solution to the maximization problem has been obtained in a closed form.

The non-linear acousto-mechanical and thermodynamic response of spherical absorbers to laser pulses of various temporal profiles

This study is to theoretically investigate shockwave and microbubble formation due to laser absorption by microparticles and nanoparticles. The initial motivation for this research was to understand the underlying physical mechanisms responsible for laser damage to the retina, as well as the predict threshold levels for damage for laser pulses with of progressively shorter durations. The strongest absorbers in the retina are micron size melanosomes, and their absorption of laser light causes them to accrue very high energy density. I theoretically investigate how this absorbed energy is transferred to the surrounding medium. For a wide range of conditions I calculate shockwave generation and bubble growth as a function of the three parameters; fluence, pulse duration and pulse shape. In order to develop a rigorous physical treatment, the governing equations for the behavior of an absorber and for the surrounding medium are derived. Shockwave theory is investigated and the conclusion is that a shock pressure explanation is likely to be the underlying physical cause of retinal damage at threshold fluences for sub-nanosecond pulses. The same effects are also expected for non-biological micro and nano absorbers. ^

Conceptual designs of multi-degree of freedom compliant parallel manipulators composed of wire-beam based compliant mechanisms

This paper proposes conceptual designs of multi-degree(s) of freedom (DOF) compliant parallel manipulators (CPMs) including 3-DOF translational CPMs and 6-DOF CPMs using a building block based pseudo-rigid-body-model (PRBM) approach. The proposed multi-DOF CPMs are composed of wire-beam based compliant mechanisms (WBBCMs) as distributed-compliance compliant building blocks (CBBs). Firstly, a comprehensive literature review for the design approaches of compliant mechanisms is conducted, and a building block based PRBM is then presented, which replaces the traditional kinematic sub-chain with an appropriate multi-DOF CBB. In order to obtain the decoupled 3-DOF translational CPMs (XYZ CPMs), two classes of kinematically decoupled 3-PPPR (P: prismatic joint, R: revolute joint) translational parallel mechanisms (TPMs) and 3-PPPRR TPMs are identified based on the type synthesis of rigid-body parallel mechanisms, and WBBCMs as the associated CBBs are further designed. Via replacing the traditional actuated P joint and the traditional passive PPR/PPRR sub-chain in each leg of the 3-DOF TPM with the counterpart CBBs (i.e. WBBCMs), a number of decoupled XYZ CPMs are obtained by appropriate arrangements. In order to obtain the decoupled 6-DOF CPMs, an orthogonally-arranged decoupled 6-PSS (S: spherical joint) parallel mechanism is first identified, and then two example 6-DOF CPMs are proposed by the building block based PRBM method. It is shown that, among these designs, two types of monolithic XYZ CPM designs with extended life have been presented.