A Constraint-Based Approach to Manipulator Kinematics and Singularities

<p>In this thesis, a differential-geometric approach to the kinematics of multibody mechanisms is introduced that enables analysis of singularities of both serial and parallel manipulators in a flexible and complete way. Existing approaches such as those of Gosselin and Angeles [1], Zlatanov et al. [2] and Park and Kim [3] make use of a combination of joint freedoms and constraints and so build in assumptions. In contrast, this new approach is solely constraint-based, avoiding some of the shortcomings of these earlier theories. The proposed representation has two core ingredients. First, it avoids direct reference to the choice of inputs and their associated joint freedoms and instead focuses on a kinematic constraint map (KCM), defined by the constraints imposed by all joints and not requiring consideration of closure conditions arising from closed loops in the design. The KCM is expressed in terms of pose (i.e. position and orientation) variables, which are the coordinates of all the manipulator’s links with respect to a reference frame. The kinematics of a given manipulator can be described by means of this representation, locally and globally. Also, for a family of manipulators defined by a specific architecture, the KCM will tell us how the choice of design parameters (e.g. link lengths) affects these kinematic properties within the family. At a global level, the KCM determines a subset in the space of all pose variables, known as the configuration space (C-space) of the manipulator, whose topology may vary across the set of design parameters. The Jacobian (matrix of first-order partial derivatives) of the KCM may become singular at some specific choices of pose variables. These conditions express a subset called the singular set of the C-space. It is shown that if a family of manipulators, parametrised by a manifold Rd of design parameters, is “well-behaved” then the pose variables can be eliminated from the KCM equations together with the conditions for singularities, to give conditions in terms of design parameters, that define a hypersurface in Rd of manipulators in the class that exhibit C-space singularities. These are referred to as Grashof-type conditions, as they generalise classically known inequalities classifying planar 4-bar mechanisms due to Grashof [4]. Secondly, we develop the theory to incorporate actuator space (A-space) and workspace (W-space), based on a choice of actuated joints or inputs and on the manipulator’s end-effector workspace or outputs. This will facilitate us with a framework for analysing singularities for forward and inverse kinematics via input and output mappings defined on the manipulator’s C-space. This provides new insight into the structure of the forward and inverse kinematics, especially for parallel manipulators. The theory is illustrated by a number of applications, some of which recapitulate classical or known results and some of which are new.</p>

A Constraint-Based Approach to Manipulator Kinematics and Singularities

<p>In this thesis, a differential-geometric approach to the kinematics of multibody mechanisms is introduced that enables analysis of singularities of both serial and parallel manipulators in a flexible and complete way. Existing approaches such as those of Gosselin and Angeles [1], Zlatanov et al. [2] and Park and Kim [3] make use of a combination of joint freedoms and constraints and so build in assumptions. In contrast, this new approach is solely constraint-based, avoiding some of the shortcomings of these earlier theories. The proposed representation has two core ingredients. First, it avoids direct reference to the choice of inputs and their associated joint freedoms and instead focuses on a kinematic constraint map (KCM), defined by the constraints imposed by all joints and not requiring consideration of closure conditions arising from closed loops in the design. The KCM is expressed in terms of pose (i.e. position and orientation) variables, which are the coordinates of all the manipulator’s links with respect to a reference frame. The kinematics of a given manipulator can be described by means of this representation, locally and globally. Also, for a family of manipulators defined by a specific architecture, the KCM will tell us how the choice of design parameters (e.g. link lengths) affects these kinematic properties within the family. At a global level, the KCM determines a subset in the space of all pose variables, known as the configuration space (C-space) of the manipulator, whose topology may vary across the set of design parameters. The Jacobian (matrix of first-order partial derivatives) of the KCM may become singular at some specific choices of pose variables. These conditions express a subset called the singular set of the C-space. It is shown that if a family of manipulators, parametrised by a manifold Rd of design parameters, is “well-behaved” then the pose variables can be eliminated from the KCM equations together with the conditions for singularities, to give conditions in terms of design parameters, that define a hypersurface in Rd of manipulators in the class that exhibit C-space singularities. These are referred to as Grashof-type conditions, as they generalise classically known inequalities classifying planar 4-bar mechanisms due to Grashof [4]. Secondly, we develop the theory to incorporate actuator space (A-space) and workspace (W-space), based on a choice of actuated joints or inputs and on the manipulator’s end-effector workspace or outputs. This will facilitate us with a framework for analysing singularities for forward and inverse kinematics via input and output mappings defined on the manipulator’s C-space. This provides new insight into the structure of the forward and inverse kinematics, especially for parallel manipulators. The theory is illustrated by a number of applications, some of which recapitulate classical or known results and some of which are new.</p>

HARLEY: A Semi-Automated detection of foci in fluorescence images of yeast

Quantification of cellular structures in fluorescence microscopy data is a key means of understanding cellular function. Unfortunately, numerous cellular structures present unique challenges in their ability to be unbiasedly and accurately detected and quantified. In our studies on stress granules in yeast, users displayed a striking variation of up to 3.7-fold in foci calls and were only able to replicate their results with 62-78% correlation, when requantifying the same images. To facilitate consistent results we developed HARLEY (Human Augmented Recognition of LLPS Ensembles in Yeast), a customizable software for detection and quantification of stress granules in S.cerevisiae. After a brief model training on ~20 cells the detection of foci is fully automated and based on closed loops in intensity contours, constrained only by the a-priori known size of the features of interest. Since no shape is implied, this method is not limited to round features, as is often the case with other algorithms. Candidate features are annotated with a set of geometrical and intensity-based properties to train a kernel Support Vector Machine to recognize features of interest. The trained classifier is then used to create consistent results across datasets. HARLEY is aimed at users without technical expertise, allows for batch processing and is freely available, which should be of broad interest to users focused on analysis of microscopy data in yeast.

Sustainable Design through Up-Cycling Crafts in the Mainstream Fashion Industry of India

Fashion is considered to be the most destructive industry, second only to the oil rigging industry, which has a greater impact on the environment. While fashion today, banks upon fast fashion to generate higher turnover of designs and patterns in apparel and relate accessories, crafts push us towards a more slow and thoughtful approach with culturally identifiably unique work and slow community centred production. Despite this strong link between indigenous crafts and sustainability, it has not been extensively researched and explored upon. In the forthcoming years, the fashion industry will have to re-invent itself to move towards a more holistic and sustainable circular model to balance the harm already caused. And closed loops of the circular economy will help the integration of indigenous craft knowledge which is regenerative. Though sustainability and crafts of a region go hand- in- hand, craft still have to find its standing in the mainstream fashion world; craft practices have a strong local congruence and knowledge that has been passed down generation-to-generation through oration or written materials. This paper aims to explore ways a circular economy can be created by amalgamating fashion and craft while creating a sustainable business model and how this is slowly being created today through brands. KEYWORDS: Circular Economy, Fashion, India, Indigenous Crafts, Slow Fashion, Sustainability, Up-cycling

Signatures of Type III Solar Radio Bursts from Nanoflares: Modeling

There is a wide consensus that the ubiquitous presence of magnetic reconnection events and the associated impulsive heating (nanoflares) are strong candidates for solving the solar coronal heating problem. Whether nanoflares accelerate particles to high energies like full-sized flares is unknown. We investigate this question by studying the type III radio bursts that the nanoflares may produce on closed loops. The characteristic frequency drifts that type III bursts exhibit can be detected using a novel application of the time-lag technique developed by Viall & Klimchuk (2012) even when there are multiple overlapping events. We present a simple numerical model that simulates the expected radio emission from nanoflares in an active region, which we use to test and calibrate the technique. We find that in the case of closed loops the frequency spectrum of type III bursts is expected to be extremely steep such that significant emission is produced at a given frequency only for a rather narrow range of loop lengths. We also find that the signature of bursts in the time-lag signal diminishes as: (1) the variety of participating loops within that range increases; (2) the occurrence rate of bursts increases; (3) the duration of bursts increases; and (4) the brightness of bursts decreases relative to noise. In addition, our model suggests a possible origin of type I bursts as a natural consequence of type III emission in a closed-loop geometry.

Revisiting the formation mechanism for coronal rain from previous studies

Solar coronal rain is classified generally into two categories: flare-driven and quiescent coronal rain. Th latter is observed to form along both closed and open magnetic field structures. Recently, we proposed that some of the quiescent coronal rain events, detected in the transition region and chromospheric diagnostics, along loop-like paths could be explained by the formation mechanism for quiescent coronal rain facilitated by interchange magnetic reconnection between open and closed field lines. In this study, we revisited 38 coronal rain reports from the literature. From theseearlier works, we picked 15 quiescent coronal rain events out of the solar limb, mostly suggested to occur in active region closed loops due to thermal nonequilibrium, to scrutinize their formation mechanism. Employing the extreme ultraviolet images and line-of-sight magnetograms, the evolution of the quiescent coronal rain events and their magnetic fields and context coronal structures is examined. We find that six, comprising 40%, of the 15 quiescent coronal rain events could be totally or partially interpreted by the formation mechanism for quiescent coronal rain along open structures facilitated by interchange reconnection. The results suggest that the quiescent coronal rain facilitated by interchange reconnection between open and closed field lines deserves more attention.

Chirality detected in Hartley’s electronic oscillator

Chirality is an elusive asymmetry important in science and technology and confined mainly to the quantum realm. This paper reports the observation of chirality in a classical (that is, not quantum) scenario, namely in stability diagrams of an autonomous electronic oscillator with a junction-gate field-effect transistor (JFET) and a tapped coil. As the number of spikes (local maxima) of stable oscillations changes along closed parameter paths, they generate two types of intricate structures. Surprisingly, such pair of structures are artful images of each other when reflected on a mirror. They are dual chiral pairs interconnecting families of stable oscillations in closed loops. Chiral pairs should not be difficult to detect experimentally. This chirality is conjectured to be a generic property of nonlinear oscillators governed by classical (that is, not quantum) equations.

Fifty Years of 3He-Rich Events

The early 1970s saw a new and surprising feature in the composition of solar energetic particles (SEPs), resonant enhancements up to 10,000-fold in the ratio 3He/4He that could even make 3He dominant over H in rare events. It was soon learned that these events also had enhancements in the abundances of heavier elements, such as a factor of ∼10 enhancements in Fe/O, which was later seen to be part of a smooth increase in enhancements vs. mass-to-charge ratio A/Q from H to Pb, rising by a factor of ∼1000. These events were also associated with streaming 10–100 keV electrons that produce type III radio bursts. In recent years we have found these “impulsive” SEP events to be accelerated in islands of magnetic reconnection from plasma temperatures of 2–3 MK on open field lines in solar jets. Similar reconnection on closed loops traps the energy of the particles to produce hot (&gt;10 MK), bright flares. Sometimes impulsive SEP intensities are boosted by shock waves when the jets launch fast coronal mass ejections. No single theory yet explains both the sharp resonance in 3He and the smooth increase up to heavier elements; two processes seem to occur. Sometimes the efficient acceleration even exhausts the rare 3He in the source region, limiting its fluence.

Study On Transfer Matrix Method for the Planar Multibody System with Closed-Loops

The conventional transfer matrix method for multibody systems (MSTMM) with closed-loops (CLs) has superiority of avoiding the global dynamics equations. However, it requires a transfer equation to link Multiple-Input Single-Output (MISO) rigid body with multi-hinge subset and supplement equations caused CLs. In order to simplify the deduction processing and improve the numerical stability, the Riccati transformation is introduced and the Riccati transfer matrix method for multibody systems (RMSTMM) with CL is proposed. In a system with CLs, each CL is cut off at the connection point, and the new unknowns generated at the cut-off point are introduced into the Riccati recurrence relation. The numerical results of the conventional MSTMM and the RMSTMM are compared, and the reliability of the RMSTMM is verified. Meanwhile, the constrained Jacobian matrix is used to eliminate the non-working reactions of the system. The variations of the constraint violation error are compared to validate necessarily of constraints.