A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Simulation of the infrared spectra of thioacetamide by the extended molecular mechanics method

The infrared spectrum of the matrix-isolated species of thioacetamide has been simulated using the extended molecular mechanics method. The equilibrium structure, vibrational frequencies, dipole moment and infrared absorption intensities of thioacetamide have been calculated in good agreement with the experiment. The vibrational frequencies and infrared absorption intensities for the isotopic molecules (CH2CSNH2)-C-13, (CH3CSNH2)-N-15 and (CH2CSND2)-C-13 have also been calculated consistent with the experiment. The infrared spectra of the matrix isolated species of N- and C- deuterated isotopomers of thioacetamide, CH3CSND2 and CD3CSNH2 have also been simulated in satisfactory agreement with the experimental spectra.

Structural vibration control using resistively shunted piezoceramics

Application of piezoceramic materials in actuation and sensing of vibration is of current interest. Potential and more popular applications of piezoceramics are probably in the field of active vibration control. However, the objective of this work is to investigate the effect of shunted piezoceramics as passive vibration control devices when bonded to a host structure. Resistive shunting of a piezoceramic bonded to a cantilevered duralumin beam has been investigated. The piezoceramic is connected in parallel to an electrical network comprising of resistors and inductors. The piezoceramic is a capacitor that stores and discharges electrical energy that is transformed from the mechanical motion of the structure to which it is bonded. A resistor across the piezoceramic would be termed as a resistively shunted piezoceramic. Similarly, an inductor across the piezoceramic is termed as a resonantly shunted piezoceramic. In this study, the effect of resistive shunting on the nature of damping enhancement to the host structure has been investigated. Analytical studies are presented along with experimental results.

A new parallel overlapped domain decomposition method for nonlinear dynamic finite element analysis

In this paper a new parallel algorithm for nonlinear transient dynamic analysis of large structures has been presented. An unconditionally stable Newmark-beta method (constant average acceleration technique) has been employed for time integration. The proposed parallel algorithm has been devised within the broad framework of domain decomposition techniques. However, unlike most of the existing parallel algorithms (devised for structural dynamic applications) which are basically derived using nonoverlapped domains, the proposed algorithm uses overlapped domains. The parallel overlapped domain decomposition algorithm proposed in this paper has been formulated by splitting the mass, damping and stiffness matrices arises out of finite element discretisation of a given structure. A predictor-corrector scheme has been formulated for iteratively improving the solution in each step. A computer program based on the proposed algorithm has been developed and implemented with message passing interface as software development environment. PARAM-10000 MIMD parallel computer has been used to evaluate the performances. Numerical experiments have been conducted to validate as well as to evaluate the performance of the proposed parallel algorithm. Comparisons have been made with the conventional nonoverlapped domain decomposition algorithms. Numerical studies indicate that the proposed algorithm is superior in performance to the conventional domain decomposition algorithms. (C) 2003 Elsevier Ltd. All rights reserved.

A Compliant Mechanism Kit with Flexible Beams and Connectors

We present the concept, prototypes, and an optimal design method for a compliant mechanism kit as a parallel to the kits available for rigid-body mechanisms. The kit consists of flexible beams and connectors that can be easily hand-assembled using snap fits. It enables users, using their creativity and mechanics intuition, to quickly realize a compliant mechanism. The mechanisms assembled in this manner accurately capture the essential behavior of the topology, shape, size and material aspects and thereby can lead the way for a real compliant mechanism for practical use. Also described in this paper are the design of the connector to which flexible beams can be added in eight different directions; and prototyping of the spring steel connectors as well as beams using wire-cut electro discharge machining. It is noted in this paper that the concept of the kit also resolves a discrepancy in the finite element (FE) modeling of beam-based compliant mechanisms. The discrepancy arises when two or more beams are joining at one point and thus leading to increased stiffness. After resolving this discrepancy, this work extends the topology optimization to automatically generate designs that can be assembled with the kit. Thus, the kit and the accompanying analysis and optimal synthesis procedures comprise a self-contained educational as well as a research and pragmatic toolset for compliant mechanisms. The paper also illustrates how human creativity finds new ways of using the kit beyond the original intended use and how it is useful even for a novice to design compliant mechanisms.

Simulation of the infrared spectra of N-methylformamide and N-methylacetamide by the extended molecular mechanics method

The infrared spectra of the matrix isolated species of N-methylformamide (NMF) and N-methylacetamide (NMA) and their N-deuterated molecules have been simulated by the extended molecular mechanics method using an empirical force field which includes charges and charge fluxes as coulombic potential parameters. The structural parameters and dipole. moments of NMF and NMA have. also been computed in satisfactory agreement with the experiment. Good agreement between experimental and calculated vibrational frequencies and infrared absorption band intensities for NMF and NMA and their deuterated molecules has been obtained. The vibrational assignments of NMF and NMA are-discussed taking also into account the infrared absorption intensities.

Ligand-modulated Parallel Mechanical Unfolding Pathways of Maltose-binding Proteins

Protein folding and unfolding are complex phenomena, and it is accepted that multidomain proteins generally follow multiple pathways. Maltose-binding protein (MBP) is a large (a two-domain, 370-amino acid residue) bacterial periplasmic protein involved in maltose uptake. Despite the large size, it has been shown to exhibit an apparent two-state equilibrium unfolding in bulk experiments. Single-molecule studies can uncover rare events that are masked by averaging in bulk studies. Here, we use single-molecule force spectroscopy to study the mechanical unfolding pathways of MBP and its precursor protein (preMBP) in the presence and absence of ligands. Our results show that MBP exhibits kinetic partitioning on mechanical stretching and unfolds via two parallel pathways: one of them involves a mechanically stable intermediate (path I) whereas the other is devoid of it (path II). The apoMBP unfolds via path I in 62% of the mechanical unfolding events, and the remaining 38% follow path II. In the case of maltose-bound MBP, the protein unfolds via the intermediate in 79% of the cases, the remaining 21% via path II. Similarly, on binding to maltotriose, a ligand whose binding strength with the polyprotein is similar to that of maltose, the occurrence of the intermediate is comparable (82% via path I) with that of maltose. The precursor protein preMBP also shows a similar behavior upon mechanical unfolding. The percentages of molecules unfolding via path I are 53% in the apo form and 68% and 72% upon binding to maltose and maltotriose, respectively, for preMBP. These observations demonstrate that ligand binding can modulate the mechanical unfolding pathways of proteins by a kinetic partitioning mechanism. This could be a general mechanism in the unfolding of other large two-domain ligand-binding proteins of the bacterial periplasmic space.

Strategies for Rescheduling Tightly-Coupled Parallel Applications in Multi-Cluster Grids

As computational Grids are increasingly used for executing long running multi-phase parallel applications, it is important to develop efficient rescheduling frameworks that adapt application execution in response to resource and application dynamics. In this paper, three strategies or algorithms have been developed for deciding when and where to reschedule parallel applications that execute on multi-cluster Grids. The algorithms derive rescheduling plans that consist of potential points in application execution for rescheduling and schedules of resources for application execution between two consecutive rescheduling points. Using large number of simulations, it is shown that the rescheduling plans developed by the algorithms can lead to large decrease in application execution times when compared to executions without rescheduling on dynamic Grid resources. The rescheduling plans generated by the algorithms are also shown to be competitive when compared to the near-optimal plans generated by brute-force methods. Of the algorithms, genetic algorithm yielded the most efficient rescheduling plans with 9-12% smaller average execution times than the other algorithms.