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Stability analysis of multiple rigid robot manipulators holding a common rigid object
The authors consider several possible control structures for multiple-arm systems by regarding either joint torques, tip force, or a generalized acceleration of the control input. They emphasize the first case, since a class of relatively model-independent control laws can be generated for both motion and internal force control. The recently developed move/squeeze orthogonal subspace decomposition coupled with the energy Lyapunov function formulation provides a basic analytical framework within which motion and force control are considered as independent problems. Simulation results of two three-link planar arms are included to demonstrate good transient performance for both motion and force that can be attained with the full dynamics control paradigm.
Stiffness-generated rigid-body mode shapes for Lanczos eigensolution with SUPORT DOF by way of a MSC/NASTRAN DMAP alter
When using all MSC/NASTRAN eigensolution methods except Lanczos, the analyst can replace the coupled system rigid-body modes calculated within DMAP module READ with mass orthogonalized and normalized rigid-body modes generated from the system stiffness. This option is invoked by defining MSC/NASTRAN r-set degrees of freedom via the SUPORT bulk data card. The newly calculated modes are required if the rigid-body modes calculated by the eigensolver are not 'clean' due to numerical roundoffs in the solution. When performing transient structural dynamic load analysis, the numerical roundoffs can result in inaccurate rigid-body accelerations which affect steady-state responses. Unfortunately, when using the Lanczos method and defining r-set degrees of freedom, the rigid-body modes calculated within DMAP module REIGL are retained. To overcome this limitation and to allow MSC/NASTRAN to handle SUPORT degrees of freedom identically for all eigensolvers, a DMAP Alter has been written which replaces Lanczos-calculated rigid-body modes with stiffness-generated rigid-body modes. The newly generated rigid-body modes are normalized with respect to the system mass and orthogonalized using the Gram-Schmidt technique. This algorithm has been implemented as an enhancement to an existing coupled loads methodology.
Flexural rigidity of the Basin and Range-Colorado Plateau-Rocky Mountain transition from coherence analysis of gravity and topography
Stochastic inversion for flexural loads and flexural rigidity of the continental elastic layer can be accomplished most effectively by using the coherence of gravity and topography. However, the spatial resolution of coherence analysis has been limited by use of two-dimensional periodogram spectra from very large (greater than 10(exp 5)sq km) windows that generally include multiple tectonic features. Using a two-dimensional spectral estimator based on the maximum entropy method, the spatial resolution of flexural proerties can be enhanced by a factor of 4 or more, enabling more detailed analysis at the scale of individual tectonic features. This new approach is used to map the spatial variation of flexural rigidity along the Basin and Range transition to the Colorado Plateau and Middle Rocky Mountains physiographic provinces. Large variations in flexural isostatic responses are found, with rigidities ranging from as low as 8.7 x 10(exp 20) N m (elastic thickness (T(sub e) = 4.6 km) in the Basin and Range to as high as 4.1 x 10(exp 24) N m T(sub e) = 77 km) in the Middle Rocky Mountains. These results compare favorably woith independent determinations of flexural rigidity in the region. Areas of low flexural rigidity correlate strongly with areas of high surface heat flow, as is expected from the contingence of flexural rigidity on a temperature-dependent flow law. Also, late Cenozoic normal faults with large displacements are found primarily in area of low flexural rigidity region. The highest flexural rigidity is found within the Archean Wyoming craton, where evidence suggests that deeply rooted cratonic lithosphere may play a role in determining the distribution of tectonism at the surface.
A new method for generating and maintaining rigid formats in NASTRAN
A new method for generating and updating Rigid Formats in NASTRAN is discussed. The heart of this method is a Rigid Format data base that is in card-image format and that can therefore be easily maintained by the use of standard text editors. Each Rigid Format entry in this data base will contain the Direct Matrix Abstraction Program (DMAP) for that Rigid Format along with the related restart, subset and substructure control tables. NASTRAN will read this data base directly in every NASTRAN run and perform the necessary transformations to allow the DMAP to be processed and compiled by the NASTRAN executive. This approach will permit Rigid Formats to be changed without unnecessary compilations and relinking of NASTRAN. Furthermore, this approach will also make it very easy for users to make permanent changes to existing Rigid Formats as well as to generate their own Rigid Formats. This new method will be incorporated in a future release of the public version of NASTRAN.
Apparatus for integrating a rigid structure into a flexible wall of an inflatable structure
For an inflatable structure having a flexible outer shell or wall structure having a flexible restraint layer comprising interwoven, load-bearing straps, apparatus for integrating one or more substantially rigid members into the flexible shell. For each rigid member, a corresponding opening is formed through the flexible shell for receiving the rigid member. A plurality of connection devices are mounted on the rigid member for receiving respective ones of the load-bearing straps. In one embodiment, the connection devices comprise inner connecting mechanisms and outer connecting mechanisms, the inner and outer connecting mechanisms being mounted on the substantially rigid structure and spaced along a peripheral edge portion of the structure in an interleafed array in which respective outer connecting mechanisms are interposed between adjacent pairs of inner connecting mechanisms, the outer connecting mechanisms projecting outwardly from the peripheral edge portion of the substantially rigid structure beyond the adjacent inner connecting mechanisms to form a staggered array of connecting mechanisms extending along the panel structure edge portion. In one embodiment, the inner and outer connecting mechanisms form part of an integrated, structure rotatably mounted on the rigid member peripheral edge portion.
Complex Phase Transitions of Fully Rigid Sphere–Rod Amphiphiles Induced by Solvent Polarity in Dilute Solutions
Here we report complex macrophase and microphase transitions of rigid amphiphiles with spherical Keggin molecular clusters as the solvophilic block and rod-like rigid oligofluorene (OF) as the solvophobic block in mixed solvents of water and polar organic solvent. By properly adjusting the solvent polarity, the amphiphiles are found to respond accordingly by self-assembling into multilayered incomplete onion-like structures (10–25 vol % THF), single-layered vesicular structures (60 vol % THF), and an unexpected macrophase separation in the middle (40–50 vol % THF), which is due to the anomalous trends in Keggin solubility as a result of the nature of TBA + counterions. The rigidity of the OF block prevents the amphiphile from assembling by following the rule of packing parameters; instead, interdigitation among different rods leads to the formation of the solvophobic domain to achieve self-assembly. The incomplete onion structures are controlled by the interdigitation of rigid rods for the number of layers and the electrostatic interaction among Keggin head groups for the interlayer distance. When the degree of interdigitation becomes lower, the self-assembly process shows a trend that can be explained by the traditional rule of packing parameter. This study demonstrates the formation of different self-assembled structures by rigid amphiphiles and their transitions induced by solvent composition. The self-assembly (microphase separation) of rigid amphiphiles in a dilute solution could indeed represent a broad area containing complicated, uncharted rules.
Influence of Rigidity–Hydration Coupling on Size-Dependent Diffusion in Hydrated Polymer Membranes
Selective ion transport in polymer membranes depends critically on how penetrant motion couples to polymer dynamics and hydration. Yet, the mechanistic interplay between polymer rigidity, water content, and penetrant size remains poorly understood, especially in the regime where the penetrant diameter, polymer Kuhn length, and correlation length are comparable. Here, we employ coarse-grained molecular dynamics simulations to systematically investigate penetrant diffusion in hydrated polymer networks across a broad range of water volume fractions, chain rigidities, and penetrant sizes. The results reveal a transition from a decoupled regime, where small penetrants diffuse nearly independently of polymer relaxation, to a coupled regime in which large penetrants require cooperative polymer motion for transport. Increasing polymer rigidity amplifies the sensitivity of diffusivity to hydration, particularly at low water content, leading to pronounced deviations from Stokes−Einstein scaling. Comparison with scaling theories and free-volume models shows that classical nanoparticle-based frameworks fail to capture this intermediate regime. To address this gap, we extend the Yasuda model to incorporate polymer rigidity through a single parameter that quantifies the dynamic contribution of chain stiffness to free-volume fluctuations. The resulting model collapses diffusivity data across all sizes, water contents, and rigidities, providing a unified description of penetrant transport in hydrated polymer matrices. Furthermore, these findings establish polymer rigidity as a key, tunable determinant of diffusion and offer a framework for interpreting size-dependent transport in ion-selective membranes.
Low thermal conductance rigidizer for reducing torsional oscillations in cryogenic Dewars
A rigidizer, which provides greater rigidity against torsional oscillations, is highly resistant to radial motions, and has low thermal conductivity, has been developed to decrease vibrational levels affecting infrared detectors operated in cryostats (e.g., HD-3L Dewar) in aircraft such as NASA's Kuiper Airborne Observatory. The rigidizer is composed of two triangular elements and an intermediate support structure which joins them at the centers of their sides. The reentrant design provides a long heat path, while the triangular truss structure provides high rigidity in the horizontal plane. The structure is relatively compliant in the vertical direction, a desirable feature since the internal structure of the Dewar contracts as it cools. Rigidity in the vertical direction is provided by the neck tube. The support structure is quite compact. Several variants of the rigidizer have been fabricated, using flat sheets of G-10 fiberglass epoxy in thicknesses between 0.75-1.5 mm for the upper and lower truss assemblies, and either G-10 or stainless steel for the intermediate structure.
Design of Rigid-Flex PCB Robotics Leveraging Validated Finite Element Simulations
The use of rigid-flex printed circuit board (PCB) as primary structure has the potential to reduce the weight and volume of robotic systems. In the case of robotics for interplanetary exploration, these systems can leverage origami-inspired folding for increased mobility options and reduced storage volume. Folding rigid-flex PCB robotics can be constructed with rigid PCB connected by short Nomex fabric hinges coupled with flex PCB ribbon cables that permits enhanced system flexibility and energy dissipation to promote impact survivability. This paper presents a design methodology of rigid-flex PCB systems with an emphasis on impact resistance. The design process considers solder joint adequacy, panel bending, and fracture using a finite element (FE) model. The proposed design methodology is developed using a case study with NASA JPL's Pop-Up Folding Flat Explorer Robot (PUFFER). First, the finite-element (FE) modeling methodology is presented with consideration to both frequency and time-domain modeling applications, which include operational self-contact analysis and high impact scenarios. The time-domain impact modeling methodology utilizes hyperelastic material properties for the Nomex hinges. This modeling method is validated using image correlation of PUFFER drop tests. A flowchart is presented to guide users through a validated Abaqus modeling procedure for highly flexible rigid-flex systems. Next, a case study is presented in which PUFFER is subject to drop heights representative of falls into Lunar pits and then the design is refined for a more optimum impact performance. Finally, the results of the case study are used to inform a generalized design methodology for rigid-flex PCB robotics subject to high-impact loads with the considerations presented.
Noninvasive measures of bone bending rigidity in the monkey /M. nemestrina/
The in vivo bending rigidity and bone mineral content of monkey ulnae and tibiae were measured. Bending rigidity in the anteroposterior plane was measured by an impedance probe technique. Forced vibrations of the bones were induced with an electromechanical shaker, and force and velocity at the driving point were determined. The responses over the range of 100-250 Hz were utilized to compute the bending rigidity. Bone mineral content in the cross section was determined by a photon absorption technique. Seventeen male monkeys (Macaca nemestrina) weighing 6-14 kg were evaluated. Bending rigidity was correlated with the mineral content of the cross section, with a correlation coefficient of 0.899. Two monkeys were evaluated during prolonged hypodynamic restraint. Restraint produced regional losses of bone most obviously in the proximal tibia. The local bone mineral content declines 17 to 24% and the average bending rigidity declines 12 to 22%. Changes in bones leading to a reduction in mineral content and stiffness are discussed.
Design of Rigid-Flex PCB Robotics Leveraging Validated Finite Element Simulations
The use of rigid-flex printed circuit board (PCB) as primary structure has the potential to reduce the weight and volume of robotic systems. In the case of robotics for interplanetary exploration, these systems can leverage origamiinspired folding for increased mobility options and reduced storage volume. Folding rigid-flex PCB robotics can be constructed with rigid PCB connected by short Nomex fabric hinges coupled with flex PCB ribbon cables that permits enhanced system flexibility and energy dissipation to promote impact survivability. This paper presents a design methodology of rigidflex PCB systems with an emphasis on impact resistance. The design process considers solder joint adequacy, panel bending, and fracture using a finite element (FE) model. The proposed design methodology is developed using a case study with NASA JPL’s Pop-Up Folding Flat Explorer Robot (PUFFER). First, the finite-element (FE) modeling methodology is presented with consideration to both frequency and time-domain modeling applications, which include operational self-contact analysis and high impact scenarios. The time-domain impact modeling methodology utilizes hyperelastic material properties for the Nomex hinges. This modeling method is validated using image correlation of PUFFER drop tests. A flowchart is presented to guide users through a validated Abaqus modeling procedure for highly flexible rigid-flex systems. Next, a case study is presented in which PUFFER is subject to drop heights representative of falls into Lunar pits and then the design is refined for a more optimum impact performance. Finally, the results of the case study are used to inform a generalized design methodology for rigid-flex PCB robotics subject to high-impact loads with the considerations presented.
Bilayer Electron Transport Layers for High–Performance Rigid and Flexible Perovskite Solar Cells
While great progress is being made in achieving high power conversion efficiency (PCE), durability, and reliability in rigid and flexible n–i–p perovskite solar cells (PSCs), there is still room for improvement. Among myriad ways this can be achieved, one way is to improve the processing and quality of electron transport layers (ETLs) used in PSCs. To that end, here we explore the use of SnO 2 /TiO 2 bilayer ETLs in both rigid and flexible PSCs. In the case of rigid PSCs, chemical bath deposition (CBD) is used where the bilayer architecture affords the CBD of high-quality ETL, which results in PSCs with up to 25.13% PCE and operational stability T 80 (80% of initial PCE retained) of 2220 h under 1-sun continuous illumination with maximum power-point tracking. In the case of flexible PSCs, once again, the bilayer architecture allows us to fabricate high-quality ETL using spin coating, which results in PSCs with up to 22.54% PCE and excellent mechanical durability, withstanding 20 000 bending cycles with ≈92% of the initial PCE retained. Mechanisms underlying the enhanced performance and stability/durability of rigid and flexible PSCs that use SnO 2 /TiO 2 bilayer ETLs are elucidated. Furthermore, this approach could be extended to other ETL systems for PSCs for further improvements in PCE, durability, and reliability.
Brush-modified fluorescent organic nanoparticles by ATRP with rigidity-regulated emission
Organic nanoparticles provide exceptional intraparticle tailorability, enabling the incorporation of functional molecules for diverse applications. In this study, we present the synthesis and characterization of fluorescent organic nanoparticles (FoNPs) with encapsulated aggregation-induced emission (AIE) luminogens with emission properties regulated by particle rigidity. Atom transfer radical polymerization (ATRP) was employed in dispersed media to develop various fluorescence colors tuned by precise control over particle rigidity. Comprehensive analyses revealed that increased particle rigidity significantly enhanced photoluminescence, achieving quantum yields of up to 22% in selected solvents. The high chain-end fidelity facilitated the grafting of hydrophilic polymer brushes from surfaces of FoNPs used as macroinitiators, enabling their dispersion in aqueous media while maintaining bright fluorescence. These findings highlight the potential of rigidity-regulated FoNPs as versatile platforms for advanced material applications, particularly in fluorescent waterborne films and aqueous-phase sensing systems.
Rigid-Mode Limit of the Yokoya Matrix Formalism and the Burov-Lebedev Dispersion Equation
Transverse single-bunch instabilities of space-charge-dominated coasting beams with round and flat transverse geometries are studied using a unified dispersion-relation framework. The analysis combines the Burov-Lebedev formalism, which captures space-charge tune spread, Landau damping, and instability threshold behavior, with Yokoya’s projection method for representing coherent transverse mode structure and its dependence on beam aspect ratio. In the rigid-beam limit, the formulation reduces to a scalar dispersion relation of Burov-Lebedev paper. For non-rigid transverse oscillations, truncation of Yokoya’s Hermite-based expansion yields a finite-dimensional matrix eigenvalue problem in which space-charge and coupling impedance effects enter through Burov-Lebedev–type denominators. This approach provides a consistent basis for comparing rigid and non-rigid instability behavior in round and flat beams and for assessing the role of beam ellipticity in modifying coherent mode structure and stability thresholds.
Numerical solution for low-velocity penetration of rigid body into still fluid
A modified marker-and-cell computational method is developed which can be used to study problems related to impact and penetration of a rigid body into a viscous medium. The method has been applied to solving (in two dimensions) the problem of low-velocity penetration of a rigid block into still water. The solution gives the complete pressure and velocity of the flow field so that the force and displacement time histories of the rigid body during the impact and entry phase are evaluated from the boundary stresses imposed by the fluid on the rigid body. Some limited experimental comparisons are also given to demonstrate the feasibility of the computational method.
Rigidity spectrum of z greater than or equal to 3 cosmic-ray nuclei in the range 4-285 GV and a search for cosmic antimatter
A measurement, using the magnetic emulsion spectrometer system, of the differential rigidity spectrum of Z greater than or equal to 3 nuclei of the galactic cosmic radiation is presented. The system was flown on Aug. 22, 1969, from Palestine, Texas. The instrument floated above 125,000 feet for eight hours. The data in the rigidity range 8-285 GV can be represented by a power-law spectrum in rigidity, J(rho) = A rho to the minus gamma power, with the exponent gamma = 2.6 plus or minus 0.10. The spectrum in the range 15-285 GV is also described by the same exponent, gamma = 2.6 plus or minus 0.25. The data below 8 GV cannot be described by the same power law without invoking solar modulation. A set of nonunique parameters for modulation are given. Upper limit for the fraction of antimatter in the rigidity range 4-125 GV is .005 with 95% confidence limit.
Mooring and ground handling rigid airships
The problems of mooring and ground handling rigid airships are discussed. A brief history of Mooring and Ground Handling Rigid Airships from July 2, 1900 through September 1, 1939 is included. Also a brief history of ground handling developments with large U. S. Navy nonrigid airships between September 1, 1939 and August 31, 1962 is included wherein developed equipment and techniques appear applicable to future large rigid airships. Finally recommendations are made pertaining to equipment and procedures which appear desirable and feasible for future rigid airship programs.