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Results for “Chain rigidity”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Conformational Dynamics of Bacteriochlorophyll c in Chlorosomes from the bchQ Mutant of Chlorobaculum tepidum

In contrast to the common viewpoint that bacteriochlorophyll (BChl) motion is largely absent within the chlorosome assembly, physics-based modeling points to a crucial role of the nanoscale librational motion of the macrocycle for the transfer of excitons. To elucidate this motion experimentally, compositional uniformity and high sensitivity are required. We focused on uniformly 13 C labeled chlorosome preparations from the bchQ mutant Chlorobaculum tepidum with significantly enhanced structural homogeneity. The librational motion is characterized using Rotational Echo DOuble Resonance (REDOR), and in addition, the impact of temperature on specific functionalities within BChl molecules is studied with 1-dimensional and 2-dimensional dipolar and scalar-based MAS NMR measurements. Results show the gradual freezing of the tails and side chains of the BChls with decreasing temperature. However, the librational motion analyzed by measuring the 5C–H dipolar coupling strength obtained from REDOR data sets persists at different temperatures. REDOR simulations show a close match to the experimental dephasing frequency of oscillation for a dipolar coupling strength of 17.5 ± 0.5 kHz which is considerably less than the dipolar coupling strength of 22.7 kHz in the rigid limit. Following a two-site jump model, we arrive at an estimate for BChl libration sampling at an angle of θ = 48 ± 4°, corroborating that the macrocycle indeed experiences significant librational motion on a time scale that is short compared to the NMR measurement time. This finding is in full quantitative support of the dominant rotational motion exhibited by the BChl macrocycle estimated from early MD simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Dynamics of polydots: Soft luminescent polymeric nanoparticles

The conformation and dynamics of luminescent polymers collapsed into nanoparticles or polydots were studied using fully atomistic molecular dynamics (MD) simulations, providing a first insight into their internal dynamics. Controlling the conformation and dynamics of confined polymers is essential for realization of the full potential of polydots in nanomedicine and biotechnology. Specifically, the shape and internal dynamics of polydots that consist of highly rigid dialkyl p-phenylene ethynylene (PPE) are probed as a function of temperature. At room temperature, the polydots are spherical without any correlations between the aromatic rings on the PPE backbone. With increasing temperature, they expand and become slightly aspherical; however, the polymers remain confined. The coherent dynamic structure factor reveals that the internal motion of the polymer backbone is arrested, and the side chains dominate the internal dynamics of the polydots. Lastly, these new soft nanoparticles retain their overall shape and dynamics over an extended temperature range, and their conformation is tunable via their degree of expansion.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

Soliton motion induced along ferromagnetic skyrmion chains in chiral thin nanotracks

Using atomistic magnetic simulations we investigate the soliton motion along a pinned skyrmion chain containing an interstitial skyrmion. We find that the soliton can exhibit stable motion along the chain without a skyrmion Hall effect for an extended range of drives. Under a constant drive the solitons have a constant velocity. We also measure the skyrmion velocity–current curves and identify the signatures of different phases including a pinned phase, stable soliton motion, and quasi-free motion at higher drives where all of the skyrmions depin from the pinning centers and move along the rigid wall. In the quasi-free motion regime, the velocity is oscillatory due to the motion of the skyrmions over the pinning sites. For increasing pinning strength, the onset of soliton motion shifts to higher values of current density. We also find that for stronger pinning, the characteristic velocity–current shape is affected by the annihilation of single or multiple skyrmions in the drive interval over which the soliton motion occurs. Our results indicate that stable skyrmion soliton motion is possible and that the solitons could be used as information carriers instead of the skyrmions themselves for technological applications.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Upcycling waste PET into functional multiblock copolymers through controlled macromolecular design

Poly(ethylene terephthalate) (PET) oligomers derived from glycolysis depolymerization were converted into multiblock copolymers through diisocyanate-mediated coupling with dihydroxy-terminated oligomers, enabling precise control over copolymer sequence distribution, connectivity, and mechanical performance. Here, we demonstrate that telechelic PET oligomers isolated directly from depolymerized consumer waste can serve as reactive building blocks for the formation of segmented multiblock copolymers, eliminating the need to revert to monomeric feedstocks. Dihydroxy-terminated PET oligomers (Mw ≈ 8 kg mol−1) were coupled with poly(ethylene oxide) (PEO, Mw ≈ 4 kg mol−1) to form PET-PEO multiblock copolymers with high molar mass (Mw ≈ 160 kg mol−1). We further show that the timing of end-capping reactions provides a key control parameter that governs the competition between chain extension and termination, thereby dictating the resulting multiblock architecture and molecular-weight evolution. Evaluation of their mechanical properties reveals that virgin PET exhibits high modulus (∼3 GPa) and strength (43 MPa) but limited ductility (<10% elongation). In contrast, PET–PEO multiblock copolymers retain comparable tensile strength (44 MPa), albeit while exhibiting dramatically enhanced ductility (>90% elongation), forming tougher materials with efficient stress transfer between the rigid PET domains and the flexible PEO segments. When incorporated into PET/PEO blends at low loadings, the multiblock copolymers serve as effective compatibilizers, yielding materials with an intermediate modulus (1.1–1.2 GPa) and improved elongation compared to uncompatibilized blends. Furthermore, the presence of PEO blocks increases water uptake and gas permeability relative to virgin PET, reflecting the tunability of molecular transport through the copolymeric blocks. To our knowledge, this represents the first report of PET–PEO multiblock copolymers derived from post-consumer PET for gas transport applications. These results demonstrate that multiblock copolymer formation from telechelic PET oligomers provides a versatile platform for tailoring the mechanical and transport behavior of polyester-based materials through controlled macromolecular design and establishes a generalizable strategy for transforming consumer plastic waste into functional segmented polymers without requiring complete depolymerization to monomers.

Watson-Sanders, Shelby [Department of Chemistry, U↗
DOE OSTI2014

Molecular interactions between photosystem I and ferredoxin: an integrated energy frustration and experimental model

The stromal domain (PsaC, PsaD, and PsaE) of photosystem I (PSI) reduces transiently bound ferredoxin (Fd) or flavodoxin. Experimental structures exist for all of these protein partners individually, but no experimental structure of the PSI/Fd or PSI/flavodoxin complexes is presently available. Molecular models of Fd docked onto the stromal domain of the cyanobacterial PSI site are constructed here utilizing X-ray and NMR structures of PSI and Fd, respectively. Moreover, predictions of potential protein-protein interaction regions are based on experimental site-directed mutagenesis and cross-linking studies to guide rigid body docking calculations of Fd into PSI, complemented by energy landscape theory to bring together regions of high energetic frustration on each of the interacting proteins. Results identify two regions of high localized frustration on the surface of Fd that contain negatively charged Asp and Glu residues. Our study predicts that these regions interact predominantly with regions of high localized frustration on the PsaC, PsaD, and PsaE chains of PSI, which include several residues predicted by previous experimental studies.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Organic nanoparticles with tunable size and rigidity by hyperbranching and cross-linking using microemulsion ATRP

Unlike inorganic nanoparticles, organic nanoparticles (oNPs) offer the advantage of “interior tailorability,” thereby enabling the controlled variation of physicochemical characteristics and functionalities, for example, by incorporation of diverse functional small molecules. In this study, a unique inimer-based microemulsion approach is presented to realize oNPs with enhanced control of chemical and mechanical properties by deliberate variation of the degree of hyperbranching or cross-linking. The use of anionic cosurfactants led to oNPs with superior uniformity. Benefitting from the high initiator concentration from inimer and preserved chain-end functionality during atom transfer radical polymerization (ATRP), the capability of oNPs as a multifunctional macroinitiator for the subsequent surface-initiated ATRP was demonstrated. This facilitated the synthesis of densely tethered poly(methyl methacrylate) brush oNPs. Detailed analysis revealed that exceptionally high grafting densities (~1 nm −2 ) were attributable to multilayer surface grafting from oNPs due to the hyperbranched macromolecular architecture. The ability to control functional attributes along with elastic properties renders this “bottom-up” synthetic strategy of macroinitiator-type oNPs a unique platform for realizing functional materials with a broad spectrum of applications.

ATRP↗
DOE OSTI2015

Thermoplastic Polyurethanes with Isosorbide Chain Extender

Isosorbide, a renewable diol derived from starch, was used alone or in combination with butane diol (BD) as the chain extender in two series of thermoplastic polyurethanes (TPU) with 50 and 70% polytetramethylene ether glycol (PTMEG) soft segment concentration (SSC), respectively. In the synthesized TPUs, the hard segment composition was systematically varied in both series following BD/isosorbide molar ratios of 100 : 0; 75 : 25; 50 : 50; 25 : 75, and 0 : 100 to examine in detail the effect of chain extenders on properties of segmented polyurethane elastomers with different morphologies. We found that polyurethanes with 50% SSC were hard elastomers with Shore D hardness of around 50, which is consistent with assumed co-continuous morphology. Polymers with 70% SSC displayed lower Shore A hardness of 74–79 (Shore D around 25) as a result of globular hard domains dispersed in the soft matrix. Insertion of isosorbide increased rigidity, melting point and glass transition temperature of hard segments and tensile strength of elastomers with 50% SSC. These effects were weaker or non-existent in 70% SSC series due to the short hard segments and low content of isosorbide. We also found that the thermal stability was lowered by increasing isosorbide content in both series.

elastomers↗
DOE OSTI2020

Blending Ionic and Coordinate Bonds in Hybrid Semiconductor Materials: A General Approach toward Robust and Solution-Processable Covalent/Coordinate Network Structures

Inorganic semiconductor materials are best known for their superior physical properties, as well as their structural rigidity and stability. However, the poor solubility and solution-processability of these covalently bonded network structures has long been a serious drawback that limits their use in many important applications. Here, we present a unique and general approach to synthesize robust, solution-processable, and highly luminescent hybrid materials built on periodic and infinite inorganic modules. Structure analysis confirms that all compounds are composed of one-dimensional anionic chains of copper iodide (Cu m I m+2 2- ) coordinated to cationic organic ligands via Cu-N bonds. The choice of ligands plays an important role in the coordination mode (μ 1 -MC or μ 2 -DC) and Cu-N bond strength. Greatly suppressed nonradiative decay is achieved for the μ 2 -DC structures. Record high quantum yields of 85% (λ ex = 360 nm) and 76% (λ ex = 450 nm) are obtained for an orange-emitting 1D-Cu 4 I 6 (L 6 ). Temperature dependent PL measurements suggest that both phosphorescence and thermally activated delayed fluorescence contribute to the emission of these 1D-AIO compounds, and that the extent of nonradiative decay of the μ 2 -DC structures is much less than that of the μ1 -DC structures. More significantly, all compounds are remarkably soluble in polar aprotic solvents, distinctly different from previously reported CuI based hybrid materials made of charge-neutral Cu m X m (X = Cl, Br, I), which are totally insoluble in all common solvents. Finally, the greatly enhanced solubility is a result of incorporation of ionic bonds into extended covalent/coordinate network structures, making it possible to fabricate large scale thin films by solution processes

36 MATERIALS SCIENCE↗
NASA NTRS1992

Dynamic modeling and control of multibody mechanical systems which are structurally flexible

This paper concerns the dynamic modeling and control of multibody, open-chained, structurally flexible, mechanical systems where the bodies are connected by revolute joints. The equations of motion are formulated based on a matrix form of Lagrange's equations for inertial quasi-coordinates. Each body is treated as a substructure of the system. For the purposes of simulation and control, the equations of motion are separated into two sets of equations using a perturbation approach: one to describe large rigid-body motions of the articulated system and the other to describe small linear motions of the bodies about the large motions. A biologically natural control strategy is used for vibration suppression and tracking the prescribed motion.

Quinn, R. D.↗
DOE OSTI2017

Enhancing Electrophoretic Display Lifetime: Thiol-Polybutadiene Evaporation Barrier Property Response to Network Microstructure

An evaporation barrier is required to enhance the lifetime of electrophoretic deposition (EPD) displays. As EPD functions on the basis of reversible deposition and resuspension of colloids suspended in a solvent, evaporation of the solvent ultimately leads to device failure. Incorporation of a thiol-polybutadiene elastomer into EPD displays enabled display lifetime surpassing six months in counting and catalyzed rigid display transition into a flexible package. Final flexible display transition to mass production compels an electronic-ink approach to encapsulate display suspension within an elastomer shell. Final thiol-polybutadiene photosensitive resin network microstructure was idealized to be dense, homogeneous, and expose an elastic response to deformation. Research at hand details an approach to understanding microstructural change within display elastomers. Polybutadiene-based resin properties are modified via polymer chain structure, with and without added aromatic urethane methacrylate difunctionality, and in measuring network response to variation in thiol and initiator concentration. Dynamic mechanical analysis results signify that cross-linked segments within a difunctionalized polybutadiene network were on average eight times more elastically active than that of linked segments within a non-functionalized polybutadiene network. Difunctionalized polybutadiene samples also showed a 2.5 times greater maximum elastic modulus than non-functionalized samples. Hybrid polymer composed of both polybutadiene chains encompassed TE-2000 stiffness and B-1000 elasticity for use in encapsulating display suspension. Later experiments measured kinetic and rheological response due to alteration in dithiol cross-linker chain length via real time Fourier transform infrared spectroscopy and real-time dynamic rheology. Distinct differences were discovered between dithiol resin systems, as maximum thiol conversion achieved in short and long chain length dithiols was 86% and 11%, respectively. Oscillatory real-time rheological experiments confirmed a more uniform network to better dissipate applied shear in short chain length dithiol systems, as long chain length dithiols relayed a steep internal stress build-up due to less cross-links and chain entanglements. Thorough understanding of network formation aids the production of a stronger and impermeable elastomeric barrier for preservation of EPD displays.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Assembly and property research on seven 0D–3D complexes derived from imidazole dicarboxylate and 1,2-bi(pyridin-4-yl)ethene

The hydrothermal reaction of transition metals, 1H-imidazole-4,5-dicarboxylic acid (H{sub 3}ImDC) and 1,2-bi(pyridin-4-yl)ethene (bpe) affords a series of new complexes, namely, [Mn(HImDC)(bpe)(H{sub 2}O)] (1), [M(H{sub 2}ImDC){sub 2}(H{sub 2}O){sub 2}]·(bpe) (M=Fe(2), Co(3), Zn(4), Cd(6)), [Zn{sub 3}(ImDC){sub 2}(bpe)(H{sub 2}O)]·3H{sub 2}O (5) and [Cd(H{sub 2}ImDC)(bpe)] (7), which are characterized by elemental analyses, IR, TG, XRPD and single crystal X-ray diffraction. Complex 1 exhibits a one dimensional (1D) zigzag chain with two types of irregular rings, and the 1D chains are linked to form a three dimensional (3D) supramolecular framework by the hydrogen bonding interactions (O–H∙∙∙O and O–H∙∙∙N). Complexes 2–4 and 6 are isomorphous, and they display the mononuclear structures. In these complexes, the O–H∙∙∙O and O–H∙∙∙N hydrogen bonds play an important role in sustaining the whole 3D supramolecular frameworks. Complex 5 shows a (3,3)-connected 3D framework with (10{sup 3}) topology, and the lattice water molecules as guest molecules exist in the 3D framework. Complex 7 is a wave-like two dimensional (2D) structure, in which the adjacent 1D chains point at the opposite directions. Moreover, the fluorescent properties of complexes 1–7 and the magnetic property of 1 have been investigated. The water vapor adsorption for complex 5 has been researched at 298 K. - Graphical abstract: Seven new complexes based on different structural characteristics have been hydrothermally synthesized by the mixed ligands. The fluorescent properties, the magnetic property and the water vapor adsorption have been investigated. - Highlights: • The semi-rigid ligand with C=C bonds and imidazole dicarboxylates with some advantages have been used. • A series of new complexes with different structural characteristics have been discussed in detail. • The fluorescent properties, the magnetic property and the water vapor adsorption have been investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Probing the Morphology and Mobility of Amines in Porous Silica CO 2 Sorbents by 1 H T 1 – T 2 Relaxation Correlation NMR

Molecular and oligomeric amines supported in porous oxide supports are a promising class of CO 2 sorbent materials studied for CO 2 removal from diverse streams such as flue gas and ambient air. Among the various amines investigated, low molecular weight, hyperbranched poly(ethyleneimine) (PEI), and tetraethylenepentamine (TEPA) are among the most extensively studied. While macroscopic structure–performance relationships relating the support structure, amine loading, and other factors affecting CO 2 sorption capacities and kinetics have been developed, structural and dynamic information about the organic amine phase in the porous support is less plentiful. The structure and mobility of amines impregnated in the pores of porous supports directly impact gas sorption, as the accessibility of amine sites in the pores directly relates to amine distribution in the pores and overall pore filling as well as the dynamics of the amine chains. Here, we prepare a family of mesoporous silica SBA-15 materials containing varying loadings of oligomeric (PEI) and molecular (TEPA) amines. 1 H T 1 –T 2 relaxation correlation solid-state NMR experiments are used to characterize the structural and dynamic properties of the confined amines. Both TEPA and PEI are shown to form multiple different domains in the pores, each with distinguishable dynamic properties. TEPA and PEI form more rigid layers around the silica support walls at lower organic loading fractions, characterized by lower mobilities, followed by the formation of more mobile domains less engaged in pore wall interactions at higher loadings. TEPA shows faster mobilities than PEI because of its lower molecular weight. TEPA also appears to more easily transfer between domains within the pores, leading to generally faster CO 2 uptake rates with higher sorption capacities, while PEI located closer to the pore walls remained much less mobile and is thus less engaged in CO 2 capture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Dynamics of Shape-Persistent Giant Molecules: Zimm-like Melt, Elastic Plateau, and Cooperative Glass-like

Giant molecules are a new class of soft matter having threedimensional (3D) shapes and composed of chemically linked rigid molecular nanoparticles. Structurally, a 3D cluster of molecular nanoparticles can be one giant molecule or a few giant molecules associated together via specific interactions. The dynamics of clusters that are smaller than a critical diameter (~5 nm) presents a power law relaxation exponent of 0.7 at the high frequency region corresponding to segmental dynamics. Such scaling is similar to the result of the Zimm model although those clusters are neither chain-like nor in solution. Clusters that are larger than this critical diameter and formed by the association of giant molecules exhibit an elastic plateau due to caging of individual giant molecules. Herein, we hypothesize that clusters of such a large size cannot move as a whole, even above the glass transition temperature of the sample. They thus are “cooperative glass-like”. A structural cluster of giant molecules could be abstracted as a dynamical cluster consisting of unlinked but cooperatively mobile beads. As derived in the random first-order transition theory, the cluster loses its mobility and reaches the glassy state when the diameter of the cluster is 6 times larger than the bead diameter. In our cases, we estimate that the critical diameter for these clusters is also approximately 6 times the bead diameter based on the glassy shear modulus of giant molecules. Thus, shape-persistent giant molecules may serve as a bridge between polymers and colloids and a platform to mimic cooperative rearrangements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Controllable growth of interpenetrating or random copolymer networks

Interpenetrating and random copolymer networks are vital in a number of industrial applications, including the fabrication of automotive parts, damping materials, and tissue engineering scaffolds. We develop a theoretical model for a process that enables the controlled growth of interpenetrating network (IPNs), or a random copolymer network (RCN) of specified size and mechanical properties. In this process, a primary gel “seed” is immersed into a solution containing the secondary monomer and crosslinkers. After the latter species are absorbed into the primary network, the absorbed monomers are polymerized to form the secondary polymer chains, which then can undergo further crosslinking to form an IPN, or undergo inter-chain exchange with the existing network to form a RCN. The swelling and elastic properties of the IPN and RCN networks can be tailored by modifying the monomer and crosslinker concentrations in the surrounding solution, or by tuning the enthalpic interactions between the primary polymer, secondary monomer and solvent through a proper choice of chemistry. This process can be used repeatedly to fabricate gels with a range of mechanical properties from stiff, rigid materials to soft, flexible networks, allowing the method to meet the materials requirements of a variety of applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Measurement of Three Transport Coefficients and the Thermodynamic Factor in Block Copolymer Electrolytes with Different Morphologies

The design and engineering of composite materials is one strategy to satisfy the materials needs of systems with multiple orthogonal property requirements. In the case of rechargeable batteries with lithium metal anodes, the system requires a separator with fast lithium ion transport and good mechanical strength. In this work, we focus on the system polystyrene-block-poly(ethylene oxide) (SEO) with bis(trifluoromethane)sulfonimide lithium salt (LiTFSI). Ion transport occurs in the salt-containing poly(ethylene oxide)-rich domains. Mechanical rigidity arises due to the glassy nature of polystyrene (PS). If we assume that the salt does not interact with the PS-rich domains, we can describe ion transport in the electrolyte by three transport parameters (ionic conductivity, κ, salt diffusion coefficient, D, and cation transference number, t + 0 ) and a thermodynamic factor, T f . By systematically varying the volume fraction of the conducting phase, Φ c between 0.29 and 1.0, and chain length, N between 80 and 8000, we elucidate the role of morphology on ion transport. We find that κ is the strongest function of morphology, varying by three full orders of magnitude, while D is a weaker function of morphology. To calculate t + 0 and T f , we measure the current fraction, ρ + , and the open circuit potential, U, of concentration cells. We find that ρ + and U follow universal trends as a function of salt concentration, regardless of chain length, morphology, or Φ c , allowing us to calculate t + 0 for any SEO/LiTFSI or PEO/LiTFSI mixture when κ and D are known. Finally, the framework developed in this paper enables predicting the performance of any block copolymer electrolyte in a rechargeable battery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Anomalous phonon characteristics of unconventional novel III-N superlattices

Comprehensive results of atomic vibrations are reported in the unconventional short-period zb BN/GaN superlatices (SLs) by exploiting a rigid-ion-model and taking into account both the short- and long-range Coulomb interactions. Besides anisotropic mode behavior of optical phonons, our study provided evidence of acoustic-mode anti-crossing, mini-gap formation, confinement as well as BN-like modes falling within the gap that separates optical phonon bands of the two materials. A bond-polarizability scheme is employed within the second-nearest-neighbor linear-chain model to simulate the Raman intensity profiles of BN/GaN SLs revealing major expected trends of the vibrational characteristics observed experimentally in many conventional superlattice systems while eliciting some interesting contrasts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Low-frequency Raman signature of Ag-intercalated few-layer MoS 2

Density functional theory based calculations and experimental analysis on a limited number of real samples are performed to study how the presence of silver intercalated in the van der Waals gap of few-layer MoS 2 affects the low-frequency Raman active modes of this material. Silver is found to predominantly affect the breathing-like and shear-like vibrational modes of MoS 2 . These modes correspond to quasi-rigid movements of each individual layer with a restoring force (and, in turn, frequency) that is determined by modulations in the weak interlayer interactions. Noticeable red-shifts with increasing Ag concentration are found for all low-frequency modes. This finding indicates the potential for low-frequency vibrations as useful gauges for practical determination of silver concentration using low-frequency Raman spectroscopy. Finally, this work also describes a semi-classical linear chain model that allows to extrapolate results to a large number of layers. Further, first-principles calculations show how Raman spectroscopy can be used to characterize the quality of the two-dimensional interface between MoS 2 and a silver substrate.

36 MATERIALS SCIENCE↗
NASA NTRS1989

Dynamic modeling of multi-jointed mechanical systems for space applications

The dynamic formulation, modeling and motion simulation of multijointed open-chained mechanical systems as applied to space-based robotic systems are presented. Equations of motion are formulated in a unique manner based on a form of Lagrange's equations for quasi-coordinates (Boltzmann-Hamel equations). In order that kinematic joint constraints can be satisfied for the situation where some joints have less than three degrees of freedom, the equations are transformed into forms in terms of relative angular velocities and Euler angles. Rigid multibody examples are presented which show that the method can provide a dynamic model of systems of varying complexity.

Quinn, R. D.↗