Inversion Motion Research Articles

The effect of microsolvation on the structure, nuclear quadrupole coupling, and internal rotation: The methyl carbamate⋯(H2O)1-3 complexes.

Microsolvation of the carbamate moiety delivers precise information on complexation effects on the N-C=O backbone and is of relevance to the peptide bond functionality. In this context, the mono-, di-, and trihydrated complexes of methyl carbamate have been studied in molecular expansion by high-resolution microwave spectroscopy, using chirped-pulse and Fabry-Perot resonator Fourier transform microwave instruments covering the frequency range from 2 to 18GHz. From the rotational constants of the parent and the 18Ow substituted monoisotopologues, accurate values have been derived for the geometries of the hydrogen bond interactions. The nuclear quadrupole coupling constant χcc of the nitrogen nucleus provides a direct measure of complexation changes and decreases with the degree of hydration, whereas the hindered internal rotation barrier increases slightly with microsolvation. Both tendencies could have a common origin in the π-cooperative inductive effects as the microsolvation series progresses. All transitions are split by the internal rotation of the methyl top and the nuclear quadrupole coupling, and in the largest cluster, they are additionally split by an inversion motion.

The tunneling splittings of the ground state and some excited vibrational states for the inversion motion in H3C− anion and H3Si[rad] radical

Splitting of the ground state and some excited symmetric bending vibrational states due to inversion tunneling in the H3C− anion and H3Si radical is analyzed by numerically solving the vibrational Schrödinger equation of restricted (2D) dimensionality. We used the following two vibrational coordinates for the H3X structure (X = C, Si): the distance of the X atom from the plane of a regular triangle formed by three hydrogen atoms (1) and a symmetry coordinate composed of three distances between chemically non-bonded hydrogen atoms (2). The kinetic energy operator in this case takes the simplest form. The 2D potential energy surface (PES) in the given coordinates was calculated for H3C− at the CCSD(T)/aug-cc-pVTZ, CCSD(T)/aug-cc-pVQZ, CCSD(T)/aug-cc-pV5Z, CCSD(T)/CBS(TQ5), CCSD(T)/d-aug-cc-pVTZ, CCSD(T)/t-aug-cc-pVTZ, and CCSD(T)/q-aug-cc-pVTZ levels of theory, based on recommendations from recently published work [M.C. Bowman, B. Zhang, W.J. Morgan, H.F. Schaefer III, Mol.Phys., 117 (2019) 1069–1077]. The same 2D PES for the H3Si radical was calculated at the CCSD(T)/aug-cc-pVDZ CCSD(T)/aug-cc-pVTZ, CCSD(T)/aug-cc-pVQZ, and CCSD(T)/CBS(D,T,Q) as well as at the CCSD(T)/d-aug-cc-pVTZ, CCSD(T)/un-aug-cc-pVTZ, CCSD(T)/un-aug-cc-pVQZ levels of theory. The tunneling splittings for the D3C− anion and D3Si radical were calculated as well. The results of calculations demonstrate good agreement with available experimental data on umbrella vibration frequencies and inversion splittings for the title molecules.

The Theory of Observation —The Propagation of Wave and the Apparent Velocity of Object Motion

This paper deepens and develops the Galileo's principle of relativity of motion, and summarizes the Laws of relativity and superposition of motion or wave (light). The essence of light is analyzed. The characteristics of various waves (sound waves, water waves, electromagnetic waves or light waves, etc.) and their relationship with the motion velocity of objects (wave sources) are analyzed. Wave acts as a messenger for people to know things, and are used as a signal to receive, perceive and know things far away. The observation of an object is a perspective effect, not represent the real motion of the object. The real motion of the wave source can exceed the velocity of wave, and the observed velocity of the object moving at the super wave (light) velocity can be much lower than the wave (light) velocity in some visual angles, while the observed speed of the object moving below the wave (light) speed will be much higher than the wave velocity in some visual angles. Objects moving at super wave (light) speed will produce special phenomena when observed from some angles. Super wave velocity (including superlight velocity) of real motion of objects and inversion of observation time sequence are common phenomena. Finally, the superluminal phenomenon of quasars and the technical application prospect of observation angle effect are discussed. This theory is widely used in remote sensing, astronomical observation, microscopic detection, satellite navigation, weather forecast, microscopic observation, medical detection, dynamic identification and so on. All of them are calibrated by the formula of observation angle effect derived in this paper, which can improve the accuracy of observation results. Especially in the observation technology of objects moving in high-speed such as high-energy collider, cosmic ray, cosmic radiation and nuclear reaction, the application effects are more remarkable, more real and accurate.

Optical pulling force on a uniaxial anisotropic sphere by a high-order Bessel (vortex) beam.

Based on the generalized Lorenz-Mie theory (GLMT) and the scattering theory of uniaxial spheres, a theoretical approach is introduced to study the axial radiation force (AOF) exerted on a uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel (vortex) beams (HOBVBs). Applying Maxwell's stress tensor, an analytical expression of the AOF on a uniaxial anisotropic sphere by the on-axis HOBVB is derived. The correctness of the theoretical and numerical results is verified by comparing the AOF on an isotropic sphere by a zero-order Bessel beam (ZOBB) with those results by a plane wave, Gaussian beam, and ZOBB. The focus of this study is to determine some conditions of the tractor beam, so as to realize the inverse motion of an anisotropic sphere through a Bessel beam. The range of optical pulling force (OPF) that can pull particles in reverse motion generated by zero-order and first-order Bessel beams is extended from isotropic spherical particles to anisotropic spherical particles. The effects of the sphere radius, conical angle, and especially electromagnetic anisotropy parameters on the OPF in water or a vacuum environment are discussed in detail. Moreover, the OPF exerted on the uniaxial anisotropic sphere illuminated by a HOBVB with l=2, 3, and 4 is also exhibited. It indicates that the HOBVB with l=2, 3 is also a good tractor beam for the uniaxial anisotropic sphere. The OPF generated by Bessel beams on uniaxial anisotropic spherical particles is not only affected by the conical angle and radius but is also significantly influenced by anisotropic parameters and topological charges. These properties of the OPF are different from those on an isotropic sphere. The theory and results are hopeful to provide an effective theoretical basis for the study of optical micromanipulation of biological and anisotropic complex particles by optical tractor (vortex) beams.

Stress-constrained topology optimization for multi-material thermo-hyperelastic compliant mechanisms based on inverse motion

A stress-constrained topology optimization design for the multi-material thermo-hyperelastic compliant mechanism is investigated in this article, using inverse motion analysis. Through the inverse motion analysis approach, precise control over the geometry of the deformed structure is achieved. A topology optimization model is established for the multi-material thermal hyperelastic compliant mechanism, incorporating constraints on volume, cost and stress, while maximizing displacement as the objective function. Filtering is implemented using an improved partial differential equation, and the stress problem is addressed using the ϵ-relaxation method and the p-norm aggregation function. The sensitivity analysis of the displacement objective function and the stress constraint is conducted. Considering the multi-material thermally actuated actuator as an example, the influence of the stress constraint on the topology optimization design is studied. The results indicate that inverse motion analysis allows for effective control of the output end position of the deformed compliant mechanism.

Modeling and Control of Two Degree of Freedom Bionic Foot

Many people are affected by conditions like stroke, spinal cord diseases, cerebral palsy, and nerve injuries, leading to impaired leg function. Bionic foot assist in maintaining stability and posture, offering vital aid to those with mobility issues for improved quality of life and rehabilitation. Consequently, the use of bionic foot has increased. Bionic foot comprising electrical and mechanical components, provide comfort and support for individuals with mobility problems. An encouraging solution is to introduce bionic foot robots to help patients having mobility problems during their recovery journey. Designed to mimic the human skeletal system, these robots offer valuable assistance in restoring the natural gait cycle of patients having mobility problems. The proposed approach introduces a bionic foot designed to support movement of human ankle joint, marking a significant advancement in rehabilitation technology. Although human ankle joint actually exhibits 3 DOF motion, we consider 2 DOF motion of human ankle joint i.e., plantarflexion and dorsiflexion and, inversion and eversion as they are dominant during normal motion of human body. We designed two systems to control the motion of human ankle joint. Firstly, we have used two actuators, one for each degree of freedom to control the motion of ankle joint. Secondly, we have used an actuator to control the plantarflexion and dorsiflexion motion and Spring-Damper system to control the inversion and eversion motion of the human ankle joint. For both systems, we derive the mathematical model and then we design the PD controller using MATLAB/Simulink. For plantarflexion and dorsiflexion motion, we give standard pattern of human ankle gait as input and for inversion and eversion motion, we provide pulsating signal as our input for both the systems. After implementation, the response of the human ankle motion was precise, accurate and smooth. The torque applied by the actuators was also in the acceptable range.

Structure and dynamics of 3'-aminoacetophenone and 4'-aminoacetophenone from rotational spectroscopy.

The rotational spectra of 4'-aminoacetophenone, and those of two conformers (Z and E arrangement of the CO and NH2 groups) of 3'-aminoacetophenone and their 13C and 15N isotopologues were investigated both in the microwave (2-8 GHz) and millimetre (59.6-74.4 GHz) frequency regions using chirped pulse Fourier transform and free-jet absorption techniques, respectively. The spectra consist of μa and μb type lines that show a hyperfine structure due to both the nuclear quadrupole coupling of the 14N nucleus and the methyl internal rotation. Relative intensity measurements show that the Z form in 3'-aminoacetophenone is favoured with respect to E and the measured energy difference upper limit is about 5.5(1) kJ mol-1. Barriers to methyl internal rotation are V3 = 7.04(2) and 6.530(6) kJ mol-1 for 3'(Z)- and 4'-aminoacetophenone, respectively. Flexible model analyses of the amino inversion motion based on ab initio potential energy paths, suggest that the corresponding vibrational splitting increases up to 78% from aniline to 3'(E)-, 3'(Z), and 4-aminoacetophenone. However, due to supersonic expansion cooling, no splitting related to amine inversion is observed.

Selective synthesis of tightly- and loosely-twisted metallomacrocycle isomers towards precise control of helicity inversion motion

Molecular twist is a characteristic component of molecular machines. Selectively synthesising isomers with different modes of twisting and controlling their motion such as helicity inversion is an essential challenge for achieving more advanced molecular systems. Here we report a strategy to control the inversion kinetics: the kinetically selective synthesis of tightly- and loosely-twisted isomers of a trinuclear PdII-macrocycle and their markedly different molecular behaviours. The loosely-twisted isomers smoothly invert between (P)- and (M)-helicity at a rate of 3.31 s–1, while the helicity inversion of the tightly-twisted isomers is undetectable but rather relaxes to the loosely-twisted isomers. This critical difference between these two isomers is explained by the presence or absence of an absolute configuration inversion of the nitrogen atoms of the macrocyclic amine ligand. Strategies to control the helicity inversion and structural loosening motions by the mode of twisting offer future possibilities for the design of molecular machines.

Developing inverse motion planning technique for autonomous vehicles using integral nonlinear constraints

The study considers issues of elaborating and validating a technique of autonomous vehicle motion planning based on sequential trajectory and speed optimization. This method includes components such as representing sought-for functions by finite elements (FE), vehicle kinematic model, sequential quadratic programming for nonlinear constrained optimization, and Gaussian N-point quadrature integration. The primary novelty consists of using the inverse approach for obtaining vehicle trajectory and speed. The curvature and speed are represented by integrated polynomials to reduce the number of unknowns. For this, piecewise functions with two and three degrees of freedom (DOF) are implemented through FE nodal parameters. The technique ensures higher differentiability compared to the needed in the geometric and kinematic equations. Thus, the generated reference curves are characterized by simple and unambiguous forms. The latter fits best the control accuracy and efficiency during the motion tracking phase. Another advantage is replacing the nodal linear equality constraints with integral nonlinear ones. This ensures the non-violation of boundary limits within each FE and not only in nodes. The optimization technique implies that the spatial and time variables must be found separately and staged. The trajectory search is accomplished in the restricted allowable zone composed by superposing an area inside the external and internal boundaries, based on keeping safe distances, excluding areas for moving obstacles. Thus, this study compares two models that use two and three nodal DOF on optimization quality, stability, and rapidity in real-time applications. The simulation example shows numerous graph results of geometric and kinematic parameters with smoothed curves up to the highest derivatives. Finally, the conclusions are made on the efficiency and quality of prognosis, outlining the similarities and differences between the two applied models.

Assistance in Teleoperation of Redundant Robots through Predictive Joint Maneuvering

In teleoperation of redundant robotic manipulators, translating an operator’s end effector motion command to joint space can be a tool for maintaining feasible and precise robot motion. Through optimizing redundancy resolution, the control system can ensure the end effector maintains maneuverability by avoiding joint limits and kinematic singularities. In autonomous motion planning, this optimization can be done over an entire trajectory to improve performance over local optimization. However, teleoperation involves a human-in-the-loop who determines the trajectory to be executed through a dynamic sequence of motion commands. We present two systems, PrediKCT and PrediKCS, for utilizing a predictive model of operator commands in order to accomplish this redundancy resolution in a manner that considers future expected motion during teleoperation. Using a probabilistic model of operator commands allows optimization over an expected trajectory of future motion rather than consideration of local motion alone. Evaluation through a user study demonstrates improved control outcomes from this predictive redundancy resolution over minimum joint velocity solutions and inverse kinematics-based motion controllers.

Evaluation of Chronic Lateral Ankle Instability with a Sprain Stimulator: A Controlled Study in Physically Active Subjects

Category: Ankle; Basic Sciences/Biologics Introduction/Purpose: Chronic Lateral Ankle Instability (CLAI) represents a significant socioeconomic burden. Paradoxically, its management has changed little over the years, notably because research is divided into functional and mechanical instability, whereas CLAI encompasses both. Sprain simulators can encompass both functional and mechanical instability by assessing the maximal ankle inversion velocity (MIV) during a simulated inversion trauma. We built a sprain simulator capable of producing a sudden ankle inversion motion during walking. We aimed to differentiate subjects with chronic lateral ankle instability (CLAI) from controls and quantify functional CLAI as well as impairments in activities of daily living and sports using a sprain simulator. Methods: Forty-five physically active subjects were included and assigned to a CLAI group, a control group, or excluded according to the International Ankle Consortium selection criteria. Each subject walked on a treadmill with instability boots after completing the Identification of Functional Ankle Instability (IdFAI) and the Foot Ankle Ability Measurement (FAAM) questionnaires. A simulated trauma was unexpectedly triggered by the observer. Maximal inversion velocities (MIV) were measured at this very moment using inertial moment units. We normalized these values by the average MIV of the 5 stance phases of the same foot preceding the simulated trauma (Ratio MIV). Normality of data were assessed with the Shapiro-Wilk test. The groups were compared using Student T test for normal and Mann-Whitney U test for nonnormal variables. Multivariate linear regressions were performed to assess the relation between, the IdFAI, the FAAM Activities of Daily Living Subscale, the FAAM Sports Subscale and the explanatory variables. Results: Twenty-six ankles were excluded, 32 composed the CLAI group and 32 the control group. Mean MIV were 213.5+/-54.7°/s and 177+/-64.2°/s (p=0.02), and mean Ratio MIV were 1.22+/-0.13 and 1.08+/-0.08 (p < 0.001) in the CLAI and Control groups respectively. In multivariate analysis, Ratio MIV was associated with higher values of IdFAI (β=42.8 [12.9;72.8],p=0.006), lower values of FAAM Activities of Daily Living Subscale (β=-14.1 [-27.8;-0.5],p=0.04) and lower values of FAAM Sports Subscale (β=-7.2 [-13.7;- 0.6],p=0.03) whereas MIV was not. Conclusion: Inversion velocities caused by a sprain simulator clearly differentiated CLAI from controls in our study. Ratio MIV showed good ability to quantify functional CLAI as well as impairments in activities of daily living and sports. This tool should be used in future studies in an attempt to provide a complete picture of CLAI encompassing its functional and mechanical aspects which may lead to improved LAS and CLAI management.

Hamiltonian Neural Network 6-DoF Rigid-Body Dynamic Modeling Based on Energy Variation Estimation

This study introduces a novel deep modeling approach that utilizes Hamiltonian neural networks to address the challenges of modeling the six degrees of freedom rigid-body dynamics induced by control inputs in various domains such as aerospace, robotics, and automotive engineering. The proposed method is based on the principles of Hamiltonian dynamics and employs an inductive bias in the form of a constructed bias for both conservative and varying energies, effectively tackling the modeling issues arising from time-varying energy in controlled rigid-body dynamics. This constructed bias captures the information regarding the changes in the rigid body’s energy. The presented method not only achieves highly accurate modeling but also preserves the inherent bidirectional time-sliding inference in Hamiltonian-based modeling approaches. Experimental results demonstrate that our method outperforms existing techniques in the time-varying six degrees of freedom dynamic modeling of aircraft and missile guidance, enabling high-precision modeling and feedback correction. The findings of our research hold significant potential for the kinematic modeling of time-varying energy systems, parallel system state prediction and control, inverse motion inference, and autonomous decision-making in military applications.

Lie Algebra Contributions to Instantaneous Plane Kinematics

Roth and Bottema obtain the instantaneous properties of a plane motion and its inverse motion by the instantaneous invariants depending on a canonical frame which was introduced in Veldkamp's dissertation(1963). We obtain the instantaneous invariants depending on the same frame by using Lie algebra of the plane motion.

Unexplored Isomerization Pathways of Azobis(benzo-15-crown-5): Computational Studies on a Butterfly Crown Ether.

Computational studies on trans → cis and cis → trans isomerizations of photoresponsive azobis(benzo-15-crown-5) have been reported in this work. The photoexcited ππ* state (S2) of the trans isomer relaxes through the planar S2 minimum and the planar S2/S1 conical intersection (both situated around 9 kcal/mol below the vertically excited S2 state) arising along the N═N stretching coordinate. The nπ* state (S1) of this isomer has both planar and rotated (clockwise and anticlockwise) minima, which may lead to a torsional conical intersection (S0/S1) geometry having a <CNNC dihedral angle value close to 90°. This rotational isomerization path is found to have an energy barrier. It has been noticed that an N-N-out-of-plane motion coupled with the torsion can bring down the barrier and may facilitate the isomerization process. On the other hand, the vertically excited S1 state of the cis-isomer undergoes a barrierless path to reach a torsional conical intersection (S0/S1) geometry (<CNNC = 88°), responsible for the trans-isomer formation. The cis-S2/S1 CI (conical intersection) torsional geometry (<CNNC = 45°) is situated around 16 kcal/mol above the vertically excited ππ* state of the cis-isomer and not reachable on S2 photoexcitation. The two optimized torsional S2 minima of this system are close to the S1 surface and seem to be involved in the S2-S1 internal conversion. A less efficient concerted inversion photoisomerization path through a linear geometry has also been identified. The thermal cis → trans isomerization has been found to undergo an inversion motion, which forms a less stable trans isomer. Possible differences between the isomerization channels of this azobis(benzo-15-crown-5) and the unsubstituted azobenzene system have also been highlighted in the work.

Laboratory and astronomical discovery of the cyanovinyl radical H2CCCN

We report the first laboratory and interstellar detection of the α-cyano vinyl radical (H2CCCN). This species was produced in the laboratory by an electric discharge of a gas mixture of vinyl cyanide, CH2CHCN, and Ne. Its rotational spectrum was characterized using a Balle-Flygare narrowband-type Fourier-transform microwave spectrometer operating in the frequency region of 8–40 GHz. The observed spectrum shows a complex structure due to tunneling splittings between two torsional sublevels of the ground vibronic state, 0+ and 0−, derived from a large-amplitude inversion motion. In addition, the presence of two equivalent hydrogen nuclei makes it necessary to discern between ortho- and para-H2CCCN. A least-squares analysis reproduces the observed transition frequencies with a standard deviation of ca. 3 kHz. Using the laboratory predictions, this radical was detected in the cold dark cloud TMC-1 using the Yebes 40 m telescope and the QUIJOTE1 line survey. The 40, 4-30, 3 and 50, 5-40, 4 rotational transitions, composed of several hyperfine components, were observed in the 31.0–50.4 GHz range. Adopting a rotational temperature of 6 K, we derived a column density of (1.4±0.2)×1011 cm−2 and (1.1±0.2)×1011 cm−2 for ortho-H2CCCN and para-H2CCCN, respectively. The reaction of C + CH3CN emerges as the most likely route to H2CCCN in TMC-1, and possibly that of N + CH2CCH as well.

High-Speed Maneuvering Target Inverse Synthetic Aperture Radar Imaging and Motion Parameter Estimation Based on Fast Spare Bayesian Learning and Minimum Entropy

High-speed maneuvering target inverse synthetic aperture radar (ISAR) imaging is always a hot topic in signal processing. High-speed maneuvering targets often have high-order maneuvering characteristics, such as translational and rotational characteristics, which destroy the signal structure of stationary targets and make basic imaging processing methods such as range-Doppler (RD) algorithm no longer suitable. In this paper, a high-resolution imaging method for high-speed maneuvering targets is proposed, which uses the fast sparse Bayesian learning (SBL) algorithm and the minimum entropy algorithm for ISAR high-resolution imaging and motion parameter estimation, respectively. Because SBL makes full use of the characteristics of the target and the environment, it can obtain an ISAR high-resolution image of the maneuvering target. However, the high computational complexity caused by matrix inversion and some matrix operations in SBL iteration limit the practical application of SBL in ISAR imaging. In view of the special structure of the matrix required to be inverted, we propose a fast SBL algorithm, which uses a new decomposition method to obtain the decomposition formula of the inverse matrix. Based on the decomposition factors, the multiplication operation involving the inverse matrix can be quickly calculated using fast Fourier transform (FFT), which greatly improves the computational efficiency. Image entropy represents the sharpness and focusing degree of an image, and so the minimum entropy algorithm can estimate the motion parameters of maneuvering targets more accurately. We combine the minimum entropy algorithm with the fast SBL algorithm to realize phase error correction and high-resolution imaging, which has better noise sensitivity and can obtain the best focusing degree image. Finally, simulation results prove the effectiveness of this algorithm.

Hybrid musculoskeletal model-based 3D asymmetric lifting prediction and comparison with symmetric lifting.

In this study, a 3D asymmetric lifting motion is predicted by using a hybrid predictive model to prevent potential musculoskeletal lower back injuries for asymmetric lifting tasks. The hybrid model has two modules: a skeletal module and an OpenSim musculoskeletal module. The skeletal module consists of a dynamic joint strength based 40 degrees of freedom spatial skeletal model. The skeletal module can predict the lifting motion, ground reaction forces (GRFs), and center of pressure (COP) trajectory using an inverse dynamics-based motion optimization method. The musculoskeletal module consists of a 324-muscle-actuated full-body lumbar spine model. Based on the predicted kinematics, GRFs and COP data from the skeletal module, the musculoskeletal module estimates muscle activations using static optimization and joint reaction forces through the joint reaction analysis tool in OpenSim. The predicted asymmetric motion and GRFs are validated with experimental data. Muscle activation results between the simulated and experimental EMG are also compared to validate the model. Finally, the shear and compression spine loads are compared to NIOSH recommended limits. The differences between asymmetric and symmetric liftings are also compared.

A convenient set of vibrational coordinates for 2D calculation of the tunneling splittings of the ground state and some excited vibrational states for the inversion motion in H3O+, H3O−, and H3O[rad

Splitting of the ground state and some excited symmetric bending vibrational states due to inversion tunneling of the oxygen atom in the H3O+, H3O− ions and in the H3O radical are analyzed by numerically solving the vibrational Schrödinger equation of restricted (2D) dimensionality. As two vibrational coordinates, we used 1) the distance of the oxygen atom from the plane of a regular triangle formed by three hydrogen atoms and 2) a symmetry coordinate composed of three distances between chemically non-bonded hydrogen atoms. The kinetic energy operator in this case takes the simplest form. The 2D potential energy surface (PES) in the given coordinates was calculated for H3O+ at the CCSD(T)/aug-cc-pVTZ and CCSD(T)-F12/cc-pVTZ-F12 levels of theory. The same 2D PES for the H3O− anion and H3O radical were calculated at the CCSD(T)/aug-cc-pVQZ, CCSD(T)/d-aug-cc-pVQZ and UCCSD(T)/aug-cc-pVQZ, UCCSD(T)/d-aug-cc-pVQZ levels of theory, respectively. The tunneling splittings were calculated for the cations H316O+, D316O+, T316O+, H318O+, D318O+, T318O+. The tunneling splittings for the H3O−, D3O−, T3O− anions and H3O, D3O, T3O radicals were calculated for the first time. The results of calculations demonstrate good agreement with experimental values of the tunneling splittings in the ground state and in some excited vibrational states of the H316O+ and D316O+ cations.

Inverse motion planning method for overhead crane systems with state constraints

AbstractThe trajectory planning problem with state constraints of overhead crane systems is considered in this paper. A new method, that is, an inverse motion planning method, is proposed. On this basis, a new trajectory planner is designed. The payload swing angle trajectory is designed first, and then by substituting it into the dynamic equations, the trolley trajectory is derived. For any transportation tasks, the adjustable parameter of the planner is computed by solving the state constraints such that the system states; that is, the trolley acceleration, trolley speed, and payload swing angle will not exceed their predefined constraints. Several experimental tests are conducted to verify the swing elimination performance of the proposed method.

Ammonia quantum tunneling in cold rare-gas He and Ar clusters and factorial design approach for methodology evaluation.

Quantum tunneling of the ammonia inversion motion and energy level splittings in He and Ar clusters were investigated. It was found that the double well potential (DWP) in He clusters is symmetrical and that the first layer of He atoms is able to model the system. The calculated tunneling splitting was in good agreement with the experimental, 36.4 and 24.6 cm[Formula: see text] respectively. For NH[Formula: see text] in Ar clusters, the DWP becomes slightly asymmetric, which is enough to decrease the resonance and make the symmetric DWP unable to model the system. An asymmetric potential was used and the result was in excellent agreement with the experimental splitting, of 9.0 and 10.6 cm[Formula: see text] respectively. Non-covalent interactions revealed that the asymmetry is caused by dissimilar interactions in each minimum of the double well potential. The effects of different methodologies were analyzed via a design of experiments approach. For the gas-phase NH[Formula: see text] molecule, only diffuse functions were statistically significant while for the NH[Formula: see text] embedded in He cluster both the MP2 method and polarization functions were significant. This tendency suggests higher order polarization functions may be essential to generate accurate barrier heights.