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Abstract This research presents a novel design of a four-bar mechanism featuring a variable stiffness link (VSL) as the output component, aimed at enabling diverse end-effector trajectories without modifying the link length or moment input. By employing both single-beam and multi-section beam configurations within a large deflection model, the study investigates the effect of varying link stiffness under constant load and geometric conditions on the mechanism’s trajectory outcomes. The proposed design was validated through both numerical modeling and experimental testing of a built prototype. The findings confirm the prototype’s alignment with theoretical predictions, highlighting the VSL’s key role in significantly enhancing the adaptability and application range of four-bar mechanisms. This advancement circumvents the traditional constraints of fixed-trajectory mechanisms, proposing a versatile, efficient, and cost-effective solution for complex motion applications in compliant mechanism design. 

Context. This is the second paper of a series aiming to determine the birth rates of supernovae (SNe) in the local Universe. Aims. We aimed to estimate the SN rates in the local Universe and fit the delay-time distribution of type Ia SNe (SNe Ia) to put constraints on their progenitor scenarios. Methods. We performed a Monte Carlo simulation to estimate volumetric rates using the nearby SN sample introduced in Paper I. The rate evolution of core-collapse (CC) SNe closely follows the evolution of the cosmic star formation history, while the rate evolution of SNe Ia involves the convolution of the cosmic star formation history and a two-component delay-time distribution including a power law and a Gaussian component. Results. The volumetric rates of type Ia, Ibc, and II SNe are derived as 0.325 ± 0.040_−0.010^+0.016, 0.160 ± 0.028_−0.014^+0.044, and 0.528 ± 0.051_−0.013^+0.162(in units of 10⁻⁴yr⁻¹Mpc⁻³h₇₀³), respectively. The rate of CCSNe (0.688 ± 0.078_−0.027^+0.0206) is consistent with previous estimates, which trace the star formation history. Conversely, the newly derived local SN Ia rate is larger than existing results given at redshifts 0.01 < z < 0.1, favoring an increased rate from the Universe at z ∼ 0.1 to the local Universe at z < 0.01. A two-component model effectively reproduces the rate variation, with the power law component accounting for the rate evolution at larger redshifts and the Gaussian component with a delay time of 12.63 ± 0.38 Gyr accounting for the local rate evolution. This delayed component, with its exceptionally long delay time, suggests that the progenitors of these SNe Ia were formed around 1 Gyr after the birth of the Universe, which could only be explained by a double-degenerate progenitor scenario. Comparison with the Palomar Transient Factory (PTF) sample of SNe Ia at z = 0.073 and the morphology of their host galaxies, reveals that the increased SN Ia rate at z < 0.01 is primarily due to the SNe Ia of massive E and S0 galaxies with old stellar populations. Based on the above results, we estimate the Galactic SN rate as 3.08 ± 1.29 per century. 

Context. This is the first paper in a series aiming to determine the fractions and birth rates of various types of supernovae (SNe) in the local Universe. Aims. In this paper, we aim to construct a complete sample of SNe in the nearby Universe and provide more precise measurements of subtype fractions. Methods. We carefully selected our SN sample at a distance of less than 40 Mpc mainly from wide-field surveys conducted over the years from 2016 to 2023. Results. The sample contains a total of 211 SNe, including 109 SNe II, 69 SNe Ia, and 33 SNe Ibc. With the aid of sufficient spectra, we obtained relatively accurate subtype classifications for all SNe in this sample. After corrections for the Malmquist bias, this volumelimited sample yielded fractions of SNe Ia, SNe Ibc, and SNe II of 30.4_−11.5^+3.7%, 16.3_−7.4^+3.7%, and 53.3_−18.7^+9.5%, respectively. In the SN Ia sample, the fraction of the 91T-like subtype becomes relatively low (~5.4%), while that of the 02cx-like subtype shows a moderate increase (~6.8%). In the SN Ibc sample, we find significant fractions of broadlined SNe Ic (~18.0%) and SNe Ibn (~8.8%). The fraction of the 87A-like subtype was determined to be ~2.3%, indicating rare explosions from blue supergiant stars. We find that SNe Ia show a double peak number distribution in S0- and Sc-type host galaxies, which may serve as straightforward evidence for the presence of “prompt” and “delayed” progenitor components that give rise to SN Ia explosions. Several subtypes of SNe such as 02cx-like SNe Ia, broadlined SNe Ic, and SNe IIn (and perhaps SNe Ibn) are found to occur preferentially in less massive spiral galaxies (i.e., with stellar mass <0.5×10¹⁰M_ʘ), thus favoring their associations with young stellar progenitors. Moreover, the 02cx-like subtype shows a trend of exploding in the outer skirt of their hosts, which is suggestive of metal-poor progenitors. 

Abstract Variable stiffness manipulators balance the trade-off between manipulation performance needing high stiffness and safe human–robot interaction desiring low stiffness. Variable stiffness links enable this flexible manipulation function during human–robot interaction. In this paper, we propose a novel variable stiffness link based on discrete variable stiffness units (DSUs). A DSU is a parallel guided beam that can adjust stiffness discretely by changing the cross-sectional area properties of the hollow beam segments. The variable stiffness link (Tri-DSU) consists of three tandem DSUs to achieve eight stiffness modes and a stiffness ratio of 31. To optimize the design, stiffness analysis of the DSU and Tri-DSU under various configurations and forces was performed by a derived linear analytical model which applies to small/intermediate deflections. The model is derived using the approach of serially connected beams and superposition combinations. 3D-Printed prototypes were built to verify the feature and performance of the Tri-DSU in comparison with the finite element analysis and analytical model results. It’s demonstrated that our model can accurately predict the stiffnesses of the DSU and Tri-DSU within a certain range of parameters. Impact tests were also conducted to validate the performance of the Tri-DSU. The developed method and analytical model are extendable to multiple DSUs with parameter configurations to achieve modularization and customization, and also provide a tool for the design of reconfigurable collaborative robot (cobot) manipulators. 

Abstract This paper presents the development of a novel Actuation-Coordinated Mobile Parallel Robot (ACMPR), with a focus on studying the kinematics of the mobile parallel robot with three limbs (3-mPRS) comprising mobile prismatic joint-revolute joint-spherical joint. The objective of this research is to explore the feasibility and potential of utilizing omnidirectional mobile robots to construct a parallel mechanism with a mobile platform. To this end, a prototype of the 3-mPRS is built, and several experiments are conducted to identify the proposed kinematic parameters. The system identification of the 3-mPRS mobile parallel mechanism is conducted by analyzing the actuation inputs from the three mobile base robots. To track the motion of the robot, external devices such as the Vicon Camera are employed, and the data is fed through ROS. The collected data is processed based on the geometric properties, CAD design, and established kinematic equations in MATLAB, and the results are analyzed to evaluate the accuracy and effectiveness of the proposed calibration methods. The experiment results fall within the error range of the proposed calibration methods, indicating the successful identification of the system parameters. The differences between the measured values and the calculated values are further utilized to calibrate the 3-mPRS to better suit the experiment environment. 

Abstract Variable stiffness manipulators balance the trade-off between manipulation performance needing high stiffness and safe human-robot interaction desiring low stiffness. Variable stiffness compliant links provide a solution to enable this flexible manipulation function in human-robot co-working scenarios. In this paper, we propose a novel variable stiffness link based on discrete variable stiffness units (DSUs). A DSU is a parallel guided beam that can adjust stiffness discretely by changing the cross-sectional area properties of the hollow beam segments. The variable stiffness link (named Tri-DSU) consists of three tandem DSUs to achieve eight stiffness modes and a maximum stiffness change ratio of 31. To optimize the design, stiffness analysis of the DSU and Tri-DSU under various configurations and forces was performed by a derived theoretical model compared with finite element analysis (FEA). The analytical stiffness model is derived using the approach of serially connected beams and superposition combinations. It works not only for thin-walled flexure beams but also for general thick beam models. 3-D printed prototypes were built to verify the feature and performance of the Tri-DSU in comparison with the FEA and analytical model results. It’s demonstrated that our analytical model can accurately predict the stiffnesses of the DSU and Tri-DSU within a certain range of parameters. The developed variable stiffness link method and analytical model are extendable to multiple DSUs with different sizes and parameter configurations to achieve modularization and customization. The advantages of the stiffness change mechanism are rapid actuation, simple structure, and compact layout. These methods and results provide a new conceptual and theoretical basis for the development of new reconfigurable cobot manipulators, variable stiffness structures, and compliant mechanisms. 

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang’s breakthrough quantum-inspired algorithm for recommendation systems [STOC’19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén et al. [STOC’19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all prior results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: ℓ²-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.