The second smallest eigenvalue of the Laplacian matrix, known as algebraic connectivity, determines many network properties. This paper investigates the optimal design of interconnections that maximizes algebraic connectivity in multilayer networks. We identify an upper bound for maximum algebraic connectivity for total weight below a threshold, independent of interconnections pattern, and only attainable with a particular regularity condition. For efficient numerical approaches in regions of no analytical solution, we cast the problem into a convex framework and an equivalent graph embedding problem associated with the optimum diffusion phases in the multilayer. Allowing more general settings for interconnections entails regions of multiple transitions, giving more diverse diffusion phases than the more studied one-toone interconnection case. When there is no restriction on the interconnection pattern, we derive several analytical results characterizing the optimal weights using individual Fiedler vectors. We use the ratio of algebraic connectivity and layer sizes to explain the results. Finally, we study the placement of a limited number of interlinks heuristically, guided by each layer’s Fiedler vector components.

This study presents a novel 4-DOF two-limb gripper mechanism with a simple design that offers high adaptability for different objects. The mechanism integrates a three-finger end effector and employs a 2-DOF driving system in both serial kinematic chains mounted on the base, addressing performance problems caused by moving actuators. First, the architecture of the gripper mechanism is described, and its mobility is verified. Next, the inverse and forward kinematic problems are solved, and the Jacobian matrix is derived to analyze the singularity conditions. The inverse and forward singularity surfaces are plotted. The workspace is investigated using a search method, and two indices, manipulability and dexterity, are studied. The proposed manipulator’s parameters are optimized for improved dexterity. The novel gripper mechanism has high potential for grasping different types of parts within a large workspace, making it a valuable addition to the field of robotics.

The performance of hypersonic vehicles in the take-off stage considerably influences their capability of accomplishing the flight tasks. This study is aimed at enhancing the take-off performance of a cruise aircraft using the improved chimp optimisation algorithm. The proposed algorithm, which uses the Sobol sequence for initial population generation and a function of the weight factors, can effectively overcome the problems of premature convergence and low accuracy of the original algorithm. In particular, the Sobol sequence aims to obtain a better fitness value in the first iteration, and the weight factor aims to accelerate the convergence speed and avoid the local optimal solution. The take-off mass model of the hypersonic vehicle is constructed considering the flight data obtained using the pseudo-spectral method in the climb phase. Simulations are performed to evaluate the algorithm performance, and the results show that the algorithm can rapidly and stably optimise the benchmark function. Compared to the original algorithm, the proposed algorithm requires 28.89% less optimisation time and yields an optimised take-off mass that is 1.72kg smaller.

We obtain a measure representation for a functional arising in the context of optimal design problems under linear growth conditions. The functional in question corresponds to the relaxation with respect to a pair $(\chi,u)$, where $\chi$ is the characteristic function of a set of finite perimeter and $u$ is a function of bounded deformation, of an energy with a bulk term depending on the symmetrized gradient as well as a perimeter term.

A mobile manipulator is treated as a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator mounted on the platform. The kinematics of the mobile manipulator can be represented as a driftless control system with outputs. By adopting the endogenous configuration space approach we propose two kinematic dexterity measures, called local and global dexterity. The local dexterity, modeled upon the manipulability of stationary manipulators, indicates how infinitesimal motions in the configuration space propagate to the taskspace of the mobile manipulator. The global dexterity corresponds to L2-norm of the local dexterity over a prescribed region of the configuration space. Advantages of the endogenous dexterity measures over traditional performance measures of mobile manipulators known from the literature are described. Both the dexterities are employed for determining optimal configurations and optimal geometries of an exemplary mobile manipulator.

This work presents a systematic design selection methodology that utilizes a co-design strategy for system-level optimization of compliantly actuated robots that are known for their advantages over robotic systems driven by rigid actuators. The introduced methodology facilitates a decision-making strategy that is instrumental in making selections among system-optimal robot designs actuated by various degrees of variable or fixed compliance. While the simultaneous co-design method that is utilized throughout guarantees systems performing at their full potential, a homotopy technique is used to maintain integrity via generation of a continuum of robot designs actuated with varying degrees of variable and fixed compliance. Fairness of the selection methodology is ensured via utilization of common underlying (variable) compliant actuation principle and dynamical task requirements throughout the generated system designs. The direct consequence of the developed methodology is that it allows robot designers make informed selections among a variety of systems which are guaranteed to perform at their best. Applicability of the introduced methodology has been validated using a case study for system-optimal design of an active knee prosthesis that is driven by a mechanically adjustable compliance and controllable equilibrium position actuator (MACCEPA) under a periodic/real-life dynamical task.

PMs with two rotations and one translation (2R1T) have been used as skeletons in various advanced manufacturing equipment where high accuracy and stiffness are basic requirements. Considering the advantages of redundant actuation and overconstrained structure, such as reduced singularities and improved stiffness, a new 2R1T overconstrained PM with actuation redundancy, called Hex4, is proposed in this paper. This is a 2-PUR/2-RPU PM (where P denotes an actuated prismatic joint, U a universal joint, and R a revolute joint) that is actuated by four prismatic joints. Compared with some existing 2R1T overconstrained PMs with actuation redundancy, the main advantage of the proposed PM is that the heavy motors of two limbs are mounted on the base to reduce the movable mass and improve dynamic response. First, mobility analysis, inverse kinematics, and velocity analysis are presented. Then, the local transmission index and good transmission workspace are used to evaluate the motion/force transmissibility of the Hex4 PM. The variation tendencies of the two indices with different link parameters are investigated. The singularity is then discussed by considering the motion/force transmissibility. Finally, link parameters are optimized to obtain an improved good transmission workspace. It is shown that the proposed PM has a good potential for high precision applications.

This paper considers simple step-stress accelerated life tests (SSALTs) for one-shot devices. The one-shot device is an item that cannot be used again after the test, for instance, munitions, rockets, and automobile air-bags. Either left-or right-censored data are collected instead of actual lifetimes of the devices under test. An expectation-maximization algorithm is developed here to find the maximum likelihood estimates of the model parameters based on one-shot device testing data collected from simple SSALTs. Furthermore, the asymptotic variance of the mean lifetime under normal operating conditions is determined under the expectation-maximization framework. On the other hand, the optimal design that minimizes the asymptotic variance of the estimate of the mean lifetime under normal operating conditions in terms of three decision variables, including stress levels, inspection times, and sample allocation is discussed. A procedure then is presented to determine the decision variables when a range of stress levels and the termination time of the test as well as normal operating conditions of the devices are given. The properties of the optimal design and the effects of errors in pre-specified planning values of the model parameters are also investigated. Comprehensive simulation studies show that the procedure is quite reliable for the design of simple SSALTs.

This paper addresses the dimensional-synthesis-based kineto-elastostatic performance optimization of the delta parallel mechanism. For the manipulator studied here, the main consideration for the optimization criteria is to find the maximum regular workspace where the robot delta must posses high stiffness and dexterity. The dexterity is a kinetostatic quality measure that is related to joint's stiffness and control accuracy. In this study, we use the Castigliano's energetic theorem for modeling the elastostatic behavior of the delta parallel robot, which can be evaluated by the mechanism's response to external applied wrench under static equilibrium. In the proposed formulation of the design problem, global structure's stiffness and global dexterity are considered together for the simultaneous optimization. Therefore, we formulate the design problem as a multi-objective optimization one and, we use evolutionary genetic algorithms to find all possible trade-offs among multiple cost functions that conflict with each other. The proposed design procedure is developed through the implementation of the delta robot and, numerical results show the effectiveness of the proposed design method to enhancing kineto-elastostatic performance of the studied manipulator's structure.

This paper investigates the reduction of backscatter radar cross section (RCS) for a rectangular cavity embedded in the ground plane. The bottom of the cavity is coated by a thin, multilayered radar absorbing material (RAM) with possibly different permittivities. The objective is to minimize the backscatter RCS by the incidence of a plane wave over a single or a set of incident angles. By formulating the scattering problem as a Helmholtz equation with artificial boundary condition, the gradient with respect to the material permittivities is determined efficiently by the adjoint state method, which is integrated into a nonlinear optimization scheme. Numerical example shows the RCS may be significantly reduced.

We present a new numerical optimal design for a redundant parallel manipulator, the eclipse, which has a geometrically symmetric workspace shape. We simultaneously consider the structural mass and design efficiency as objective functions to maximize the mass reduction and minimize the loss of design efficiency. The task-oriented workspace (TOW) and its partial workspace (PW) are considered in efficiently obtaining an optimal design by excluding useless orientations of the end-effector and by including just one cross-sectional area of the TOW. The proposed numerical procedure is composed of coarse and fine search steps. In the coarse search step, we find the feasible parameter regions (FPR) in which the set of parameters only satisfy the marginal constraints. In the fine search step, we consider the multiobjective function in the FPR to find the optimal set of parameters. In this step, fine search will be kept until it reaches the optimal set of parameters that minimize the proposed objective functions by continuously updating the PW in every iteration. By applying the proposed approach to an eclipse-rapid prototyping machine, the structural mass of the machine can be reduced by 8.79% while the design efficiency is increased by 6.2%. This can be physically interpreted as a mass reduction of 49 kg (the initial structural mass was 554.7 kg) and a loss of 496 mm3/mm in the workspace volume per unit length. The proposed optimal design procedure could be applied to other serial or parallel mechanism platforms that have geometrically symmetric workspace shapes.

In this paper, the definition of generalized symmetric Gough–Stewart parallel manipulators is presented. The concept of dynamic isotropy is proposed and the singular values of the bandwidth matrix are introduced to evaluate dynamic isotropy and solved analytically. Considering the payload's mass-geometry characteristics, the formulations for completely dynamic isotropy are derived in close form. It is proven that a generalized symmetric Gough–Stewart parallel manipulator is easer to achieve dynamic isotropy and applicable in engineering applications. An optimization procedure based on particle swarm optimization is proposed to obtain better dexterity and large singularity-free workspace, which guarantees the optimal solution and gives mechanically feasible realization.

Dexterity and workspace are two of the most important design criteria in developing manipulators. This paper presents algorithms for developing contour surfaces with specified dexterities and evaluating the area of the surfaces or the volume of the enclosed regions. The obtained results can be utilized to evaluate the dexterity and the rate of change of dexterity. Any closed curve or surface can be used to determine the singularity-free workspace of a manipulator with better dexterity. The proposed algorithms can be employed to study the dexterity and singularity-free workspace of 3-DOF manipulators and 4-DOF redundant serial manipulators. The contour surfaces in some subspaces of 6-DOF manipulators can also be investigated.

In this paper, the optimization of architectural parameters for a class of translational parallel kinematic machine (PKM) is performed with the particle swarm optimization (PSO) to achieve the best accuracy characteristics. The conventional error transformation matrix (ETM) is derived based on the differentiation of kinematic equations, and a new error amplification index (EAI) over a usable workspace is proposed as an error performance index for the optimization. To validate the efficiency of the PSO method, both the traditional direct search method and the genetic algorithm (GA) are implemented as well. The simulation results not only show the advantages of PSO method for the architectural optimization, but also reveal the necessity to introduce the EAI for the optimal design. And the results are valuable for architectural design of the PKM for machine tool applications.