Fractional models and their parameters are sensitive to intrinsic microstructural changes in anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of mechanical systems. In particular, we study the vibration of a fractional, geometrically nonlinear viscoelastic cantilever beam, under base excitation and free vibration, where the viscoelasticity is described by a distributed-order fractional model. We employ Hamilton's principle to obtain the equation of motion with the choice of specific material distribution functions that recover a fractional Kelvin-Voigt viscoelastic model of order . Through spectral decomposition in space, the resulting time-fractional partial differential equation reduces to a nonlinear time-fractional ordinary differential equation, where the linear counterpart is numerically integrated through a direct L1-difference scheme. We further develop a semi-analytical scheme to solve the nonlinear system through a method of multiple scales, yielding a cubic algebraic equation in terms of the frequency. Our numerical results suggest a set of -dependent anomalous dynamic qualities, such as far-from-equilibrium power-law decay rates, amplitude super-sensitivity at free vibration, and bifurcation in steady-state amplitude at primary resonance.

For theoretical study and engineering application, it is necessary to provide an accurate and simple dynamical model to simulate the multibody mechanical systems with clearance joints and it is also the subject of this article. Based on Lagrange equations of the first kind, a different numerical methodology, the length and rotation angle of the clearance joints are looked as independent coordinates for the first time, is presented in detail. The slider-crank mechanism, with a single or double adjustable revolute clearance joints, is used as a numerical model. A test rig and a simulink model, fully in accordance with the numerical model, are used to measure the velocity, displacement, and acceleration. The numerical results tally with experimental and simulink results reveal that the new methodology, presented in this paper, provides a correct approach to build the dynamical equations of mechanism with clearance joints. Lyapunov exponent is used to analyze the motion status, chaotic or periodic, of the slider. Based on data points, mean absolute deviation (MAD) is applied to judge the dynamical errors, displacement, velocity, and acceleration, of the slider due to clearance joints. With the help of Lyapunov exponent and MAD, the results indicated that various clearance sizes and drive speeds can change the dynamical behaviors of the slider, which is complex but can be predicted in some way.

Ultrasound guidance is used for a variety of surgical needle insertion procedures, but there is currently no standard for the teaching of ultrasound skills. Recently, computer ultrasound simulation has been introduced as an alternative teaching method to traditional manikin and cadaver training because of its ability to provide diverse scenario training, quantitative feedback, and objective assessment. Current computer ultrasound training simulation is limited in its ability to image tissue deformation caused by needle insertions, even though tissue deformation identification is a critical skill in performing an ultrasound-guided needle insertion. To fill this need for improved simulation, a novel method of simulating ultrasound tissue-needle deformation is proposed and evaluated. First, a cadaver study is conducted to obtain ultrasound video of a peripheral nerve block. Then, optical flow analysis is conducted on this video to characterize the tissue movement due to the needle insertion. Tissue movement is characterized into three zones of motion: tissue near the needle being pulled, and zones above and below the needle where the tissue rolls. The rolling zones were centered 1.34 mm above and below the needle and 4.53 mm behind the needle. Using this characterization, a vector field is generated mimicking these zones. This vector field is then applied to an ultrasound image using inverse mapping to simulate tissue movement. The resulting simulation can be processed at 3.1 frames per second. This methodology can be applied through future optimized graphical processing to allow for accurate real time needle tissue simulation.

Achieving coordinated motion between transfemoral amputee patients and powered prosthetic joints is of paramount importance for powered prostheses control. In this article, we propose employing an algebraic curve representation of nominal human walking data for a powered knee prosthesis controller design. The proposed algebraic curve representation encodes the desired holonomic relationship between the human and the powered prosthetic joints with no dependence on joint velocities. For an impedance model of the knee joint motion driven by the hip angle signal, we create a continuum of equilibria along the gait cycle using a variable impedance scheme. Our variable impedance-based control law, which is designed using the parameter-dependent Lyapunov function framework, realizes the coordinated hip-knee motion with a family of spring and damper behaviors that continuously change along the human-inspired algebraic curve. In order to accommodate variability in the user's hip motion, we propose a computationally efficient radial projection-based algorithm onto the human-inspired algebraic curve in the hip-knee plane.

Functional electrical stimulation (FES) is prescribed as a treatment to restore motor function in individuals with neurological impairments. However, the rapid onset of FES-induced muscle fatigue significantly limits its duration of use and limb movement quality. In this paper, an electric motor-assist is proposed to alleviate the fatigue effects by sharing work load with FES. A model predictive control (MPC) method is used to allocate control inputs to FES and the electric motor. To reduce the computational load, the dynamics is feedback linearized so that the nominal model inside the MPC method becomes linear. The state variables: the angular position and the muscle fatigue are still preserved in the transformed state space to keep the optimization meaningful. Because after feedback linearization the original linear input constraints may become nonlinear and state-dependent, a barrier cost function is used to overcome this issue. The simulation results show a satisfactory control performance and a reduction in the computation due to the linearization.

This paper presents a simplistic passive dynamic model that is able to create realistic quadrupedal walking, tölting, and trotting motions. The model is inspired by the bipedal spring loaded inverted pendulum (SLIP) model and consists of a distributed mass on four massless legs. Each of the legs is either in ground contact, retracted for swing, or is ready for touch down with a predefined angle of attack. Different gaits, that is, periodic motions differing in interlimb coordination patterns, are generated by choosing different initial model states. Contact patterns and ground reaction forces (GRFs) evolve solely from these initial conditions. By identifying appropriate system parameters in an optimization framework, the model is able to closely match experimentally recorded vertical GRFs of walking and trotting of Warmblood horses, and of tölting of Icelandic horses. In a detailed study, we investigated the sensitivity of the obtained solutions with respect to all states and parameters and quantified the improvement in fitting GRF by including an additional head and neck segment. Our work suggests that quadrupedal gaits are merely different dynamic modes of the same structural system and that we can interpret different gaits as different nonlinear elastic oscillations that propel an animal forward.

This paper provides the model predictive control (MPC) of fractional order systems. The direct method will be used as internal model to predict the future dynamic behavior of the process, which is used to achieve the control law. This method is based on the Grünwald-Letnikov's definition that consists of replacing the noninteger derivation operator of the adopted system representation by a discrete approximation. The performances and the efficiency of this approach are illustrated with practical results on a thermal system and compared to the MPC based on the integer ARX model.

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.