Accepted Manuscripts

Mohammad Sharif Shourijeh, Reza Sharif Razavian and John McPhee
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036288
A model for forward dynamic simulation of the rapid tapping motion of an index finger is presented. The finger model was actuated by two muscle groups: one flexor and one extensor. The goal of this analysis was to estimate the maximum tapping frequency that the index finger can achieve using forward dynamics simulations. To this goal, each muscle excitation signal was parameterized by a seventh-order Fourier series as a function of time. Simulations found that the maximum tapping frequency was 6~Hz, which is reasonably close to the experimental data. Amplitude attenuation (37% at 6Hz) due to excitation/activation filtering, as well as the inability of muscles to produce enough force at high contractile velocities, are factors that prevent the finger from moving at higher frequencies. Musculoskeletal models have the potential to shed light on these restricting mechanisms and help to better understand human capabilities in motion production.
TOPICS: Simulation, Muscle, Musculoskeletal system, Excitation, Engineering simulation, Fourier series, Dynamics (Mechanics), Filtration, Signals
Mohammad S. Shourijeh, Naser Mehrabi and John McPhee
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036195
Static optimization has been used extensively to solve the muscle redundancy problem in inverse dynamics. The major advantage of this approach over other techniques is the computational efficiency. This study discusses the possibility of applying static optimization to solve the muscle force distribution in forward dynamics. A simple forearm model with seven muscles is considered as an example, and static optimization is used for both inverse and forward dynamics and the results are compared. The computational costs are also detailed. In terms of simulation time, forward static optimization is found to be a suitable method for solving forward dynamic musculoskeletal simulations.
TOPICS: Simulation, Optimization, Musculoskeletal system, Dynamics (Mechanics), Muscle, Redundancy (Engineering)
A. M. Shafei and H. R. Shafei
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036197
In this article, a recursive approach is used to dynamically model a tree-type robotic system with floating-base. Two solution procedures are developed to obtain the time responses of the mentioned system. A set of highly nonlinear differential equations is employed to obtain the dynamic behavior of the system when it has no contact with the ground or any object in its environment (flying phase); and a set of algebraic equations is exploited when this tree-type robotic system collides with the ground (impact phase). The Gibbs-Appell (G-A) formulation in recursive form and the Newton's impact law are applied to derive the governing equations of the aforementioned robotic system for the flying and impact phases, respectively. The main goal of this article is a systematic algorithm that is used to divide any tree-type robotic system into a specific number of open kinematic chains and derive the forward dynamic equations of each chain, including its inertia matrix and right hand side vector. Then, the inertia matrices and the right hand side vectors of all these chains are automatically integrated to construct the global inertia matrix and the global right-hand-side vector of the whole system. Finally, to show the effectiveness of the suggested algorithm in deriving the motion equations of multi-chain robotic systems, a ten-link tree-type robotic system with floating base is simulated.
TOPICS: Inertia (Mechanics), Collisions (Physics), Equations of motion, Algorithms, Chain, Robotics, Manipulators, Nonlinear differential equations, Algebra, Open kinematic chains
Yuwen Li, Jiancheng Ji, Shuai Guo and Fengfeng (Jeff) Xi
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036196
This paper proposes a method for process parameter optimization of a mobile robotic percussive riveting system with flexible joints to guarantee the rivet gun alignment during the operation. This development is motivated by the increasing interest in using industrial robots to replace human operators for percussive impact riveting in aerospace assembly. In percussive riveting, the rivet gun generates repetitive impacts acting on the rivet. These impacts not only deform the rivet but also induce forced vibration to the robot, and thus the robot must hold the gun firmly during riveting. The process parameters for the mobile robotic riveting system include those related to the impact force generation for planning the rivet gun input and those related to the robot pose with respect to the joined panels for planning the mobile platform motion. These parameters are incorporated into a structural dynamic model of the robot under a periodic impact force. Then an approximate analytical solution is formulated to calculate the displacement of the rivet gun mounted on the end-effector for its misalignment evaluation. It is found that both the force frequency and the mobile platform position have strong influence on the robotic riveting performance in terms of alignment during operation. Global optimization of these process parameters is carried out to demonstrate the practical application of the proposed method for the planning of the robotic percussive riveting system.
TOPICS: Robotics, Optimization, Riveting, Rivets, Robots, Manufacturing, Structural dynamics, Aerospace industry, Vibration, Displacement, End effectors
Juan Carlos García Orden and Javier Cuenca Queipo
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036116
This paper describes a very simple beam model, amenable to be used in multibody applications, for cases where the effects of torsion and shear are negligible. This is the case of slender rods connecting different parts of many space mechanisms, models useful in polymer physics, computer animation, etc. The proposed new model follows a lumped parameter method that leads to a rotation-free formulation. Axial stiffness is represented by a standard nonlinear truss model, while bending is modeled with a force potential. Several numerical experiments are carried out in order to assess accuracy, which is usually the main drawback of this type of approach. Results reveal a remarkable accuracy in nonlinear dynamical problems, suggesting that the proposed model is a valid alternative to more sophisticated approaches.
TOPICS: Shear (Mechanics), Torsion, Multibody dynamics, Physics, Rotation, Trusses (Building), Polymers, Computers, Rods, Stiffness
Ren Ju, Wei Fan, Weidong D. Zhu and Jianliang L. Huang
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036118
A modified two-timescale incremental harmonic balance (IHB) method is introduced to obtain quasi-periodic responses of nonlinear dynamic systems with combinations of two incommensurate base frequencies. Truncated Fourier coefficients of residual vectors of nonlinear algebraic equations are obtained by a frequency mapping-fast Fourier transform procedure and complex two-dimensional integration is avoided. Jacobian matrices are approximated by Broyden's method and resulting nonlinear algebraic equations are solved. These two modifications lead to a significant reduction of calculation time. To automatically calculate amplitude-frequency response surfaces of quasi-periodic responses and avoid non-convergent points at peaks, an incremental arc-length method for one time-scale is extended for quasi-periodic responses with two timescales. Two examples: a Duffing equation and a van der Pol equation with quadratic and cubic nonlinear terms, both with two external excitations, are simulated. Results from the modified two-timescale IHB method are in excellent agreement with those from Runge-Kutta method. The total calculation time of the modified two-timescale IHB method can be more than two orders of magnitude less than that of the original quasi-periodic IHB method when complex nonlinearities exist and high-order harmonic terms are considered.
TOPICS: Nonlinear systems, Fourier transforms, Jacobian matrices, Nonlinear dynamical systems, Runge-Kutta methods, Steady state, Algebra, Excitation
Kazuya Sakamoto, Ryosuke Kan, Akihiro Takai and Shigehiko Kaneko
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036115
A free-standing rack (FS rack) is a type of a spent nuclear fuel rack, which is just placed on a floor of a pool. For this characteristic, seismic loads can be reduced by fluid force and friction force, but a collision between a rack and another rack or a wall must be avoided. Therefore, it is necessary for designing an FS rack to figure out how it moves under seismic excitation. In this research, a dynamic model of an FS rack is developed considering seismic inertial force, friction force and fluid force. This model consists of two sub-models: a translation model, which simulates planar translational and rotational motion; and a rocking model, which simulates non-slide rocking motion. First, simulations with sinusoidal inertial force were conducted, changing values of a friction coefficient. Next, to validate this dynamic model, a miniature experiment was conducted. Finally, the model is applied to a real-size FS rack and actually observed seismic acceleration. It is found that translational movement of a rack varies depending on the value of friction coefficient in the simulation with sinusoidal and actual acceleration. Also, simulation results are similar to the experimental results in the aspects of translational and rocking motion provided friction coefficient is selected properly. Through this research, the knowledge is acquired that friction force plays a significant role in a motion of FS rack so that estimating and controlling a friction coefficient is important in designing an FS rack.
TOPICS: Fuels, Dynamic models, Excitation, Friction, Fluids, Design, Simulation, Stress, Collisions (Physics), Simulation results, Rotation, Spent nuclear fuels
Antonio Simon Chong Escobar, Piotr Brzeski, Marian Wiercigroch and Przemyslaw Perlikowski
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4036114
In this paper we perform a path following bifurcation analysis of church bell to gain an insight into the governing dynamics of the yoke-bell-clapper system. We use an experimentally validated hybrid dynamical model based on the detailed measurements of a real church bell. Numerical analysis is performed both by a direct numerical integration and a path-following methods using a new numerical toolbox ABESPOL (Chong, Numerical modelling and stability analysis of non-smooth dynamical systems via ABESPOL) based on Coco (Dankowicz et al., Recipes for continuation). We constructed one-parameter diagrams that allow to characterize the most common dynamical states and to investigate the mechanisms of their dynamic stability. A novel method allowing to locate the regions in the parameters space ensuring robustness of bells effective performance is presented.
TOPICS: Dynamic systems, Bifurcation, Dynamic stability, Robustness, Dynamics (Mechanics), Stability, Modeling, Non-smooth dynamics, Numerical analysis
Van-Du Nguyen, Huu-Cong Nguyen, Nhu-Khoa Ngo and Ngoc-Tuan La
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4035933
This paper presents a development in design, mathematical modeling and experimental study of a vibro-impact moling device which was invented by the author before. A vibratory unit deploying electro-mechanical interactions of a conductor with oscillating magnetic field has been realized and developed. The combination of resonance in an RLC circuit including a solenoid is found to create a relative oscillatory motion between the metal bar and the solenoid. This results in impacts of the solenoid on an obstacle block, which causes the forward motion of the system. Compared to the former model which employs impact from the metal bar, the improved rig can offer a higher progression rate of six times when using the same power supply. The novel geometrical arrangement allows for future optimization in terms of system parametric selection and adaptive control. This implies a very promising deployment of the mechanism in ground moling machines as well as other self-propelled mobile systems. In this paper, insight to the design development based on physical and mathematical models of the rig is presented. Then the obtained coupled electro-mechanical equations of motion are solved numerically, and a comparison between experimental results and numerical predictions is presented.
TOPICS: Design, Solenoids, Metals, Machinery, Magnetic fields, Adaptive control, Equations of motion, Modeling, Optimization, Circuits, Resonance
Louay S. Yousuf and Dan B. Marghitu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4035824
A cam is a mechanical device used to transmit motion to a follower by direct contact. In this study a cam and follower mechanism is analyzed. The proposed cam can be used for controlling valve and also on motor car camshafts to operate the engine valves. The dynamic analysis presents follower displacement driven by a cam rotating at a uniform angular velocity. There is a clearance between the follower and the guide. The mechanism is analyzed using computer simulations taking into account the impact and the friction between the flat-faced follower and the guide. Four different follower guide's clearances have been used in the simulations and the Largest Lyapunov Exponents have been calculated. An experimental set up is developed to capture the general planar motion of the cam and follower. The measures of the cam and the follower positions are obtained through high-resolution optical encoders (markers) mounted on the cam and follower shaft. The effect of guide clearance is investigated for different angular velocities of the cam. The largest Lyapunov exponents for the simulated and experimental data are analyzed and selected.
TOPICS: Friction, Computer simulation, Engines, Simulation, Resolution (Optics), Clearances (Engineering), Dynamic analysis, Engineering simulation, Valves, Camshafts, Displacement, Simulation results
Saleh Ashrafi and Ali Khalili Golmankhaneh
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4035718
In this manuscript we have used the recently developed Fα-calculus for calculating the energy straggling function in the fractal distributed structures. We have shown that such fractal structure of space causes the fractal pattern of the energy loss. Also, we have offered Fα-differential Fokker-Planck equation for thick fractal absorbers.
TOPICS: Energy dissipation, Fokker-Planck equation, Fractals
Jeremy Kolansky and Corina Sandu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4031194
The Generalized Polynomial Chaos mathematical technique, when integrated with the Extended Kalman Filter method, provides a parameter estimation and state tracking method. The truncation of the series expansions degrades the link between parameter convergence and parameter uncertainty which the filter uses to perform the estimations. An empirically derived correction for this problem is implemented, that maintains the original parameter distributions. A comparison is performed to illustrate the improvements of the proposed approach. The method is demonstrated for parameter estimation on a regression system, where it is compared to the Recursive Least Squares method.
TOPICS: Kalman filters, Parameter estimation, Polynomials, Chaos, Filters, Uncertainty

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