Forward Dynamic Analysis Research Articles

Review of Modelling Techniques for In Vivo Muscle Force Estimation in the Lower Extremities during Strength Training.

Background. Knowledge of the musculoskeletal loading conditions during strength training is essential for performance monitoring, injury prevention, rehabilitation, and training design. However, measuring muscle forces during exercise performance as a primary determinant of training efficacy and safety has remained challenging. Methods. In this paper we review existing computational techniques to determine muscle forces in the lower limbs during strength exercises in vivo and discuss their potential for uptake into sports training and rehabilitation. Results. Muscle forces during exercise performance have almost exclusively been analysed using so-called forward dynamics simulations, inverse dynamics techniques, or alternative methods. Musculoskeletal models based on forward dynamics analyses have led to considerable new insights into muscular coordination, strength, and power during dynamic ballistic movement activities, resulting in, for example, improved techniques for optimal performance of the squat jump, while quasi-static inverse dynamics optimisation and EMG-driven modelling have helped to provide an understanding of low-speed exercises. Conclusion. The present review introduces the different computational techniques and outlines their advantages and disadvantages for the informed usage by nonexperts. With sufficient validation and widespread application, muscle force calculations during strength exercises in vivo are expected to provide biomechanically based evidence for clinicians and therapists to evaluate and improve training guidelines.

Exploring the Secret of the Ancient Chinese Character’s Development: A Hindsight After Reading The Development of Ancient Chinese Character

With regard to analyzing the form of the ancient Chinese character, The Development of Ancient Chinese Character puts forward dynamic analysis and static analysis. It makes attempt to study the history of ancient Chinese character from both diachronic and synchronic perspectives, and combine the dynamic analysis of the character’s form with the static analysis. Besides, according to The Development of Ancient Chinese Character, “the change of Chinese character’s form into lines”, “symbolization”, and “uniformity” are the general direction that the form of ancient Chinese character develops towards. Besides, the development of ancient Chinese character also shows the features of the times. Moreover, the book compares the structures of the characters in the periods from the Shang dynasty to Qin dynasty, revealing the formation mode of ancient Chinese character which is in a dynamic transformation. Furthermore, the usage of ancient Chinese character is also included in the book, which encompasses many aspects, such as the total number of the different characters in different periods, the frequency of characters, commonly-used characters and rarely-used characters, and so on. Through detailed numbers, the book makes its argumentation convincing and vivid. In addition, the book is also filled with creative ideas in the interpretation of individual characters and in the establishment of new theories.

Parameter identification method for a three-dimensional foot–ground contact model

A new parameter identification method for a three-dimensional foot–ground contact model is presented. The model is used to reproduce the relationship between the contact forces and the relative foot–ground displacements and velocities. The parameters of the contact model are estimated using the optimization method known as covariance matrix adaptation evolution strategy. An extended Kalman filter is implemented as a controller to compute a forward dynamic analysis of the foot motion using body segment parameters and the ankle joint wrench as input data. The aim of this work is to adjust the position and size of the contact elements (spheres) and the model parameters in order to obtain both, a predicted motion provided by forward dynamics as faithful as possible to the captured motion and a resultant foot–ground wrench (obtained through the foot–ground contact model) as close as possible to the measured foot–ground reactions. The results show that the obtained motion is really similar to the captured one and, moreover, the vertical force and the moments in the horizontal plane are in agreement with the experimental mesurments. However, the bristle friction model used for tangential forces provides lower level of agreement with the experimental data.

A novel approach for forward dynamic analysis of 3-PRS parallel manipulator with consideration of friction effect

In this paper, a novel decomposition approach to formulate the dynamic model of a 3-Prismatic, Revolute, Spherical (3-PRS) parallel manipulator is proposed. Since the constraint forces arising from the holonomic constraints would not generate a net force or torque to manipulate the motion of the moving platform, the fact motivates to decompose the reaction forces applied to the connecting joints. The decomposition leads to a transformation matrix which can project the dynamic forces of the moving platform formulated in the task space into the joint space. A sufficient condition is determined to guarantee the existence of the projection matrix . Based on the proposed approach, the inverse of 21×21 augmented matrix formulated by conventional approach in solving forward dynamic problem can be decomposed into that of 6×6 and 15×15 matrices. The computational efficiency can therefore be improved about 23.5%. Besides, since the reaction forces can be calculated simultaneously, each of the actuated legs can be decoupled to calculate the normal forces applied to the sliding planes of the prismatic joints . This feature makes it possible to include the effect of corresponding friction forces into consideration. Since the normal forces applied to the sliding planes vary with the reaction forces, the corresponding friction forces are not only the function of sliding velocities but also the dynamics of the whole mechanism. Computer simulations are performed to verify the proposed approach and analyze the effect of the friction forces on the motion accuracy of the moving platform. • We propose a novel decomposition approach to formulate the dynamic model of a 3-PRS (Prismatic, Revolute, Spherical) parallel manipulator. The dynamic model can be utilized to simulate the motion trajectory of the moving platform once the externally applied forces are given. • The decomposition approach leads to a transformation matrix which can project the dynamic forces of the moving platform formulated in the task space into the joint space. • The inverse of 21×21 augmented matrix formulated by conventional approach in solving forward dynamic problem can be decomposed into that of 6×6 and 15×15 matrices. The computational efficiency can therefore be improved about 23.5%. • Each of the actuated legs can be decoupled to calculate the normal forces applied to the sliding planes of the prismatic joints. • The effect of corresponding friction forces is included into consideration.

Kinematic and dynamic modeling of spherical joints using exponential coordinates

Traditional Euler angle-based methods for the kinematic and dynamic modeling of spherical joints involve highly complicated formulas that are numerically sensitive, with complex bookkeeping near local coordinate singularities. In this regard, exponential coordinates are known to possess several advantages over Euler angle representations. This paper presents several new exponential coordinate-based formulas and computational procedures that are particularly useful in the modeling of mechanisms containing spherical joints. Computationally robust procedures are derived for evaluating the forward and inverse formulas for the angular velocity and angular acceleration in terms of exponential coordinates. We show that these formulas simplify the parametrization of joint range limits for spherical joints, and lead to more compact equations in the forward and inverse dynamic analysis of mechanisms containing spherical joints.

114 ボールキック運動における逆-順動力学解析環境の構築(サッカーキックほか)

In studies dealing with body movement and sports techniques, a method that is commonly used involves analysing joint torque using inverse dynamics based on kinematic data obtained through motion capture systems. On the other hand, another analytic technique that has become increasingly common entails generating movements and performing simulations on the basis of the force data for joint torque and the like; this technique employs forward dynamics to calculate the kinematic data. In general, however, the inverse dynamics and forward dynamics analyses are performed independently, and there have been almost no studies in which analysis is conducted by combining the two analyses. Therefore, in this study, an analytic environment was constructed for analysing the motion of kicking a soccer ball, in which inverse dynamics and forward dynamics were combined; the environment was constructed by using a formula manipulation language based on a simple two-dimensional double pendulum model. The results showed that although the kinematic data obtained from the motion capture system did not completely match the kinematic data obtained from the simulation in which forward dynamics was used, adequate agreement was observed between the two sets of data. In this study, it was considered that the development of an analytic environment that combined inverse dynamics and forward dynamics enabled a more refined analysis of the motion of kicking a ball.

Interval Analysis for System Identification of Linear MDOF Structures in the Presence of Modeling Errors

AbstractModeling errors, represented as uncertainty associated with the parameters of a mathematical model, inevitably exist in the process of constructing a theoretical model of real structures and limit the practical application of system identification. They are usually represented either in a deterministic manner or in a probabilistic way. However, if the available information is uncertain but of a nonprobabilistic nature, as it may emerge from a lack of knowledge about the sources and characteristics of model uncertainties, a third type of approach may be useful. Presented in this paper is an approach to treat modeling errors with the aid of intervals, resulting in bounded values for the identified parameters. Compared with the traditional identification procedures where model-based forward dynamic analysis is often involved, computing bounded time history responses from a computational model with interval parameters is avoided. Two required submatrices are firstly extracted from identified state-spa...

Inverse and Forward Dynamic Analysis of Two Link Manipulator

Abstract In the paper we show the possibilities of physical modeling in Matlab/SimMechanics on a simple mechanical model of two link manipulator. We deal with its direct and inverse dynamics. Considering direct problem we investigate mechanical movement of the robot under the action of given forces and moments. As regards the issue of inverse motion we identify forces which cause a prescribed motion of the effector. Both problems are solved using block diagrams in Simulink and SimMechanics. Results are presented graphically.

Elastodynamic Inversion of Multilayered Media via Surface Waves—Part II: Implementation and Numerical Verification

An effective inverse analysis computer program that integrates nonlinear optimization algorithm and forward dynamic analysis of multilayered medium is developed for inferring structural and material properties (e.g., modulus, thickness, and the number of layers) of the medium. Using dynamic deflection information obtained from forward dynamic analysis of the multilayered medium as a hypothetical deflection measured from the field during pavement nondestructive evaluation (NDE) using falling weight deflectometer, the estimated parameters of the medium are compared with the known true parameters of the medium used to perform the static and forward dynamic analyses. Based on two different multilayered media, a number of important observations and conclusions are made regarding the accuracy and efficiency of the proposed numerical algorithms and developed computer program. The inversion methods presented in this paper show improved NDE results over many of the existing algorithms.

Elastodynamic Inversion of Multilayered Media via Surface Waves—Part I: Methodologies

A rigorous theoretical foundation for solving elastodynamic inverse problem of multilayered media under an impulse load is established in this paper. The inversion is built upon the forward dynamic analysis of multilayered elastic media using transfer matrix approach, with which displacement continuity is assumed at the interfaces of upper and lower adjacent layers. Formulations for inverse analysis are derived in both the time domain and the complex frequency domain. Least square estimates and nonlinear optimization algorithms are used to implement parameter identification. The proposed theory and formulae can be utilized to develop a computer software for nondestructive evaluation of laminated civil and aerospace structure (highway and airport pavements, bridge decks, soil foundations, aircraft wing, etc.), exploration and dynamic source detection and identification, and petroleum exploration in geophysics.

An efficient muscle fatigue model for forward and inverse dynamic analysis of human movements

The aim of this work is to present the integration of a simple and yet efficient dynamic muscle fatigue model in a multibody formulation with natural coordinates. The fatigue model considers the force production history of each muscle to estimate its fitness level by means of a three-compartment theory approach. The model is easily adapted to co-operate with standard Hill-type muscle models, allowing the simulation and analysis of the redundant muscle forces generated in the presence of muscular fatigue. This has particular relevance in the design of orthotic devices to support human locomotion and manipulation.

Compliant contact force approach for forward dynamic modeling and analysis of biomechanical systems

This work deals with the problem of contact modeling and analysis of biomechanical systems involving contact events between soft materials, such as in the case of natural and artificial joints. Modeling contacts with high degree of energy dissipation plays a crucial role in the analysis, design and control of many biomechanical systems in the measure that soft materials are characterized by low or medium values of the coefficient of restitution. The contact force model presented in this work is developed with basis on the foundation of the Hertz law together with a hysteresis damping parameter that accounts for the energy dissipation during the contact process. This approach is based on the analysis of dissipated energy related to the coefficient of restitution, stored elastic energy and the dissipated energy associated with the internal damping of the contacting bodies. A demonstrative application example is used to provide the results that support the analysis and discussion of procedures, methodologies and assumptions adopted throughout this work.

A Penalty Formulation for Dynamics Analysis of Redundant Mechanical Systems

Redundancy in the constraining of mechanical systems achieves more stability and larger load capacity for the system, while in actuation it provides better robustness against singularities and higher maneuverability. Few techniques have been developed with the aim to handle redundancy and singularities in dynamics analysis, and further research is still needed in this area. In this paper, we illustrate the concept of actuating and passive constraints. Then, we expand on the existing penalty techniques by incorporating the concept of actuating and passive constraints to present a penalty formulation that is capable of efficiently handling singularities and redundancy in constraining and actuation and can carry out either forward or inverse dynamics analysis of mechanical systems. As such, the proposed approach is referred to as the actuating-passive constraints penalty approach.

Reorganization of Finger Coordination Patterns During Adaptation to Rotation and Scaling of a Newly Learned Sensorimotor Transformation

We examined how people organize redundant kinematic control variables (finger joint configurations) while learning to make goal-directed movements of a virtual object (a cursor) within a low-dimensional task space (a computer screen). Subjects participated in three experiments performed on separate days. Learning progressed rapidly on day 1, resulting in reduced target capture error and increased cursor trajectory linearity. On days 2 and 3, one group of subjects adapted to a rotation of the nominal map, imposed either stepwise or randomly over trials. Another group experienced a scaling distortion. We report two findings. First, adaptation rates and memory-dependent motor command updating depended on distortion type. Stepwise application and removal of the rotation induced a marked increase in finger motion variability but scaling did not, suggesting that the rotation initiated a more exhaustive search through the space of viable finger motions to resolve the target capture task than did scaling. Indeed, subjects formed new coordination patterns in compensating the rotation but relied on patterns established during baseline practice to compensate the scaling. These findings support the idea that the brain compensates direction and extent errors separately and in computationally distinct ways, but are inconsistent with the idea that once a task is learned, command updating is limited to those degrees of freedom contributing to performance (thereby minimizing energetic or similar costs of control). Second, we report that subjects who learned a scaling while moving to just one target generalized more narrowly across directions than those who learned a rotation. This contrasts with results from whole-arm reaching studies, where a learned scaling generalizes more broadly across direction than rotation. Based on inverse- and forward-dynamics analyses of reaching with the arm, we propose the difference in results derives from extensive exposure in reaching with familiar arm dynamics versus the novelty of the manual task.

Reaction Forces and Moments in Carved Turns

AbstractWe computed reaction forces and moments acting on a skier during a carved turn. We performed an inverse and a forward dynamic analysis. For a run of an elite skier, marker positions on skier and skis were obtained as functions of time from a video analysis and smoothed by splines. Linear velocities and accelerations were computed by differentiating the splines, angular velocities, and accelerations via rotation matrices. The forces acting at the right ski were measured with two Kistler force plates. For the inverse dynamics, we used an adapted Hanavan model for a skier consisting of upper body, left and right thighs, shanks, and skis. Applied forces considered were weight and ski-snow friction. Drag was neglected. By prescribing a lateral weight distribution from the outer to the inner ski during the turn, reaction forces and moments at the left and right ankle, knee and hip joints were computed from the Newton–Euler equations of motion for constrained rigid multibody systems. The forward dynamics was performed with a three-segment model of a mono-skier consisting of trunk, thigh, and shank. Rotational joints were assumed in knee and hip. The track and the joint angles were prescribed. The inward lean angle was determined by a balance condition that led to nonholonomic constraints. After formulating the equations of motion in descriptor form, the resulting differential-algebraic system was solved with the numerical code RADAU5. Computed and measured reaction forces and moments agreed well within the accuracy of the measurements. The calculated joint loads are consistent with results from the literature. The forward dynamics model can be used to simulate consecutive ski turns. With parameter studies, the effects of slope, tracks, segment properties, ski-snow friction, and velocity of the skier on joint loads and performance of a run can be investigated. Further, injury mechanisms can be analyzed.

125666 FORWARD DYNAMICS OF THE 6-PUS PARALLEL MANIPULATOR BASED ON THE FORCE COUPLING AND GEOMETRY CONSTRAINT OF THE PASSIVE JOINTS(Robotics and Mechatronics)

This paper presents a simplified approach for the forward dynamics analysis of the 6-P__-US parallel manipulator, as shown in figure.1, based on the force coupling and geometry constraint of the passive spherical joints. In the proposed method, the parallel manipulator is divided, at the passive joints, into the limbs parts and the platform part. And for both kinds of parts, the equivalent dynamic equations relating to the decomposing joints are obtained based on the transformation principles of dynamic equations between different spaces. Then, in the acceleration level, the dynamic models for both parts can be rewritten in the form of linear equations on the generalized constraint forces and the accelerations of the passive joints on the condition that the state (position and velocity) of the manipulator is specified. Thus, according to the force coupling and geometry constraints of the passive joints, the closed form solution for the generalized constraint forces can be derived readily from the linear equations system combined by the separated parts. Additionally, in the position/velocity level, the task space variables of the manipulator (the position and orientation of the platform) are chosen as the system generalized coordinates, which only results in the utilization of the inverse kinematics for the state transformation between the workspace and the passive joints space. Hence, by virtue of the constraint forces obtained from the above linear equations, the dynamic model of the parallel manipulator can be replaced by a single free rigid body (the platform) with specified external applied forces, provided by the environment through the end-effector and the limbs through the passive spherical joints, respectively. In the end, some numerical results are provided and compared to validate the correctness and effectiveness of the proposed approach.

Constraints on the Complete Optimization of Human Motion

In sport and exercise biomechanics, forward dynamics analyses or simulations have frequently been used in attempts to establish optimal techniques for performance of a wide range of motor activities. However, the accuracy and validity of these simulations is largely dependent on the complexity of the mathematical model used to represent the neuromusculoskeletal system. It could be argued that complex mathematical models are superior to simple mathematical models as they enable basic mechanical insights to be made and individual-specific optimal movement solutions to be identified. Contrary to some claims in the literature, however, we suggest that it is currently not possible to identify the complete optimal solution for a given motor activity. For a complete optimization of human motion, dynamical systems theory implies that mathematical models must incorporate a much wider range of organismic, environmental and task constraints. These ideas encapsulate why sports medicine specialists need to adopt more individualized clinical assessment procedures in interpreting why performers' movement patterns may differ.

Forward Dynamics Analysis of the 6-PUS Mechanism Based on Platform-Legs Composite Simulation

The dynamics analysis plays an important role for the control,simulation and optimization of the parallel manipulators. Normally,the Stewart type manipulators have a platform and several legs. The inverse dynamics can be solved efficiently by taking the advantage of such structural characteristics. However,for the forward dynamics analysis,this structural decomposition still faces challenges from both modeling and computation. In this paper,an efficient approach is proposed for the forward dynamics of the 6-PUS manipulator based on the platform-legs composite simulation. By composite method,the dynamics modeling of the parallel manipulator is separated into the forward dynamics of the platform and the kineto-statics of the legs. The global simulation model can be constructed by connecting the predefined platform model and leg models according to the manipulator's topology. Thus,the global simulation can be decomposed into the independent calculations of purely algebraic equations and ordinary differential equations (ODEs),the computational cost can be reduced and the stability of the simulation can be improved. For the purpose of solving the manipulator's forward dynamics accurately,the algebraic-loop problem is discussed and a closed form algorithm is proposed. A numerical example of the 6-PUS manipulator is given to demonstrate the effectiveness of the proposed approach. The example results show that the modeling efficiency can be improved and the simulation stability can be ensured for decomposing the system equations into purely algebraic equations and ODEs.

A-15 テニスサーブ動作における上肢のラケット速度生成メカニズム : 競技レベルの違いが順動力学的貢献に与える影響(テニス・バドミントン1)

A-15 テニスサーブ動作における上肢のラケット速度生成メカニズム : 競技レベルの違いが順動力学的貢献に与える影響(テニス・バドミントン1)

Forward Dynamics Analysis of Spatial Parallel Mechanisms Based on the Newton-Euler Method with Generalized Coordinates

A general method for the forward dynamics modeling and simulation of spatial parallel mechanisms is proposed on the basis of Newton-Euler method with generalized coordinates. The task-space variables are chosen as the generalized coordinates during the dynamics modeling. The equations of motion and reaction can be obtained from the Newton-Euler equations of all the bodies in the mechanism according to the inverse kinematics and the principle of virtual work. The 6-UPS mechanism is studied as an example to verify the validity of the method, and the forward dynamic model and the simulation results are presented. The theoretical analysis and case study show that the method can simplify the procedure of the forward dynamics modeling of spatial parallel mechanisms and improve the computational efficiency.