Forward dynamics

For the l 27j problem the. forward dynamic programming technique is used (see Held and Karp 1962). The following observation is crucial. If the sequence ypjj,. . . , j , a given permutation of 1,.. . , n, is optimal for the problem under consideration, then the subsequence 71,72, , jh where k n, has to be optimal for the smaller k-job problem, which contains only jobs Let... 

Dynamic analysis Analytic simulation of movements of the system considering forces, torques, and kinematics. Forward dynamics uses the geometry and kinematics as input, and provides forces and torques as outputs inverse dynamics starts from forces and torques and determines kinematics and geometry of the system. 

There are two fundamentally different approaches to studying the biomechanics of human movement forward dynamics and inverse dynamics. Either can be used to determine Joint kinetics (e.g., estimate joint moments during movements). 

FIGURE 5.1 Forward dynamics approach to studying human movement This simplified figure depicts the neural command and forces for three muscles and the moments and joint angles for a two-joint system. See text for details. 

Given the limitations of each method, which should be used forward or inverse dynamics That depends on the question being asked. If one s primary interest is in joint kinematics, it makes more sense to start with a measurement of position as in the invmse dynamics approach. If one is primarily interested in muscle forces, one could argue that forward dynamics has more advantages. For esti-... 

For the remainder of this chapter, we will concentrate on the inverse dynamics approach for the study of human movement. Inverse dynamics is more commonly used than forward dynamics for studying human movement. A forward dynamics approach will be addressed in a subsequent chapter (Chap.6, Biomechanics of the Musculoskeletal System, by Marcus G. Pandy and Ronald E. Barr). 

FIGURE 6.22 Comparison of the forward- and inverse-dynamics methods for determining muscle forces during movement. Top Body motions are the inputs and muscle forces are the outputs in inverse dynamics. Thus, measurements of body motions are used to calculate the net muscle torques exerted about the joints, from which muscle forces are determined using static optimization. Bottom Muscle excitations are the inputs and body motions are the outputs in forward dynamics. Muscle force (F ) is an intermediate product (i.e., output of the model for musculotendon dynamics). 

Equations (6.1) and (6.7) can be combined to form a model of the musculoskeletal system in which the inputs are the muscle activation histories (a) and the outputs are the body motions (q, 4, q) (Fig. 6.22). Measurements of muscle EMG and body motions can be used to calculate the time histories of the musculotendinous forces during movement (Hof et al., 1987 Buchanan et al., 1993). Alternatively, the goal of the motor task can be modeled and used, together with dynamic optimization theory, to calculate the pattern of muscle activations needed for optimal performance of the task (Hatze, 1976 Pandy et al., 1990 Raasch et al., 1997 Pandy, 2001). Thus, one reason why the forward-dynamics method is potentially more powerful for evaluating musculotendinous forces than... 

If accurate measinements of body motions and external forces are available, then inverse dynamics should be used to determine musculotendinous forces durii movement, because this method is much less expensive computationally. If, instead, the goal is to study how changes in body structure affect function and performance of a motor task, then the forward-dynamics method is preferred, for measurements of body motions and external forces are a priori not available in this instance. 

Because muscle, ligament, and joint-contact forces cannot be measured noninvasively in vivo, estimates of these quantities have been obtained by combining mathematical models with either the inverse-dynamics or the forward-dynamics approach (Sec. 6.6). Below we review the levels of musculoskeletal loading incurred in the lower-limb during rehabilitation exercises, such as isokinetic knee extension, as well as during daily activity such as gait. 

Muscle and joint loading are much lower during gait than during knee-extension exercise. Various studies have used inverse-dynamics or static optimization (Hardt, 1978 Crowninshield and Brand, 1981 Glitsch and Baumann, 1997) and forward-dynamics or dynamic optimization (Davy and Audu,... 

Serpas, F., Yanagawa, T., and Pandy, M. G. (2002). Forward-dynamics simulation of anterior cruciate ligament forces developed during isokinetic dynamometry. Computer Methods in Biomechanics and Biomedical Engineering, 5 33-43. 

If we consider a plant, or section thereof, with one or more recycle flows it can schematically be represented by the block-diagram in Fig. 4. Here G(s) represents the forward dynamics, determined by the properties of the individual units, while g/j(s) are the dynamics of the recycle path. The inputs w and W2 may be either disturbances or manipulated variables. Note that we make a distinction between variables which are cormected via the recycle loop only, and those that are connected external to the recycle loop. For instance, for the reactor-separator problem... 

The previously introduced method is now applied to a benchmark problem. The forward dynamics of a serial chain of n rigid bodies, connected by revolute joints, is solved with the recursive method, see Fig. 5. 

Keywords— Rehabilitation Robot, Modeling, Neural MEMO NARX Model, Forward Dynamic Identification. 

Forward Dynamic Neural MIMO NARX model used in this paper is a combination between the Multi-Layer Perception Neural Networks (MLPNN) stiucturc aird the Auto-Regressive with exogenous input (ARX) model. Due to this corrrbirratiorr. Forward MIMO NARX model possesses both of powerful universal approximating feature from MLPNN stmcturc aird strong predictive feature from nonlinear ARX model. 

E. Musculoskeletal Models and Inverse/Forward Dynamics Analysis... 

Forward dynamics Determination of the force and torque by the known trajectories (geometry and kinematics). 

Dupont PE (1992) The use of compliance to resolve the existence and uniqueness of the forward dynamics solution with coulomb friction. In Proceedings of CSME forum 1992, Montreal, Canada... 

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