Inverse-dynamics method

In the inverse-dynamics method, noninvasive measurements of body motions (position, velocity, and acceleration of each segment) and external forces are used as inputs in Eq. (6.1) to calculate the net actuator torques exerted about each joint (see Fig. 6.22). This is a determinate problem because the number of net actuator torques is equal to the number of equations of motion of the system. Specifically, from Eq. (6.1), we can write... 

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). 

The previous chapters dealt with ISE systems at zero current, i.e. at equilibrium or steady-state. The properties of the interface between two immiscible electrolyte solutions (ITIES), described in sections 2.4 and 2.5, will now be used to describe a dynamic method based on the passage of electrical current across ITIES. Voltammetry at ITIES (for a survey see [3, 8, 9, 10, 11, 12,18]) is an inverse analogue of potentiometry with liquid-membrane ISEs and thus forms a suitable conclusion to this book. 

Vapour and gas sorption measurements can be performed with static or dynamic methods, either of which can provide information on equilibrium behaviour. Furthermore, the measurements can be performed using gravimetric or volumetric based instrumentation. The most common flow methods are inverse gas chromatography (IGC) [1] for volumetric studies and dynamic gravimetric instrumentation [2]. 

In the situation described above, the dynamic experiment was cturied out in dilation the resulting complex modulus was divided into a real ( elastic ) and an imaginary ( viscous ) part. As a counterpart, the experiment can also be carried out in shear, resulting in a complex surface shear viscosity G°, consisting of a real (viscous) part, the surface shear viscosity G° and the surface shear loss viscosity, G"" identical to the elasticity. This inversion of method is formally identical to measuring complex dielectric permittivities instead of complex conductivities, discussed in sec. I1.4.8a. In that case, flg. 3.26 is modified in that panel (b) describes G°, panel (c) G " and jianel (d) the sum, with - tan 0 = G" /G. ... 

Feedback error learning (FEL) is a hybrid technique [113] using the mapping to replace the estimation of parameters within the feedback loop in a closed-loop control scheme. FEL is a feed-forward neural network structure, under training, learning the inverse dynamics of the controlled object. This method is based on contemporary physiological studies of the human cortex [114], and is shown in Figure 15.6. 

Physical motion is common to most situations in which the human functions and is therefore fundamental to the analysis of performance. Parameters such as segment position, orientation, velocity, and acceleration are derived using kinematic or dynamic analysis or both. This approach is equally appropriate for operations on a single joint system or linked multibody systems, such as is typically required for human analysis. Depending on the desired output, foreword (direct) or inverse analysis may be employed to obtain the parameters of interest. For example, inverse dynamic analysis can provide joint torque, given motion and force data while foreword (direct) dynamic analysis uses joint torque to derive motion. Especially for three-dimensional analyses of multijoint systems, the methods are quite complex and are presently a focal point for computer implementation [Allard et al., 1994]. 

The main parameter determining the gas rarefaction is the Knudsen number Kn = Ha, where I is the mean free path of fluid molecules and a is a typical dimension of gas flow. If the Knudsen number is sufficiently small, say Kn < 10 , the Navier-Stokes equations are applied to calculate gas flows. For intermediate and high values of the Knudsen number, the Navier-Stokes equations break down, and the implementation of rarefied gas dynamics methods is necessary. In practical calculations usually the rarefaction parameter defined as the inverse Knudsen number, i.e.. 

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-... 

In this chapter we have examined forward and inverse dynamics approaches to the study of human motion. We have outlined the steps involved in using the inverse approach to studying movement with a particular focus on human gait. This is perhaps the most commonly used method for examining joint kinetics. The forward or direct dynamics approach requires that one start with knowledge of the neural command signal, the muscle forces, or, perhaps, the joint torques. These are then used to compute kinematics. 

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. 

This chapter proposes motion control method for deformable machines consisting of actively deformable materials. If the problem is stated in inverse dynamics form, the required method is to move typical position of the robot on the objective trajectory by deforming its whole body. It was neither the selection of typical points nor objective trajectory was clear for the beginning. 

Sorption measurements are a useful method in the characterization of solid materials. From these data, it is possible to obtain information about the capacity of adsorption, but also thermodynamic properties—enthalpies of adsorption, surface energy—as well as kinetic information, such as diffusion rates. Sorption measurements can be obtained either by static or dynamic methods. Static methods carried out the adsorption measurements under vacuum, after a pre-treatment at high temperature in order to clean the material surface. Dynamic methods use a flowing gas device. Inverse gas chromatography (IGC) is a dynamic method. In comparison to static adsorption systems, dynamic sorption techniques show shorter measurement time, and a wider range of experimental possibilities. 

Fig. 10 The dynamic behavior of the particle using inverse rotation method...

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