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Inertia articulated-body

Feathmtone defines the articulated-body inertia of a link as the 6 x 6 matrix which relates a spatial force applied to the link and the spatial acceleration of the link, taking into account the dynamics of the rest of the articulated body. This relationship is linear, and for link t, it may be written as follows [9] ... [Pg.54]

In Equation 4.51, L acts as a spatial transformation which prqjagates the spatial accel tion vector, a,- i, across joint i. We will call a matrix which transforms spatial vectcs s across actuated joint structures a spatial articulated tran ormation. In general, an articulated transformation is a nonlinear function of the articulated-body inertia and is a dimensionless 6x6 matrix. Featherstone calls the articulated transformation, L,, the acceleration propagator [9]. It relates the spatial acceleration of one link of an articulated body to the spatial acceleration of a neighbraing link in the same articulated body (ignoring bias... [Pg.57]

Note that I], the articulated-body inertia of link 1, is the same whether the chain is constrained or unconstrained. The force vector, f, defined by the equation ... [Pg.59]

Note the position of the coordinate transformations in this equation compared to the link coordinate version of the articulated-body inertia equation given in Thble 4.S. This difference in position is due to a difference in the order of tq)plication of the transformations across joints and links in the two algorithms. As a chain is traversed in the recursion for A, the ( rational space inertia matrix of a link is first transformed across the present link (via X) and then transfomed across the next joint (via L). In contrast, as a chain is traversed in the recursion for I. the articulated-body in a is first transfomed across a joint and then transfnmed back across the preceding link. [Pg.70]

Brandi, Johanni, and Otter [3] computes the articulated-body inertia of each link in the chain, starting at the tip and moving back to the base. This same recursion is the first recursion in the Force Propagation Method for computing A. That is, there is an overlap of computations between the solution for the q)en-chain acceleration terms, tjopen and Xopen. and the calculation of the inverse ( rational space inertia matrix, A for this case. This fact was taken into account when the operations were tabulated. The ( rations listed for SI and A in Table 5.2 include only the second recursion for A and the additional opoations needed for SI. The recursion which computes the articulated-body inertias is included in the computatimis for open and x<,pe . [Pg.102]

R. Featherstone. The Calculation of Robot Dynamics Using Articulated-Body Inertias. The International Journal of Robotics Research, 2(l) 13-30, Spring 1983. [Pg.129]

Mazur et al. [103, 104] demonstrated the conformational dynamics of biomacromolecules. However, their method scaled exponentially with size and relied on an expensive expression for the inter-atomic potentials in internal coordinates. Subsequently, our group pioneered the development of internal coordinate constrained MD methods, based on ideas initially developed by the robotics community [102, 105-107], reaching 0(n) serial implementations, using the Newton-Euler Inverse Mass Operator or NEIMO [108-110] and Comodyn [111] based on a variant of the Articulated Body Inertia algorithm [112], as well as a parallel implementation of 0(log n) in 0(n) processors using the Modified Constraint Force Algorithm... [Pg.26]

Featherstone R (1983) The calculation of robot dynamics using articulated-body inertias. Int J Rob Res 2(l) 13-30... [Pg.41]

A number of important recurrence relations in the articulated-body fwmula-tion may be derived by analyzing a simple two-link articulated body as shown in Figure 4.3. This articulated body is made up of links 1 and 2 with spatial link inertias of Ii and I2, respectively. The two links are connected by a general joint, joint 2, which is characterized by its motion space, < 2> Recall from Chapter 2 that 2 represents the free modes of this joint In this analysis, it is assumed that the two bodies are initially at rest and experience no applied joint forces or torques on or about 2 (t2 = 0). The tip force, f, is zero b ause the chain is unconstrained. The only spatial force vector exerted on the articulated body is fi, which is applied to link 1, the handle of the articulated body. For the moment, we will assume that the physical parameters describing the links and joints, including the spatial link inertias, are given in absolute coordinates. [Pg.54]

There are two mechanisms by which the ribs tend to increase the stability (and decrease the motion) of the thoracic spine. The first mechanism involves the articulation of the head of the ribs with the body and transverse processes of the vertebrae. The second mechanism increases the spine s moment of inertia via an increase in the transverse and anteroposterior dimensions of the spine structure. This results in increased resistance to motion in all directions. [Pg.178]


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See also in sourсe #XX -- [ Pg.42 , Pg.54 , Pg.79 ]




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