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ÿþthat they do in Fairfield County, Connecticut, or Westchester County, New all black puma shoes York, they would appear to have colonized under four square miles. If they achieve only the normal habitat density for most of their U.S. kin, they may affect 40 square miles, which if evenly distributed from their escape point would be a radius of about seven miles. The slow and limited spread of a species in which contagious disease spreads at about 50 miles per year in the U.S. suggests that the feral German immigrants actually have only a tenuous hold on survival. England and France have even had homegrown cases of classic PU M A PA N I C.

The method presented here for factoring the dynamicappendiz. equations has yielded a dynamic model of the PUMA 560 all black puma sneakers arm1. I n t r o d u c t i o n Table 1. CalculationsRequired to Compute the Forces of Motion by 3 Methods.The Implementation of dynamic control systems for manip- Method Calculationsulatorshasbeenhamperedbecausethemodelsare difficult to Recursive Newton-Eulerderive andcomputationally expensive, and because the all puma shoes needed Evaluation of the Full 1560 Explicit PUMA Model 1165parameters of the manipulator are generally unavailable. Recur- 305 Evaluation of t,he Abbreviatedsive methods for computing the dynamic forces have been avail- Explicit PUMA Modelableforseveralyears[Luh, Walker and Paul 1980a;Hollerbach19801.

Theirmodelsincorporatenestedfactorizations,decomposition based on a significance criterion or other criteria, which were not used here.and provides a more direct solution for dynamic simulation. The count of 1165 calculations for the full PUMA model is the totalrequired to evaluate the model presented in the appendixThetremendous size of an explicitdynamicmodel is all red puma shoes the and equation (1) below. This total and other totals presented do notinclude the calculationsrequired to evaluatethesinesandgreatest barrier to its realization.Correspondingly,aconsider- cosines.

Thirty four lumped constants are needed 1. Symbolic Generation of the kinetic energy matrix and by the full PUMA model, 8 fewer than the count of 42 simple pa- gravity vector elements by performing the summations of rameters required to describe the arm. either Lagrange's or the Gibbs-Alembert formulation.

In the second step of this procedure, the kinetic energy ma- The reduction of Equation (7) arises from the symmetry oftrix elements are simplified by combining inertia constants that the kineticenergymatrix.Equation (8) obtains because the ki-multiply common variable expressions. This is the greatest source netic energy imparted by the velocity of a joint is independent ofof computational efficiency. Looking to the dynamic model of a 3 theconfiguration of thepriorjoints.Equation (9) resultsfromdof manipulator presented in [Murry and Neuman 19841,we see the symmetry of the sixth and terminal link of all white puma shoes the PUMA arm.

that the kinetic energy matrix element a11 is given by: Andequation (10) holdsbecausethesecond a d third axes of a11 = J322 c o s 2 ( & 83) J a Y y sin2(82 83) JzZr &m3 thePUMAarmareparallel. Of the reductionfrom 126 to 39 2 kf3za" cos(82)cos(82 d 3 ) uzm3 cos2(e2) unique Christoffel symbols, 61 eliminations are obtained with the 2 Mzza3 cos"(82 03) a$m3 c0s2(82 83) general equations, 14 more with (9)and a further 12 with (10). $2 a2a3m3 eos(Bz)<�oos(82 6 3) JpYy sin"(62) (2) Step four requires differentiating the mass matrix elements withrespect to the configurationvariables.