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ÿþ d i m 3 dZm3 2 d2d3m3 dgm2 J3yy J3== puma australia is the generalizedjoint force vector. r J2== Jzyv Jlzr Jizz; etc.The symbols [ q q ] and [q"] are notation for the n(-l)/Z-vector of C eating Z1 through 1 4 , which are constants of the mecha- nism, leads to a reduction from 35 to 3 multiplications and from[aq]velocity products and the n-vectorof squared velocities. and 18 to 3 additions. Computing the constant Z1 involves 18 calcu- lations. Since the simple parameters required for the calculation[ q 2 ] are given by: of 11 are the input to the RNE, theRNE will effectively carry out The procedure used to derive the dynamimc odel entails four the calculation of Z1 on every pass, producing considerable m-steps: necessary computation.

-- 2 (4) in terms of partial derivatives of kinetic energy matrix *J elements; and reduction of these expressions with four relations that hold on these puma shoes partial derivatives. J -- ,p',jj (5) 4. Formation of the needed partial derivatives, expansion of where (qk * it) is the j t h velocity product in the [q4]vector, and the Coriolis and centrifugal matrix elements in terms of the derivatives, and simplification by combining is the Christoffel symbol. inertia constants puma suede as in 2. The number of unique non-zero Christoffel symbols required .

* The French authors seem to assume the use of Cristoffel symbols, while the American authors seem unaware ofBy combining inertial constants with common variable termsand them.CorbenandStehle,inthe 1950 edition of theirexpanding sin2(82) into (1- c o s 2 ( & ) ) , equation (2) can be re- text, derive the results required here; but the derivationduced to: is largely omitted from their 1960 edition.of gravity and the terms of the inertia dyadic.Thewrist,link where I I = M-wg2 ** r12three and link two of a PUMA 560 arm were detached in puma womens shoes order Mgto measure these parameters.

Themotors were mass of thearm. To makethismeasurementourcontrolsys-left installed in linkstwo and three when the inertia of these links tem was configured to command a motor torque proportional towere measured, so the effect of their mass as the supporting links displacement, effecting a torsional spring. By measuring the pe-move is correctly considered. The gyroscopic forces imparted by riod of oscillation of the resultant mass-spring system, the totalthe rotating motor armatures is neglected in the model, but the rotational inertia about each joint was determined. By subtract-data presented below include armature inertia andgear ratios, so ing the arm contributions, determinedfrom direct measurements,these forces can be determined.

Link 4: The origin is at the intersection of the axes of joints * Values derived from external dimensions; &25%. 4 5 and 6; 24 is along the axis of rotationand The effective torsional spring methodof inertia measurement was appliedateachjoint.Themotor and drive inertia, Imotor, direct.ed away from link 2; Y4 11 Z3 whenjoint were foundby subtractingtheinertialcontributiondue to the arm dynamics, known from direct measurements, from the total 4 is in the zero position. inert,ia measured.Theuncertainty in the total inertia measure- ment is somewhat higher at joint one becauseof the larger frictionLink 5: The origin coincides withthat of frame 4; Z5 puma mens shoes is di- at that joint.

The gear ratios,maximummotortorque, and break away torque for eachjoint of thePUMA is reported in Table 7. The maximum motor torque and break away torque values have been taken from data collected during our motor calibration process. Thecurrentamplifiers of the Unimatecontrolleraredriven by 12 bit D/A converters, so the nominal torque resolution can be 7btained by dividing the reported maximum joint torqueby 2048. Table 7 . Motor and Drive ParametemTheinertiadyadicand effect,ive motorand driveinertia I Joint I Joint 2 Joint 3 Joint 4 Joint 5 Joint ti Gear [img]http://www.simplypotterheads.com/images/lose/puma mens shoes-967raz.jpg[/img] Ratio 107.36 53.69 76.01 71.91 76.73terms are reported in Table6.