ÿþwhere A(q) is the n X n kineticenergymatrix; puma creeper a l l = 11 12 coa2(82) 13 cos(82)co8(82 63) (3) B(q) is the n x n(n-1)/2matrix of Coriolistorques; z4 cos2(e2 03) C(q) is the n x n matrix of centrifugaltorques; Calculations required: 3 multiplications, 3 additions. g(q) is then-vector of gravitytorques; q is thne-vector of accelerations; where ZI.= d i m 3 dZm3 2 d2d3m3 dgm2 J3yy J3== 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 Creating Z1 through 1 4 , which are constants of the mecha- nism, leads to a rihanna fenty puma 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[ rihanna puma shoes q 2 ] are given by: of 11 are the input to the RNE.

The rigid bodyassumption;link 6 hasbeenassumed to besymmetric, that isI,% = Zyy; and only the mass moments of inertia are considered,that is I,,, Zyy and Z z z . The original output of EMDEG, includ-ing Coriolisand centrifugal terms, required 15,000 multiplicationsand 3,500 additions. This step might also have been performedwith the momentum theorem method used in [lzaguirre and Paul19851.In puma by rihanna creeper 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.

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 fenty puma creepers 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.

To obtain the inertialterms, the wrist links were modeled as thin shells. A tolerance for each direct measurement was established as the measurement was taken.ThetolerancevaluesarederivedMeasurement of Rotational Inertia from the precision or smallestgraduation of the measuring in- strument used, or from the repeatability of the measurement it- The two wire suspension shown in Figure1 was used to mea- self. Thetolerancesarereportedwhere the data are presented.