In thethirdstepthe puma shoes elements of the Coriolis matrix,Qij, 2. Simplification of the kinetic energy matrix elements by and of the centrifugal matrix, ci,, arewritten in terms of the combining inertia constants that multiply common Christoffelsymbols of the first kind [Corbenand Stehle 1950; variable expressions. Likgeois et al. 1976]* giving: 3.Expression of the Coriolis and centrifugal matrix elements b.. -- 2 (4) in terms of partial derivatives of kinetic energy matrix *J elements;

The rigid bodyassumption;link 6 hasbeenassumed to besymmetric, that isI,% = Zyy; and only the puma trainers 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. puma suede This step might also have been performedwith the momentum theorem method used in [lzaguirre and Paul19851.In the second step of this procedure.

So the total Measurement of the Motor and Drive Inertiamotor and drive contribution ateach joint was determined by anidentification method. This contribution is considered separately A parameter identificationmethod was used t o learnthefrom the I,, puma sliders term of the link itself because the motor and drive totalrotationalinertiaateachjoint.Thisinertiaincludes t,heinertia seen through the reduction gear does not contribute to the effective motor and drive inertia and the contribution due .

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 puma uk 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.