The symbols [ q q ] and [q"] are puma creepers notation for the n(-l)/Z-vector of Creating 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.

RNE 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. Thirty four puma rihanna 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 puma fenty required to describe the arm. either Lagrange's or the Gibbs-Alembert formulation.

In thethirdstepthe 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) puma slides in terms of partial derivatives of kinetic energy matrix *J elements;

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.

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 puma fenty slides learnthefrom the I,, 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 .

The tolerance values assigned to calculated parameters were de-With this arrangement a rotational pendulum is created about termined by RMS combination of the tolerance assigned to eachanaxisparallel toand halfwaybetween the suspension wires.The link's center of gravity must lie on this axis.The inertiasuspension method of measuring the rotational inertia requires dyadic and center of gravity parameters of link 3 were measuredknowledge of parameters that are easily measured.