The symbols [ q q ] and puma creepers [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 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.

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 puma rihanna 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 puma fenty *J elements;

And reduction of these expressions with four relations that hold on these 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 as in 2. The number of unique puma slides non-zero Christoffel symbols required The first step was carried out with a LISP program.

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 the second step of this procedure.

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 order Mgto measure these parameters. The mass of each component was r is theinertiaabouthe axis of puma fenty slides rotation;determined with a beam balance; the cenotfergravity was located is the weight of the link;by balancing each link on a knife edge, once orthogonal to each w is thdeistance fromeacshuspensionaxis;

And the diagonal terms of the inertia dyadic were measured wire to the axis of rotation;with a two wire suspension. 1 is the oscillatiofnrequency in radians per second;The motor and drive mechanism at each joint contributes to is thelength of thesupporting wires.the inertia about that joint an amount equal to the inertia of therotating pieces magnified by the gear ratio squared. The drivesand reduction gears were not removed from the links.