puma shoes

ÿþwhere A(q) is the n X n kineticenergymatrix; a l l puma shoes = 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.

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 puma trainers 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; puma suede

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,, 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 puma sliders 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.

By subtract-data presented below include armature inertia andgear ratios, so ing the arm contributions, determinedfrom direct measurements,these forces can be determined. from the measured total inertia, the motor and drive inertial con- The parametersof the wrist linkswere not directly measured. tributions were found.The wrist itself was not disassembled. But the needed parameterswere estimatedusingmeasurements of the puma uk wristmass and the Measurement Toleranceexternal dimensions of the individual links.

Tolerance values are reported with the values for link 3 plus wrist, as these are the original measure- ments. 6. T h e Measured PUMA 660 Parameters "9 The mass of links 2 through 6 of the PUMA arm are reported in Table4;the mass of link 1in not included becausethat link was Figure 1. The two wire suspension used for Rotational not removed fromthe base. Separately measured mass and inertia Inertia Measurement. terms are not required for link one because

that link rotates only about its own 2 axis .