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Thirty four lumped constants are needed 1.Symbolic puma shoes for women 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 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.

Of the reductionfrom 126 to 39 2 kf3za" cos(82)cos(82 d 3 ) uzm3 cos2(e2) unique Christoffel symbols, 61 eliminations are obtained with the 2 Mzza3 cos"(82 03) a$m3 c0s2(82 83) general equations, 14 more with (9)and a puma shoes men further 12 with (10). $2 a2a3m3 eos(Bz)<�oos(82 6 3) JpYy sin"(62) (2) Step four requires differentiating the mass matrix elements withrespect to the configurationvariables.Themeans to carry Jz=, cos2(82) 2 dzdsms 2 Mz2a2 cos2(&) outdifferentiationauto,naticallyhavebeenavailableforsome a;mz cos2(&) d i m s dZm2 J2zz Jizz JizzCalculationsrequired: 37 multiplications,18additions.

from puma shoes for men 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 wristmass and the Measurement Toleranceexternal dimensions of the individual links. 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.

If one is carefulwhenreleasing the link, it Link 2 17.40is possible to start fundamentalmodeoscillationwithout visi- Link 3 4.80blyexcitingany of the other modes. The relationshipbetween Link 4* 0.82measured puma shoes women properties and rotational inertia is: Link 5* 0.34 Link 6* 0.09 * This method was suggested by Prof. David Powell. Link 3 wiCthomplete LVrist 6.04 Detached Wrist 2.24 * Values derived from external dimensions; f 2 5 % . The positions of the centers of gravity are reported in Table 5. The dimensions rz! ry and rz refer to the x, y and z coordinates 513of the center of gravity in the coordinate frame attached t o the Table 5 . Centers of Gravity.

Link 4: The origin is at the intersection of the axes of joints * Values derived from external dimensions; &25%. 4 5 and 6; 24 is along the axis of rotationand The effective torsional spring methodof inertia measurement was appliedateachjoint.Themotor and drive inertia, Imotor, direct.ed away from link 2; Y4 11 Z3 whenjoint were foundby subtractingtheinertialcontributiondue to the arm dynamics, known from direct measurements, from the total 4 is in the zero position. inert,ia measured.Theuncertainty in the total inertia measure- ment is somewhat higher at joint one becauseof the larger frictionLink 5: The origin coincides withthat of frame 4; Z5 puma thunder is di- at that joint.

The gear ratios,maximummotortorque, and break away torque for eachjoint of thePUMA is reported in Table 7. The maximum motor torque and break away torque values have been taken from data collected during our motor calibration process. Thecurrentamplifiers of the Unimatecontrolleraredriven by 12 bit D/A converters, so the nominal torque resolution can be 7btained by dividing the reported maximum joint torqueby 2048. Table 7 . Motor and Drive ParametemTheinertiadyadicand effect,ive motorand driveinertia I Joint I Joint 2 Joint 3 Joint 4 Joint 5 Joint ti Gear [img]http://www.simplypotterheads.com/images/lose/puma thunder-367nfo.jpg[/img] Ratio 107.36 53.69 76.01 71.91 76.73terms are reported in Table6.ÿþ d i m 3 dZm3 2 puma slides 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 C eating 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, theRNE 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.

Of the reductionfrom 126 to 39 2 kf3za" cos(82)cos(82 d 3 ) uzm3 cos2(e2) puma fenty unique Christoffel symbols, 61 eliminations are obtained with the 2 Mzza3 cos"(82 03) a$m3 c0s2(82 83) general equations, 14 more with (9)and a further 12 with (10). $2 a2a3m3 eos(Bz)<�oos(82 6 3) JpYy sin"(62) (2) Step four requires differentiating the mass matrix elements withrespect to the configurationvariables.Themeans to fenty by puma carry Jz=, cos2(82) 2 dzdsms 2 Mz2a2 cos2(&) outdifferentiationauto,naticallyhavebeenavailableforsome a;mz cos2(&) d i m s dZm2 J2zz Jizz JizzCalculationsrequired: 37 multiplications,18additions.

The mass of each component was r is theinertiaabouthe axis of 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 puma thunder spectra 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, 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 to theinertialforcesattheotherjointsinthearm.

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 wristmass and the Measurement Toleranceexternal dimensions of the individual links. 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.

If one is carefulwhenreleasing the link, it Link 2 17.40is possible puma football boots to start fundamentalmodeoscillationwithout visi- Link 3 4.80blyexcitingany of the other modes. The relationshipbetween Link 4* 0.82measured properties and rotational inertia is: Link 5* 0.34 Link 6* 0.09 * This method was suggested by Prof. David Powell. Link 3 wiCthomplete LVrist 6.04 Detached Wrist 2.24 * Values derived from external dimensions; f 2 5 % . The positions of the centers of gravity are reported in Table 5. The dimensions rz! ry and rz refer to the x, y and z coordinates 513of the center of gravity in the coordinate frame [img]http://www.simplypotterheads.com/images/lose/puma fenty-286dtd.jpg[/img] attached t o the Table 5 . Centers of Gravity.