puma slides

[Susan Penn]

Of the reductionfrom 126 to puma slides 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 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.

* The French authors seem to assume the use of Cristoffel symbols, while the American authors seem unaware ofBy combining inertial constants with common variable termsand them.CorbenandStehle,inthe 1950 edition of theirexpanding sin2(82) into (1- c o s 2 ( & ) ) , equation (2) can be re- text, derive the results required here; but the derivationduced to: is largely omitted from their 1960 edition.of puma fenty 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 rotation;determined with a beam balance; the cenotfergravity fenty by puma 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.

Themotors were mass of thearm. To makethismeasurementourcontrolsys-left installed in linkstwo and three when the inertia puma thunder spectra 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, but the rotational inertia about each joint was determined. By subtract-data presented below include armature inertia andgear ratios, so ing the arm contributions, determinedfrom direct measurements,these forces can be determined.

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.surethe I,,, Iyyand I,, parameters of linkstwo and three *. 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.

(meters 3=0.003)link. Thecoordinateframesusedareassigned by a modifiedDenavit-Hartenbrrgmethod[Craig 85j. In thisvariant of theDenavit-Hartenbergmethod,frame i is attached to link i, and puma football boots 0.006axis 2i lies along the axis of rotation of joint i. The coordinateframe attachments are shown inFigure 2; theyarelocated as Link 3 -0.070 0.014follows:Link 1: Z axisalong the axis of rotation, Z up; Y1 11 5 Link 3 -0.143 10.014 With Wrist Z2. Link 4* -0.019 Link 5* 0.032Link 2: Z axisalong the axis of rotation , Z awayfrom Link 6* Wrist 0 -0.064 the base; X-Y plane in the center of the link, with X toward link 3.Link 3: 23 11 22; X-Y plane is in the center of [img]http://www.simplypotterheads.com/images/lose/puma fenty-286dtd.jpg[/img] l i d 3; Y is away from the wrist.