Design and Analysis of Kinematic Couplings for Modular Machine ...

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tion. The serial multiplication of the HTM’s gives the total interface error at the TCP. First, the nominalgeometries of the interface plates, the kinematic couplings, and the measurement feature are specified. Theinterface plates are perturbed by error in placement of the coupling mounting holes (T holerror ), the kinematiccoupling is perturbed by form error in machining (T formerror ), and the measurement feature (assumedmodular) is perturbed by form error in machining (T ballerror ). Insertion error (T tballinsert ) between the measurementfeatures and the kinematic couplings, and between the kinematic couplings and the interfaceplates (T kcinsert ) is added next. The serial addition of these transformations represents the true interfacetransformation (T interface ), which when extended to the TCP can be compared in magnitude with and withoutcalibration. Assuming full measurement of the contact positions and orientations, the only differencebetween the true and the calibrated kinematic error of the interface comes from the error in the measurementfeature form and offset, the inaccuracy of the measurement system (T measerror ) itself, and the nonmodeledhigher-order effects.44
MeasurementErrorT measerrorInterfaceError Model(In systemcontrollersoftware)CalculatedinterfaceerrorT interface,calINTERFACEPLATE:NominalGeometryKINEMATICCOUPLING:NominalGeometryForm, featureerrors frommachiningT holeerrorForm, featureerrors frommachiningT formerrorX =XInsertionerrorT kcinsertInsertionerror-TrueinterfaceerrorT interface-ΣΣNominal(identity)transformationT interface,nom==Error atTCP withcalibration(
Page 1: Design and Analysis of Kinematic Co
Page 4 and 5: kinematic couplings. Most powerfull
Page 6 and 7: 6. Toward Standard, Low-Cost, Intel
Page 8 and 9: Chapter 44.1 Six-axis industrial ro
Page 10 and 11: Chapter 66.1 Parameter heirarchy fo
Page 13 and 14: Chapter 1Introduction1.1 Motivation
Page 15 and 16: 2. How can the deterministic nature
Page 17: Chapter 2 is an overview of the bas
Page 20 and 21: Figure 2.1: Model of three-ball/thr
Page 22 and 23: For a case study of a simple symmet
Page 24 and 25: contacting space all the way around
Page 26 and 27: 2.2 Canoe Ball CouplingsThe main ca
Page 28 and 29: strength materials) and create a so
Page 30 and 31: ⎧112 ⎛ ⎛ ⎛ --δ ⎛f n ---
Page 32 and 33: F 11 sin( α)- sin( β)0 0 0- 1 D -
Page 34 and 35: contact, and translation of the ass
Page 36 and 37: K1--2⎛3F⎝------⎞ 1= ⎛2 ⎠
Page 39 and 40: Chapter 3Interchangeability of Dete
Page 41 and 42: coordinate frame by a translation a
Page 43: in translation error normal to the
Page 47 and 48: interfaces can approach their indiv
Page 49 and 50: Figure 3.5: Canoe ball mount with i
Page 51 and 52: they directly become the rows of th
Page 53 and 54: δ xcδ ycε interchange=δ zc(3.19
Page 55 and 56: 2. p Sn,1 , p Sn,2 , etc. = Relativ
Page 57 and 58: parameters are directly the points
Page 59 and 60: nominal thickness, and the magnitud
Page 61 and 62: y measy measy ballyy ballzyFigure 3
Page 63 and 64: The angular alignment of the groove
Page 65 and 66: while the couplings and measurement
Page 67 and 68: Complexity Example Calibration Proc
Page 69 and 70: Error Component [units]Valueh tol [
Page 71 and 72: 0.20Tool Point Error [mm]0.150.100.
Page 73 and 74: Figure 3.14: Prototype groove base
Page 75 and 76: Figure 3.17: Interchangeability set
Page 77 and 78: 0.00450.00400.0035MeasuredAfter Exc
Page 79 and 80: 3.7.1 Variable DimensionsThe interc
Page 81 and 82: This model is used in the next chap
Page 83 and 84: appropriate calibration procedures
Page 87 and 88: Chapter 4Machine Case Study: Mechan
Page 89 and 90: ures empirically cause a per shift
Page 91 and 92: 4.2 Current Interface Design and Ro
Page 93 and 94: 4.2.2 Current Robot Calibration Pro
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ally demanded for continuous path a
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In the canoe ball case, design a pr
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unseating, reseating, and measuring
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Although dynamic tests were not run
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For the first step, the coupling lo
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Figure 4.16: Interface plates fitte
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Figure 4.18: Prototype shouldered c
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Knowing 50 N-m of torque would be a
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constraint, then applying a preload
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4.5 Prototype Repeatability TestsWi
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Two test procedures were establishe
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For the basic mounting procedure, s
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torque was more than sufficient to
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The measurements of static quasi-ki
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neighborhood) trial to the outlying
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Deviation [mm]0.200.150.100.050.00-
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Figure 4.44: Canoe ball surface aft
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4.6.1.2 ResultsTable 4.9: Error com
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the accuracy of the base interface
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interface produces perfect intercha
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0.20Tool Point Error [mm]0.180.160.
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Figure 4.49: Split groove canoe bal
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Generally, the concept of a determi
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20 C) and dirt buildup and harsh tr
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Chapter 5Instrumentation Case Study
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that many of them may be used simul
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diameter, with equilaterally triang
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Figure 5.4: Theorized constant temp
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Therefore, with the goal to minimiz
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All heat transfer relations are ref
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Angular drift of the stack was meas
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knowledge of the resistance across
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4. After these six hours of heating
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5.3.3 Results5.3.3.1 Finite Element
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Figure 5.15: Axial displacement con
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0.200.10Tilt Angle [arcsec]0.00-0.1
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superior in disturbance rejection,
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1.801.601.40Temperature [C]1.201.00
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Temperature [C]1.801.601.401.201.00
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0.2000.150Temperature [C]0.1000.050
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of heat, the temperature difference
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0.200 50 100 150 200 250 300 350 40
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Table 5.3 gives the results of the
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0.350.3One-Piece5 Segments1-9 Segme
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copper tube segments. Individual 1W
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Fixed-base parallel manipulators ca
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Chapter 6Toward Standard, Low-Cost,
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The efficiency of the standard mech
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6.1.2 Building and Using a Web-Base
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tor, offers similar design guidance
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other unit can be homogeneous with
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dcontactRcoupLtRoutRinθFigure 6.4:
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parallel arrangement of springs for
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Wireless Close Read ORDirect Entry-
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matted as XML schemas and broadcast
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PROCESS FEEDBACKSYSTEMADMINISTRATOR
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Furthermore, a fourth class of inte
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For datum point (rather than custom
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OFFLINECOMPUTERInteractive display
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Chapter 7ConclusionThis thesis soug
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Appendix AReferencesChapter 2[1] Sl
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Appendix BKinematic Coupling Design
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MLz + FLy*XL - FLx*XL];% Coupling D
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end% Computation of coupling locati
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ctthree = Rethree*sqrt((1/Rgrv3)^2+
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% New ball coordinatesxboneN = xbon
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four))^2)*sign(Abc*delthree+Abd*del
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B.2 Contact Force Calculation for T
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Rpins = 0.5;yo = 0.5;% radius offse
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f2_torquevector = mut*cross(v_fr2_c
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n3_torquevector = cross(v_cont3,v3_
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Appendix CKinematic Exchangeability
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tol_msys = 0.1; % measurement syste
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% Nominal groove normal vectorsn11
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pvr_grooves = randn(3,1).*pt_ps;pvt
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a21b = -1*sin(th2b)/sqrt(1+tan(thg)
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32gt = -cos(th3g)/sqrt(1+tan(thga3_
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% 14 = using offset measurement fea
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function [errorHTM] = errortransfor
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% of a three-pin kinematic coupling
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mag(normal1)*radii(1) + normal1(1)*
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Appendix DAppended Thermal Stabilit
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Temperature [C]0.800.700.600.500.40
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Temperature [C]0.800.700.600.500.40
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Appendix ERobot Calibration Pose Se
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