8046bfe0-0a9e-4ed3-9a5d-38f2061b97bf 233 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Kinematik Pantograph (Bsp. gem. Zeichn 65256)

P1 00031 mat mm * :

Drehpunkt Hebel 1

Achsabstände

a1 85 mm * :

a2 435 mm * :

a3 80 mm * :

a4 70 mm * :

P2 a2 - a4 a3 31 mat : mm 435 - 708031 mat

Drehpunkt Hebel 2

x.P2 P2 1 el : mm 435 -

x.P3 x.P2 : 0.435 m * -

y.P2 P2 2 el : mm 70

y.P3 y.P2 : mm 70

Z.P2 P2 3 el : mm 80

y.P4 y.P2 : mm 70

Radien der Hebel

R.H1 97 mm * :

R.H2 80 mm * :

x.P4 a1 - : mm 85 -

R.H3 80 mm * :

R.H4 80 mm * :

Länge Gestänge 1

L.G1 393.856 mm * :

(Distanz PH1 zu PH2)

Länge Gestänge 2

L.G2 331 mm * :

(Distanz PH3 zu PH4)

Winkel Hebel 3 zu Hebel 4

Δα.H34 31 ° * :

α.H1start α.H1end Δdeg get_aHout nval α.H1end α.H1start - Δdeg / : i 1 nval 1 + range α.H1 α.H1start Δdeg i 1 - (* (+ : resa i 1 el α.H1start Δdeg i 1 - (* (+ : resa i 2 el x.P2 R.H2 α.H2 cos * + R.H1 α.H1 cos * - (2^y.P2 R.H2 α.H2 sin * + (2^+ Z.P2 R.H1 α.H1 sin * - (2^+ (sqrt L.G1 ≡ α.H2 π 3 / 2 π * solve max : resa i 3 el x.P3 resa i 2 el Δα.H34 + (cos R.H3 * + (x.P4 α.H4 cos R.H4 * + (- (2^y.P3 resa i 2 el Δα.H34 + (sin R.H3 * + y.P4 α.H4 sin R.H4 * + (- (2^+ (sqrt L.G2 ≡ α.H4 15 solve min : 21 line 11 line 21 line 21 line for 21 line res resa π / 180 * : 21 line :

31

Funktion zur Ermittlung von α_H2 in Abhängigkeit von α_H1

Startwinkel Eingangswelle

α.H1start 90 ° * :

Drehwinkel Eingangswelle

Δα.H1 90 ° * :

Winkel-Schrittweite

Δdeg 10 ° * :

Endwinkel Eingangswelle

α.H1end α.H1start Δα.H1 + : ° 180

Ausgabe Matrix (Winkel in Grad)

mat_wink α.H1start α.H1end Δdeg get_alH2 :

0.3066 - (2^0.1124 - (2^+ sqrt 0.3266

Armstellungen Arme unten (zur Horizontalen gemessen)

φ.arm_li_start 35 ° * : 0.6109

(bei Eingangswelle in Stellung αH1start)

φ.arm_re_start 35 ° * :

α.H1

α.H2

α.H3

(Winkel in Grad)

mat_wink α.H1start α.H1end Δdeg get_aHout : 90 301.3 65.7 100 287.9 79.8 110 275.9 92.8 120 264.8 104.4 130 254.7 114.5 140 245.8 123.1 150 238.7 129.8 160 233.9 134.3 170232136180 233.5 134.6 103 mat

mat get_c13only nrow mat length 3 / : i 1 nrow range res i 1 el mat i 1 el : res i 2 el mat i 3 el : 21 line for res 21 line 21 line :

mat get_c12only nrow mat length 3 / : i 1 nrow range res i 1 el mat i 1 el : res i 2 el mat i 2 el : 21 line for res 21 line 21 line :

mat get_c23only nrow mat length 3 / : i 1 nrow range res i 1 el mat i 2 el : res i 2 el mat i 3 el : 21 line for res 21 line 21 line :

mat get_deltawink nrow mat length 3 / : i 1 nrow range res i 1 el mat i 1 el : res i 2 el mat i 2 el mat 12 el - abs : res i 3 el mat i 3 el mat 13 el - abs : 21 line 21 line for res 21 line 21 line :

mat get_deltawink nrow mat length 3 / : i 1 nrow range res i 1 el mat i 1 el α.H1start 180 π / * - : i 2 < res i 2 el φ.arm_li_start 180 π / * : res i 3 el φ.arm_re_start 180 π / * : 21 line res i 2 el mat i 2 el mat 12 el - abs φ.arm_li_start 180 π / * + : res i 3 el mat i 3 el mat 13 el - abs φ.arm_re_start 180 π / * + : 21 line if 21 line for res 21 line 21 line :

mat_winkH2only mat_wink get_c12only : 90 301.2605 100 287.949 110 275.9136 120 264.8243 130 254.7073 140 245.8302 150 238.6717 160 233.8645 170 232.0264 180 233.4843 102 mat

mat_winkH3only mat_wink get_c13only : 90 65.6815 100 79.7852 110 92.7608 120 104.3606 130 114.5057 140 123.0731 150 129.8007 160 134.2589 170 135.9568 180 134.6103 102 mat

wink_arm mat_wink get_deltawink : 0353510 48.3115 49.1037 20 60.3468 62.0793 30 71.4362 73.6791 40 81.5532 83.8242 50 90.4302 92.3916 60 97.5888 99.1192 70 102.396 103.5774 80 104.2341 105.2753 90 102.7762 103.9288 103 mat

wink_arm_li wink_arm get_c12only : 03510 48.3115 20 60.3468 30 71.4362 40 81.5532 50 90.4302 60 97.5888 70 102.396 80 104.2341 90 102.7762 102 mat

mat_winkH2only 1 1 sys

wink_arm_re wink_arm get_c13only : 03510 49.1037 20 62.0793 30 73.6791 40 83.8242 50 92.3916 60 99.1192 70 103.5774 80 105.2753 90 103.9288 102 mat

mat_winkH3only 1 1 sys

Übersetzungsverhältnis (Winkelbezogen)--> Änderung Ausgangswinkel zu Änderung Eingangswinkel

mat get_i nrow mat length 3 / : i 1 nrow 1 - range üv i 1 el mat i 1 + (1 el : üv i 2 el mat i 1 + (2 el mat i 2 el - mat i 1 + (1 el mat i 1 el - / abs : üv i 3 el mat i 1 + (3 el mat i 3 el - mat i 1 + (1 el mat i 1 el - / abs : 21 line 21 line for 21 line res üv : 21 line :

α.H1

iüber

iü mat_wink get_i : 100 1.33 1.41 110 1.2 1.3 120 1.11 1.16 130 1.01 1.01 140 0.89 0.86 150 0.72 0.67 160 0.48 0.45 170 0.18 0.17 180 0.15 0.13 93 mat

wink_arm_li wink_arm_re 2 1 sys

l.AO 0.425 m * :

l.b 0.652606 m * :

ct 0.0221 m * :

et 0.317 m * :

l.AO 2^l.b et - (2^- sqrt ct + 0.2829 m *

l.AO 2^et 2^- sqrt 0.2831 m *

at 425 mm * :

ct 652.98 mm * :

alphat ct 2^2 at * ct * / acos : ° 39.8064

wink_arm 0353510 48.3115 49.1037 20 60.3468 62.0793 30 71.4362 73.6791 40 81.5532 83.8242 50 90.4302 92.3916 60 97.5888 99.1192 70 102.396 103.5774 80 104.2341 105.2753 90 102.7762 103.9288 103 mat

Berechnung in xy-Ebene

Wellenabstand Getriebekasten

aw a2 a1 - : mm 350

Länge Arme unten

La.u 300 mm * :

(Distanz PS1 zu PS3 resp. PS2 zu PS4)

Abstand Kniegelenke zu Kreuzgelenk

a.kk 425 mm * :

(Distanz PS3 zu PS5 resp. PS4 zu PS5)

x.PS1 aw 2 / - : mm 175 -

Drehpunkte Getriebekasten

x.PS2 x.PS1 - : mm 175

mat get_PS3 nrow mat length 3 / : i 1 nrow range res i 1 el π mat i 2 el π 180 / * - cos La.u * (x.PS1 + : res i 2 el π mat i 2 el π 180 / * - sin La.u * : 21 line for res 21 line 21 line :

mat get_PS4 nrow mat length 3 / : i 1 nrow range res i 1 el mat i 3 el π 180 / * cos La.u * (x.PS2 + : res i 2 el mat i 3 el π 180 / * sin La.u * : 21 line for res 21 line 21 line :

x

y

x

y

wink_arm get_PS3 mm 420.7 - 172.1 374.5 - 224 323.4 - 260.7 270.5 - 284.4 219.1 - 296.7 172.7 - 300 135.4 - 297.4 110.6 - 293 101.2 - 290.8 108.7 - 292.6 102 mat

wink_arm get_PS4 mm 420.7 172.1 371.4 226.8 315.5 265.1 259.3 287.9 207.3 298.3 162.5 299.7 127.5 296.2 104.6 291.6 96 289.4 102.8 291.2 102 mat

mat gett_PS5 nrow mat length 3 / : i 1 nrow range ci mat i 3 el π 180 / * cos La.u * (x.PS2 + (π mat i 2 el π 180 / * - cos La.u * (x.PS1 + (- (2^mat i 3 el π 180 / * sin La.u * (π mat i 2 el π 180 / * - sin La.u * (- (2^+ sqrt : αi ci 2 a.kk * / acos : 21 line for 21 line :

mat gett_delta nrow mat length 3 / : i 1 nrow range Δxi.PS43 mat i 3 el π 180 / * cos La.u * (x.PS2 + (π mat i 2 el π 180 / * - cos La.u * (x.PS1 + (- : Δyi.PS43 mat i 3 el π 180 / * sin La.u * (π mat i 2 el π 180 / * - sin La.u * (- : 21 line res i el Δyi.PS43 Δxi.PS43 / atan : 21 line for res 180 π / * 21 line 21 line :

mat gettt_PS5 nrow mat length 3 / : i 1 nrow range ci mat i 3 el π 180 / * cos La.u * (x.PS2 + (π mat i 2 el π 180 / * - cos La.u * (x.PS1 + (- (2^mat i 3 el π 180 / * sin La.u * (π mat i 2 el π 180 / * - sin La.u * (- (2^+ sqrt : αi ci 2 a.kk * / acos : Δxi.PS43 mat i 3 el π 180 / * cos La.u * (x.PS2 + (π mat i 2 el π 180 / * - cos La.u * (x.PS1 + (- : Δyi.PS43 mat i 3 el π 180 / * sin La.u * (π mat i 2 el π 180 / * - sin La.u * (- : 21 line δi Δyi.PS43 Δxi.PS43 / atan : εi αi δi - : Δxi.PS54 a.kk εi cos * : Δyi.PS54 a.kk εi sin * : xi.PS4 mat i 3 el π 180 / * cos La.u * (x.PS2 + : yi.PS4 mat i 3 el π 180 / * sin La.u * : 21 line 21 line 21 line 21 line 21 line 21 line 21 line 21 line res i 1 el mat i 1 el m 1000 / * : 11 line res i 2 el xi.PS4 Δxi.PS54 - : res i 3 el yi.PS4 Δyi.PS54 + : 21 line 21 line 21 line 11 line for res 21 line 21 line :

PS5 wink_arm gettt_PS5 : mm 0 8.8818 1014 -^* - 232.0573 10 2.3062 - 429.1622 20 5.8914 - 543.1958 30 7.8094 - 618.4782 40 7.2017 - 665.172 50 4.8385 - 690.4165 60 2.1738 - 700.9573 70 0.3576 - 703.4592 80 0.2747 703.4892 90 0.2226 - 703.5067 103 mat

wink_arm 0353510 48.3115 49.1037 20 60.3468 62.0793 30 71.4362 73.6791 40 81.5532 83.8242 50 90.4302 92.3916 60 97.5888 99.1192 70 102.396 103.5774 80 104.2341 105.2753 90 102.7762 103.9288 103 mat

y

x

PS5x PS5 get_c12only : mm 0 8.8818 1014 -^* - 10 2.3062 - 20 5.8914 - 30 7.8094 - 40 7.2017 - 50 4.8385 - 60 2.1738 - 70 0.3576 - 80 0.2747 90 0.2226 - 102 mat

PS5xy PS5 get_c23only : mm 8.8818 1014 -^* - 232.0573 2.3062 - 429.1622 5.8914 - 543.1958 7.8094 - 618.4782 7.2017 - 665.172 4.8385 - 690.4165 2.1738 - 700.9573 0.3576 - 703.4592 0.2747 703.4892 0.2226 - 703.5067 102 mat

PS5xy