An Introduction to Robot Kinematics. Renata Melamud
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1 A Itrdut t Rt Kemt Ret Memud
2 Kemt tude the mt f de
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9 rtg term f Υ
10 rt g the -A d -A
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16 θ θ θ θ HMGEEUS RERESEAI uttg t t Mtr θ θ θ θ θ θ θ θ ht we fud dg trt d rtt ddg wth d Smpfg t mtr frm θ θ θ θ H Hmgeu Mtr fr rt pe, fwed Rtt rud the -
17 R Rtt Mtre 3D K,et retur frm hmgeu rep θ θ θ θ Rtt rud the Z-A R θ θ θ θ Rtt rud the -A R θ θ θ θ Rtt rud the -A
18 H Hmgeeu Mtre 3D H 44 mtr tht dere trt, rtt, r th e mtr rt wthut rtt H Z Z A A Rtt wthut trt Rtt prt: Cud e rtt rud -, -, - r mt f the three.
19 A H A Hmgeeu Ctued. he (,, pt f pt retve t the urret rdte frme u re. he rtt d trt prt e med t ge hmgeeu mtr IF d L IF th re retve t the me rdte frme. A
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21 Z A J I Z K J I Z Suttutg fr K J I A Z
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24 F r w r d K e m t
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26 Empe rem: u re hve three rm tht trt ut ged the -. Eh h egth,, 3, repetve. u te the frt e t mve Υ, d the dgrm ugget.fd the Hmgeeu mtr t get the pt f the ew dt the frme. 3 Υ 3 Υ 3 3 H R (Υ * ( * R (Υ * ( * R (Υ 3 Υ.e. Rttg Υ w put u the frme. rte the g the. Rttg Υ w put u the frme. d ut u re the 3 3 frme. he pt f the ew dt retve t the 3 3 frme (,. Mutpg H tht pt vetr w gve u the rdte f the ew pt retve the the frme.
27 Sght vrt the t ut: Me the ew dt the rg f ew rdte 4 4 frme 3 Υ 3 4 Υ H R (Υ * ( * R (Υ * ( * R (Υ 3 * 3 ( 3 h te u frm the frme t the 4 4 frme. Υ he pt f the ew dt retve t the 4 4 frme (,. Z H te tht mutpg the (,,, vetr w equ the t um f the H mtr.
28 Mre Frwrd Kemt Devt -Hrteerg rmeter
29 Devt-Hrteerg tt Z ( - ( - Z ( - ( - d Υ α ( - IDEA: Eh t ged rdte frme. Ug the Devt- Hrteerg tt, u eed 4 prmeter t dere hw frme ( rete t prevu frme ( -. HE ARAMEERS/ARIABLES: α,, d, Υ
30 he rmeter Z ( - ( - ( - ( - d Z u g the tw ut ug the 4 prmeter Υ α ( - (- eh Deft: (- the egth f theperpeduretwee the t e. he t e the e rud whh revut te pe whh re the Z (- d Z ( e. hee tw e e vewed e pe. he mm perpedur the hrtet e etwee the tw -e d perpedur t th -e.
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33 he Devt-Hrteerg Mtr θ θα θα ( ( θ θ α θ α ( ( α α ( ( ( α α ( ( d d Jut e the Hmgeeu Mtr, the Devt-Hrteerg Mtr trfrmt mtr frm e rdte frme t the et. Ug ere f D-H Mtr mutpt d the D-H rmeter te, the f reut trfrmt mtr frm me frme t ur t frme. ut the trfrmt here Z (- α ( - (- (- ( - d Z Υ
34 3 Revute Jt Z Z d rmeter e Devt-Hrteerg L te tht the te h tw ue: α (- (- d θ dere the rt wth t vre d prmeter. dere me tte f the rt hvg umer vue fr the vre. θ θ -9 d θ
35 Z Z α (- (- d θ d θ θ -9 d θ Z ( ( ( Z te: the D-H mtr wth (- d.
36 θ θ θ θ α (- (- d θ θ θ -9 d θ h ut rtt rud the Z θ θ θ θ θ θ d θ θ h trt fwed rtt rud the Z h trt d the d fwed rtt rud the d Z ( ( (
37 I v e r e K e m t Frm t t Age
38 A Smpe Empe Revute d rmt Jt Cmed (, Fdg Υ: θrt( Mre Spef: θrt( rt( pefe tht t the frt qudrt Υ S Fdg S: S (
39 Ivere Kemt f w L Mputr (, Gve:,,, Υ Fd: Υ, Υ Υ Redud: A uque ut t th prem de t et. te, tht ug the gve tw ut re pe. Smetme ut pe. (,
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