International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 KINEMATI ANALYI OF VARIOU ROBOT ONFIGURATION Game R. U., Davkhare A. A., Pakhale.. 3, Ekhande. B. 4, hinde V. B.,,3,4 tudent, Dept. of Prodution Engineering, Amrutvahini ollege of Engineering, Maharahtra, India. Aitant Profeor, Dept. of Prodution Engineering, Amrutvahini ollege of Engineering, Maharahtra, India. ---------------------------------------------------------------------***--------------------------------------------------------------------- Abtrat - Robot are very powerful element of today indutry and they are apable of performing many different tak and operation preiely and do not require ommon afety and omfort element that human need, however it take muh effort and many reoure to make a robot funtion properly. Roboti arm are widely ued in indutrial manufaturing. There i no doubt that robot have inreaed in apability and performane through improved mehanim, ontroller, oftware development, ening, drive ytem, and material. The goal of thi tudy i to analyze forward and invere kinemati of robot manipulator. The tudy inlude ue of D-H parameter for tudying of both DK and IK. The tudy model robot kinemati for R, 3R, 3R-P, R, 6R uing algebrai method along with RoboAnalyer and MATLAB. All reult of thee method are ompared and validated.. LITERATURE REVIEW and ontrol. A robot manipulator onit a et of link onneted together either in erial or parallel manner. The FK analyi i imple to do analyi of model and alulate the poition uing the joint angle. But the hallenge i to analyze the IK olution uing the poition. o aim i to tudy omplexity of the IK whih inreae with inreae in the DOF. In thi ae we would be tudying robot onfiguration i.e. R, 3R, 3R-P, R, 6R where R and P tand for revolute and primati joint. The main motive of the tudy i to alulate the robot parameter i.e. tudy forward and invere kinemati uing algebrai method and then validate thi alulation with the output from RoboAnalyer and MATLAB. Key Word: Forward and Invere Kinemati, Robot Manipulator, D-H parameter, Arm Matrix, RoboAnalyer, MATLAB.. INTRODUTION Robot kinemati applie geometry to the tudy of the movement of multi-degree of freedom kinemati hain that form the truture of roboti ytem. The emphai on geometry mean that the link of the robot are modelled a rigid bodie and it joint are aumed to provide pure rotation or tranlation. Robot kinemati tudie the relationhip between the dimenion and onnetivity of kinemati hain and the poition, veloity and aeleration of eah of the link in the roboti ytem, in order to plan and ontrol movement and to ompute atuator fore and torque. The relationhip between ma and inertia propertie, motion, and the aoiated fore and torque i tudied a part of robot dynami. Forward kinemati ue the kinemati equation of a robot to ompute the poition of the end-effetor from peified value for the joint parameter. The revere proe that ompute the joint parameter that ahieve a peified poition of the end-effetor i known a invere kinemati. [] The ontrolling of robot manipulator ha been hallenging with higher DOF. Poition and orientation analyi of roboti manipulator i an eential tep to deign The tudy of forward kinemati i eay a it analyi i imple to do. The hallenge i to do analyi of invere kinemati. The tudy of invere kinemati an be done by variou mean. Thee variou mean i.e. algebrai method [], [3], [4], uing oftware tool uh a RoboAnalyer and MATLAB [] are tudied by variou author. The algebrai method i the traditional way to tudy the kinemati of robot manipulator wherea RoboAnalyer and MATLAB are ued to validate thee mathematial reult. Here we would be uing all three way to ompare their reult and validate the reult. 3. METHODOLOGY The tep followed to do thi tudy are named and explained in the next line along with flowhart a in Fig. :. tudy the robot kinemati both forward and invere kinemati of robot manipulator.. ollet information regarding forward and invere kinemati for variou robot onfiguration under tudy i.e. R, 3R, 3R-P, R and 6R. 3. ollet formulae for thi onfiguration to alulate their parameter for diret and invere kinemati by algebrai method. 4. tudy the RoboAnalyer for variou robot onfiguration and uing the ame alulate the arm matrix and the onfiguration of the robot for diret and invere kinemati.. Jut like tep 4 tudy the MATLAB for variou robot onfiguration and uing the ame alulate the arm matrix and the onfiguration of the robot for diret and invere kinemati. 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 9
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 6. Next ompare the reult of algebrai method and oftware reult for eah of the robot onfiguration. 7. Finally validate the reult for all three way of tudying DK and IK. 4...3 Arm Matrix T = a a a a 4...4 alulation Forward Kinemati θ d a α Bae θ a houlder θ a a = mm θ =6 a = mm θ =3 Fig-: Work Methodology 4. KINEMATI ANALYI OF VARIOU ROBOT MANIPULATOR 4. R Mehanim [Two Axi Planar Artiulated Robot Arm] [] olution P x = a +a P y = a +a P x = mm Invere Kinemati P y = 86.6 mm 4.. Algebrai Method 4... 3D Model 86.6 olution Fig-: 3D Model of Two Axi Planar Artiulated Robot Arm 4... Kinemati Parameter Table θ = 9.99999863 Table-: Kinemati Parameter Table θ = ±3.663 Row of Table Type of θ k d k a k α k HP θ,d,a,α Bae θ a 6 4.. Uing RoboAnalyer 4... Forward Kinemati θ,d,a,α houlder θ a -6 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 9
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 Fig-3: Reult of Two Axi Planar Artiulated Robot Arm for Diret Kinemati 4... Invere Kinemati Fig-6: MATLAB Reult for IK of Two Axi Planar Artiulated Robot Arm 4. 3R Mehanim [3-Axi Planar Artiulated Arm i.e. Mini Drafter] [] 4.. Algebrai Method 4... 3D Model Fig-4: Reult of Two Axi Planar Artiulated Robot Arm for Invere Kinemati 4..3 Uing MATLAB Fig-7: 3D Model of 3-Axi Planar Artiulated Arm 4... Kinemati Parameter Table Table-: Kinemati Parameter Table Row of Table Type θ d a α HP θ,d,a,α Bae θ a 6⁰ θ,d,a,α houlder θ a -6⁰ 3 θ3,d3,a3,α3 Roll θ3 d3 4...3 Arm Matrix Fig-: MATLAB Program for IK of Two Axi Planar Artiulated Robot Arm T 3 = 3 3 3 3 a a a a d 3 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 93
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 4...4 alulation: Forward Kinemati 4.. Uing RoboAnalyer 4... Forward Kinemati θ d a α Bae θ a houlder θ a Roll θ3 d3 olution a =a = mm d 3= mm θ =6 θ =3 θ 3= T 3 = 86.6 Fig-8: Reult of 3-Axi Planar Artiulated Arm for Forward Kinemati 4... Invere Kinemati Invere Kinemati P x = mm P y = 86.6 mm 86.6 olution Fig-9: Reult of 3-Axi Planar Artiulated Arm for Invere Kinemati 4..3 Uing MATLAB θ 3 = θ +θ +θ 3 θ 3 = θ 3- θ +θ θ =9.9999938 θ = ± 3.8634 θ 3 = 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 94
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 4.3.. Kinemati Parameter Table Table-3: Kinemati Parameter Table Row of KP Table Type of θk dk ak αk θ,d,a,α Bae θ d a ±π θ,d,a,α Elbow θ a 3 θ3,d3,a3,α3 Vertial Extenion θ3=⁰ d3 4 θ4,d4,a4,α4 Roll θ4 d4 Fig-: MATLAB program for IK of 3-Axi Planar Artiulated Arm 4.3..3 Arm Matrix 4 4 T 4 = 4 4 a a a a d q 3 d 4 4.3..4 alulation: Forward Kinemati Fig-: MATLAB Reult for IK of 3-Axi Planar Artiulated Arm 4.3 3R-P Mehanim [4-Axi Adept- ARA Robot] [] 4.3. Algebrai Method 4.3.. 3D Model θ d a α Bae θ 877 4 ±π houlder θ 37 VE d3 Roll θ4 Fig-: 3D Model of 4-Axi Adept- ARA Robot olution θ =6, θ = θ 4=3 d 3= mm.866. T 4 =. 4.866 69.8 77 P x = 4 mm P y = 69.8 mm P z = 77 mm 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 9
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 Invere Kinemati 4.3.. Invere Kinemati olution.866...866 4 69.8 77 Due to ertain limitation invere kinemati for thi onfiguration ouldn t be ompleted by RoboAnalyer. o uing Arm Matrix from DK we have alulated IK value uing algebrai method. imilarly for R and 6R i done. Reult θ = 6⁰ θ = ⁰ θ 4 = 3.⁰ d 3= mm 4.6.3.3 Uing MATLAB p 3 or w 3 =d -q 3 -d 4 q 3 i.e d 3 = d -d 4 -w 3 θ d 3= mm 4.3. Uing RoboAnalyer 4.3.. Forward Kinemati Fig-4: MATLAB program for IK of 4-Axi Adept- ARA Robot Fig-3: Reult of 4-Axi Adept- ARA Robot for Forward Kinemati 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 96
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 3 θ3,d3,a3,α3 Elbow θ3 a3 4 θ4,d4,a4,α4 Tool Pith θ4 a4-9⁰ θ,d,a,α Tool Roll Θ d 4.4..3 Arm Matrix T = 34 34 34 34 34 34 34 34 34 ( a a 3 3 d 34 ) ( a a 3 3 d 34 ) d a a 3 3 d 34 Fig-: MATLAB Reult for IK of 4-Axi Adept- ARA Robot 4.4 R Mehanim [Five Axi Artiulated Mirobot α-ii Robot Arm] [] 4.4. Algebrai Method 4.4.. 3D Model 4.4..4 alulation Forward Kinemati Type of θ d a α Bae θ -9⁰ houlder θ 77.8 Elbow θ3 77.8 Tool Pith θ4 a4-9⁰ Tool Roll Θ 9. Fig-6: 3D Model of Five Axi Artiulated Mirobot α-ii Robot Arm 4.4.. Kinemati Parameter Table Table-4: Kinemati Parameter Table Row of KP Table Type of θk dk ak αk θ,d,a,α Bae θ d -9⁰ θ,d,a,α houlder θ a olution θ =3 θ = -6 θ 3=9 θ 4= θ =4 a 4=.8839.36 T =.336.768.986.336.433..866 P x = 4.6 mm P y = 89.6 mm P z = 67.99 mm 4.6 89.6 67.99 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 97
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 Invere Kinemati.8839.36.336.768.986.336.433..866 4.6 89.6 67.99 olution Fig-7: Reult of Five Axi Artiulated Mirobot α-ii Robot Arm for Forward Kinemati 3.4.. Invere Kinemati Reult 4.4.3 Uing MATLAB θ = 3. θ = -9.999 θ 3 = 9 θ 4 = θ = 4 4.4. Uing RoboAnalyer 4.4.. Forward Kinemati 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 98
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 4... Kinemati Parameter Table Table-: Kinemati Parameter Table Row of KP Table Type of θk dk ak αk θ,d,a,α Bae θ -9⁰ θ,d,a,α houlder θ d a 3 θ3,d3,a3,α3 Elbow θ3 d3 a3 9⁰ 4 θ4,d4,a4,α4 Tool Pith θ4 d4-9⁰ Fig-8: MATLAB program for IK of Five Axi Artiulated Mirobot α-ii Robot Arm θ,d,a,α Tool Yaw Θ 9⁰ 6 θ6,d6,a6,α6 Tool Roll θ6 d6 4...3 Arm Matrix r r r 3 r r r 3 r 3 r 3 r 33 p x p y p z Fig-9: MATLAB Reult for IK of Five Axi Artiulated Mirobot α-ii Robot Arm 4. 6R Mehanim [Puma 6 6R Robot] [],[3] 4.. Algebrai Method 4... 3D Model For lat 3 angle i.e. θ 4, θ, θ 6 Fig-: 3D Model of Puma 6 6R Robot 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 99
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 4...4 alulation Forward Kinemati Type of θ d a α Bae θ -9⁰ houlder θ 7 Elbow θ3 94.8 948 9⁰ Tool Pith θ4 68-9⁰ Tool Yaw Θ 9⁰ Tool Roll Θ6 83 4.48 9.99863678 olution θ =6 θ =3 θ 3=4 θ 4= θ =9 θ 6=.489.836 T 6 =.88.866..94.4.969.7 6 44.6 4.. Uing RoboAnalyer 4... Forward Kinemati P x = x =.7 mm P y = y = 6 mm P z = z = -44.6 mm Invere Kinemati Where, Fig-: Reult of Puma 6 6R Robot for Forward Kinemati 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 93
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 4... Invere Kinemati Reult θ =7.46387 θ= 46.3399-6.4i θ3=3.6+3.96i θ 4= θ =9 θ 6= 4..3 Uing MATLAB Fig-: MATLAB program for IK of Puma 6 6R Robot Fig-3: MATLAB Reult for IK of Puma 6 6R Robot 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 93
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7. REULT AND DIUION Table-7: Perentage Error in alulation Robot onfiguration Table-6: omparion of Reult Angle (input in degree ) Method for tudy of IK (output in degree ) Algebrai Robo MATLAB Robot onfiguration Angle (input in degree ) Algebrai Perentage Error (in %) Robo MATLAB Analyer Analyer R onfiguration θ=6 9.99999863 6 6 R onfiguration θ=6.8* -6 θ=3.* -4 3.33* -4 3.33* -4 θ=3 3.663 3. 3. θ=6.3* - θ=6 9.9999938 6 6 3R θ=3.878* -4 3.33* -4 3.33* -4 onfiguration 3R onfiguration θ=3 3.8634 3. 3. θ3= - θ3= -.4 θ=6 3.8* -.7 θ=6 6.34 6 6.4 3R-P θ= - - onfiguration 3R-P θ=..96 d3= onfiguration d3= θ4=3 8.4* -3 3.33* -4.47 θ4=3 9.99747686 3. 9.89 θ=3.64* -6 3.33* -4 θ=3 3.69 3. 3. θ=-6.86* -3.67* -3.67* -3 θ=-6-9.99988837-9.999-9.9993 R θ3=9.83* -4.* -4 onfiguration R onfiguration θ3=9 89.99974 9 9. θ4= - θ4= -.476 θ=4 θ=4 4 4 4 θ=6.87* -.9.83 θ=6 7.46387 9.999 θ=3 4.4* -3 4.47-7.3i.833 θ=3 9.99863678 46.3399-6.4i 9.994 6R onfiguration θ3=4.7* -3.78+3.i.78* -3 6R onfiguration θ3=4 4.48 3.6+3.96i 4.6 θ4= θ4= θ=9 θ=9 9 9 9 θ6= θ6= o from above Table it i imminent that there a minute perentage error in alulation by all the three way of tudying invere kinemati i.e. by algebrai method, uing RoboAnalyer and uing MATLAB. In mot of the ae the reult of RoboAnalyer and MATLAB are ame a ompared to algebrai method. The differene in algebrai method i motly due to the fat that during alulation mot of the value were approximated. Alo from above way of tudying IK and it output, it i lear that the impliity level of tudying invere kinemati goe on inreaing with inreaing robot onfiguration. 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 93
International Reearh Journal of Engineering and Tehnology (IRJET) e-in: 39-6 Volume: 4 Iue: May -7 www.irjet.net p-in: 39-7 6. ONLUION ine the forward kinemati analyi of any robot onfiguration i imple to do analyi of model and alulate the poition uing the joint angle, it tudy i not of muh bother to u. However the greater hallenge i to analyze the invere kinemati olution of the robot onfiguration uing the final poition the robot. Thu the aim wa to tudy omplexity of the IK with inreaing degree of freedom. o in the tudy thi aim have been materialized by mean of three way for analyzing the invere kinemati olution uing algebrai method, uing RoboAnalyer and uing MATLAB. o the tudy of the omplexity of variou robot onfiguration with inreaing degree of freedom i done for robot onfiguration i.e. R, 3R, 3R-P, R, 6R where R and P tand for revolute and primati joint. The reult of thee 3 method ugget that the tudy of IK definitely i of omplex nature for inreaed degree of freedom. In other word, the reult of algebrai method are validated with the output from RoboAnalyer and MATLAB. REFERENE [] erdar Kuuk and Zafer Bingul, Indutrial Roboti: Theory, Modelling and ontrol, IBN 3-866-8-8, pp. 964, AR/plV, Germany, Deember 6. [] Tarun Pratap ingh, Dr. P. ureh, Dr. wet handan, Forward and Invere Kinemati Analyi of Robot Manipulator, International Reearh Journal of Engineering and Tehnology, Vol 4 Iue, February 7. [3] Ahitava Ghohal, Kinemati of erial manipulator, Department of mehanial engineering, Indian Intitute of iene, Bangalore. [4] andipan Bandyopadhyay, Introdution to the invere kinemati of erial manipulator, Department of Engineering Deign, Indian Intitute of Tehnology Madra, hennai [] Manjunath T.., Fundamental of Roboti, Volume-, th Edition, 8, pp 6-7, -4. 7, IRJET Impat Fator value:.8 IO 9:8 ertified Journal Page 933