Design, Manufacturing and Kinematic Analysis of a Kind of 3-DOF Translational Parallel Manipulator

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1 mme.modares.ac.ir 2* mo_taghizadeh@sbu.ac.ir, * : : : Design, Manufacturing and Kinematic Analysis of a Kind of -DOF Translational Parallel Manipulator Mahmood Mazare 1, Mostafa Taghizadeh 1*, Mohammad Rasool Najafi 2 1- Department of Mechanical engineering, Shahid Beheshti University, Tehran, Iran. 2- Department of Mechanical Engineering, University of Qom, Qom, Iran. * P.O.B , Tehran, Iran, mo_taghizadeh@sbu.ac.ir ARTICLEINFORMATION ABSTRACT OriginalResearchPaper Received05March2016 Accepted17June2016 AvailableOnline06August2016 Keywords: Design Manufacturing translational parallel manipulator kinematics analysis workspace. [1]... Parallel manipulators are mechanisms with closed kinematic chains that have been developed in different forms, but these manipulators have several drawbacks such as small workspace, existence of singular points in their workspace, and complex kinematics and dynamics equations that lead to increased difficulty in their control. In spite of this, these mechanisms have been conventionally used in many different industrial applications such as machining, motion simulators, medical robots, etc. To overcome these drawbacks, design and manufacturing of a manipulator with three translational degrees of freedom are provided. Design of this manipulator was based on the possibility of three translational motions for its end-effector. The manipulator degrees of freedom are obtained via screw theory. Basic features, consisting of forward and inverse kinematics, workspace and singularity analyses and also velocity analysis, are considered in this paper. A numerical algorithm is implemented to determine the workspace regarding applied joint limitations and the design parameters were extracted based on whether the desired workspace was achieved or not. The robot motion was created by three pneumatic actuators which receive their commands from pneumatic servo valves. After design steps, the required elements were provided and assembled in a robotic lab. Finally, the simulation results have clearly approved the robot improvement Pleasecitethisarticleusing: : M. Mazare, M. Taghizadeh, M. R. Najafi, Design, Manufacturing and Kinematic Analysis of a Kind of -DOF Translational Parallel Manipulator, Modares Mechanical Engineering, Vol. 16, No. 7, pp. 27-4, 2016 (in Persian)

2 2 : (1 : (2. (. (4. ( ().... -[P2(US)]. -[P2(US)] [,2]..[4].. -.[6,5] [8,7].[9] [10].[11].[12] [1]...[15,14]...[16] -PRS -PRC.[17]

3 Fig.2 Manufactory model of the -[P2(US)] parallel manipulator -[P2(US)] :.[20-18]... ( )(2) = ( 1) + f i j L 2. i. = 6 ( ) +[(6 ) + (6 2) + ( 1)] = (2) (1) Fig.1 Schematic of the -[P2(US)] parallel manipulator -[P2(US)] Table 1 Characteristics of designed robot (mm) )

4 L i. 5. (7) (6) i = + = + (6) (7) cos cos = cos sin (8) sin = 40 = ( 1) cos cos = sin, =, = sin 0 0 = (9) (1) (2) (10) (). = = 0.[21] () : ( ) = ( ) (4) ( ) ( ) 0 (4) (e ) e 2 e 1. = [0 = [0 = [0 ] ] ] (5) (5). (5) Fig. 4 Schematic of one limb of the -[P2(US)] robot -[P2(US)] 4 Fig. Diagram of the -[P2(US)] -[P2(US)]

5 (19) BC 4 2 = + ( )sin + cos sin sin + (19) (19) (20) ) = 2[( )cos + cos cos ] = 2[( )sin + cos sin ] = 2sin = [( )cos + cos cos ] +[( )sin + cos sin ] ++ sin (20) (21) = ( ) + ( ) + ( ) = ( ) + ( ) + ( ) = Table 2 Dimensions and angles of the robot ( 1) (21) 2 (mm) (mm) (mm) Fig. 5 Top view of the -[P2(US)] robot -[P2(US)] 5 cos cos cos = + sin + cos sin 0 sin cos (11) sin 0 + cos + cos cos cos = + sin + cos sin sin (12) + sin C i B i 2 = 2 (11) (10) (1) 2 = + ( )cos + cos cos ( )sin + cos sin + + sin (14) - q i (14) = 2 + 2{ sin + [ + ( )cos cos + + ( )sin sin cos ( )cos + + ( )sin = 0 (15) : = sin + [ + ( )cos cos + + ( )sin sin ]cos (16) Fig. 6 Configuration of the robot for end-effector position of (-0.2,-0.2,- 0.4)m using inverse kinematic analysis (-0.2,-0.2,-0.4)m 6 = + ( )cos ( )sin 2 + (17) (15) (17) (16) -. (18) = ± 2 (18)

6 =0. = = (21) =( = T ). 1 2 = (22) (17) z (17).. ( 1 ) 1 = cossin cossin ( 1 ) 2 = coscos + coscos ( 1 ) 2 = sin sin = + ( )sin = + ( )cos sin cossin cos (24) (2) (2) (2) (24) = Fig.7 Singular point of robot 7 Fig.8 A typical singular configuration for robot for end-effector position of (-0.15,-0.140,-0.145)m (-0.15,-0.140,-0.145)m = =, = = =. (25) (26) (27) (28) = 0, = 0 (29) =

7 mm 600mm (0) ) ( ( = 10, = 10, 55mm) 9 Table Inverse kinematic error in positioning of end-effector at ( = 10, = 10, 55mm) (mm) (mm) (mm) Fig. 10 Workspace finding Flowchart 10 Fig.9 Control of workspace point in ADAMS software

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