設(shè)計(jì)與氣動(dòng)平移三自由度并聯(lián)機(jī)器人的實(shí)驗(yàn)測(cè)試

1、Design and experimental test of a pneumatic translational 3dof parallel manipulatorH. Giberti, P. Righettini, A. TasoraPolitecnico di Milano, Dipartimento di Ingegneria Strutturale -STMP.zza L. da Vinci 32, 20133, Milano, Italygibertimech.polimi.it,righettinimech.polimi.ittasoramech.polimi.itAbstrac

2、t:Parallel robots exhibit high stiness, low weight and low dynamic forces, mostly because of the closed loop chains implied by their structure, and allow the po-sitioning of the actuators on the truss. These characteristics outline the possibility of actuating such kind of robotic devices by means o

3、f pneumatic actuators.The position control of pneumatic cylinders through proportional valves satises the positioning accuracy of many industrial applications, where the features of the parallel robots and the performances of the servo-pneumatic cylinders may allow fast spatial movements with high p

4、ay-load.The current work presents the mechatronic design of a low-cost pneumatic parallel manipulator, named TORX, where three pneumatic cylinders have been used to control the three translational DOFs of the end eector through three couples of universal joints. 1IntroductionMechanical industries ar

5、e showing a growing interest to devices based on parallel kine-matics, because these architectures often provide excellent performances in terms of sti-ness/weightratio if compared to traditional serial robots. This is expecially true when considering applications involving packaging applications, a

6、ssembly lines, or pick and place automation in general, where the benet of a sti architecture allows the achievement of light -hence extremely fast-robotic manipulators.In similar contexts, parallel robots can perform many tasks which are traditionally performed by 4DOF SCARA robots, that is applica

7、tions where high operating speed is mandatory. For example, the DELTA architecture developed by R.Clavel 1has been adopted with success in cookie-packaging lines, thank to the fast speed of this extremely light, yet sti, parallel robot.A denite advantage of parallel architectures is the fact that, i

8、n most cases, actuators can be placed on the truss, hence allowing the design of very light moving parts, even when adopting powerful and huge motors because their mounting wont move as the end-eector moves. This is one of the main reasons which encouraged us to adopt linear pneumatic actuators for

9、a low-cost parallel robot. In fact pneumatic cylinders could be hardly used for serial robots, but they can be easily employed in a parallel device because cylinders and accessories would be simply xed to the truss, thus achieving a limited weight for the moving parts.Also, most applications of pick

10、 and place do not require all 6degrees of freedom for the end eector, since 3or 4can be enough. This means that specic parallel kinematic trusscylinderlinear guideuniversaljointshaftuniversaljointFigure 1:Side, top and perspective view of the TORX parallel robot.schemes can be developed in order to

11、provide just the three x,y,z translation in space of the end eector, avoiding extra complexity of further actuators like in the 6-DOF Stewart platforms. Therefore, dierent solutions have been developed to obtain pure x,y,z traslation of the end eector, without rotation, such as the 3-UPU scheme 2whe

12、re three couples of universal joints are used to keep the end-eector alignment constant and independent from its cartesian motion.Starting from these considerations, we developed a 3-DOF kinematical scheme similar to the 3-UPU robot, with three universal joints mounted on three shafts. However, the

13、pure translational motion of the end eector is provided by driving the pivot points of the three legs along linear guides on the truss, instead of changing the lenght of the shafts with prismatic guides. Hence, our scheme is rather 3-PUU, and allow us to x on the truss either the pneumatic linear ac

14、tuators and their heavy prismatic guides, with evident benets in terms of little moving masses and simplied design.2Kinematics of the robotLet consider the 3-PUU scheme of gure 2, where three inextensible shafts with universal joints on both ends are used to join the end eector to the three linear b

15、earings which slide on vertical ground-xed guides.Applying the Kutzback or the Gruebler formulas, one gets the degrees of freedom of the structure. In this case, considering all the revolute joints which build up the universal joints:n dof =6 n bodies 5 n revolutes 5 n prismatics that is, in the thr

16、ee-dimensional case, n dof =3as expected, showing that three coordinates of the end eector can be controlled by moving the pivot points on the linear guides through three actuators.Now consider the special case where each universal joint on the end eector shares the same mounting alignment of the co

17、rresponding universal joint on the other end of the shaft, that is the pivot on the bearing of the linear guide.With this assumption one can move the ground position of pivot points and, as far as Figure 2:Main geometric parameters of the TORX architecture.the pivot points are not rotated, the align

18、ment of the end eector will remain constant, thus allowing just pure x,y,z translation. Proof of this property for 3-UPU robots can be found in D.Gregorio 3,and can be extended to the 3-PUU architecture as well.With the above assumptions on pure translation of the end eector, we can easily write the

19、 equations for the direct and inverse kinematics of the robot, using a geometric approach. Considering the geometric parameters of gure 2, we can write the three vectorial closure equationsa i + d i + l i b i p = 0(1where the unknown terms are the lenght of di . Hence, after some algebraic manipulat

20、ions, one gets the inverse kinematics in analytical closed form:d i =p z ± ( e i 2 p x 2 p y 2+2e ix p x +2e iy p y +( l i 2(2where e i = a i b i , and d i is the joint-coordinate of the i -th linear actuator as a function of the carthesian position of the end-eector p i .Note that two solution

21、s exist, according to the fact that there may be symmetric mountings of the rods about the x-y horizontal plane.The forward kinematic, as for most parallel machines, is more complex than the inverse kinematics. In fact we found both a closed form analytical solution and a numerical solution:here we

22、expose the latter.Starting from the closure equations 1one can write the following system:2A 2xA 2y A 3x A 3y · p x p y = C 1 C 2C 2 C 3 (3where A ix =e ix e 1x , A iy =e iy e 1y and C i =( l i 2 (d i p z 2 ( e i 2. The system must besolved iteratively, updating p z =d 1 d 12 p x 2 p y 2+2e 1y

23、p y +2e 1x p x +l 21 e 21 d 21until convergence. Figure 3:Jacobian in xy plane. Figure 4:Working volume.Figure 5:Eective volume.3Design and optimizationIn order to choose the dimensions of the linkages and the stroke of the actuators it is necessary to nd a good compromise between wide working volum

24、e and manipulator stiness 5.Therefore we developed a MATLAB program which optimized the geometry of our robot, trying to achieve good dynamical performances in the entire working volume. For this purpose, it is necessary to know the determinant of the IK/FKcoordinate transfor-mations (seeg.3.We foun

25、d that, for actuators with a stroke max d i =800mm , we get a good working volume and satisfactory dynamic properties with l i =1100mm and a i =600mm. The nal working volume is reported in g.3, showing also the volume of the upward symmetric mounting. Note that the eective working volume is delibera

26、tely limited by a cylinder with diameter r wa =600mm, as in g.5.We also studied the dynamic performance of the robot by using our in-house multibody software 6,which helped us to choose the proper actuators (namely,three double-acting pneumatic cylinders with a 50mm diameter and 800mm stroke, each p

27、roviding 1037N of max static thrust at 6bar.4ControlThe control scheme of a single actuator is represented in gure 6. The signal coming from the linear encoder is processed by an encoder-counter board which is mounted on a commercial PC (550Mhz Pentium III processor, 128Mb RAM. Then, through another

28、 I/Oboard, an apposite analog signal is sent to the 5/2proportional valve which feeds the pneumatic cylinder. The PC performs the closure of the control loop, thank to an operating system working in hard real time (RT-LinuxV 2.2, a real-time release of the popular OS 8which easily allows a sustained

29、 thick of 0.001s.The implemented control scheme (g. 7 is based on the PID theory, consisting on two loops, the inner acting on speed and the outer acting on position. To this controller, we added an open speed loop acting in feedforward mode. We obtained experimentally the curve of pistons steady-st

30、ate speed, as a function of valve opening. This experimental Figure 6:Control devices (single actuator Figure 7:Scheme of controllerdata is used to tune the feedforward contribute. The formulas used in our controller are based on the mathematical model of the pneumatic system 9,a theoretical backgro

31、und which is founded on the elliptical approximation of ows in outlets 8.We improved the controller by implementing a strategy which compensates the asym-metric shape of cylinder chambers (asa consequence of the piston rod. Depending on the direction of the movement of the actuator, dierent sets of

32、constants for the PID con-troller have been used, for a total of 3sets. The rst set of constants is used for pistons shrinking, the second for expansion, the third is applied to the situation of zero speed. Customizing this latter set of values is mandatory if one wants to achieve an high stiness of

33、 the robot in stationary conditions, and exploits very high values in PID constants. In order to avoid the discontinuities caused by sudden activations of the feedforward eect, we decided to modulate such contribution as a function of the acceleration of the system:the feedforward eect works when th

34、e speed must change, but fades away when speed must be constant.5TestsWe tested the prototype of the robot (g.8 with dierent pay loads and various trajec-tories, in order to measure the precision and the upper limits for performances. As an example, for a 20kg pay-load repeating a pick-and place tra

35、jectory of 300x300mm with v max =2m /s, the cartesian error is less than 10mm while moving, and less than 2mm at the positioning.Our tests showed that the disadvantage of low precision of pneumatic actuators is counterbalanced by the benet that the robot performances are scarcely aected by in-creasi

36、ng payloads, because the precision remains almost constant even when moving heavy loads, up to 30-40kg. For instance, the graph of g. 9shows the set-point error for an axis, while moving 30kg on a fast and oddly-shaped trajectory:the joint error is under 20mm during fast motion and about 1mm at the

37、positioning.6ConclusionThe adoption of standard pneumatic actuators allowed us to design a low cost parallel robot with high pay-load and high operating speed. This design, based on a 3degrees of freedom kinematic scheme, can perform basic tasks like pick-and-place cycles with0.8 setpoint axis n.1 p

38、osition m axis n.1 position m error in axis n.1 position m 0.7 0.6 0.5 0.4 m 0.3 0.2 0.1 0 -0.1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 time s 6 6.5 7 7.5 8 8.5 9 9.5 10 Figure 8: The TORX robot Figure 9: Example of setpoint vs. real motion enough precision for industrial applications. Future researches

39、 will be addressed either at improved control strategy, either at a new joint design exploiting reduced backlash. References 1 R.Clavel, M.Bouri, S.Grousset, M.Thurneysen, A new 4 D.O.F. parallel robot: the Manta, The International Workshop on Parallel Kinematics Machines, UCIMU, Milano 1999. 2 R.Di Gregorio, V.Parenti-Castelli, Inuence of the geometric parameters of the 3-UPU parallel manipulat