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Robotica (2003) volume 21, pp. 645653. 2003 Cambridge University PressDOI: 10.1017/S0263574703005198Printed in the United KingdomA three translational DoFs parallel cube-manipulatorXin-Jun Liu*, Jay il Jeong, and Jongwon KimRobust Design Engineering Lab. (Room 210, Building 301), School of Mechanical and Aerospace Engineering,Seoul National University, (South) KOREA 151742(Received in Final Form: April 5, 2003)SUMMARYbased on redundant actuators. And Liu et al. proposed a8This paper concerns the presentation and analysis of a typeof three translational degrees of freedom (DoFs) parallelcube-manipulator. The parallel manipulators are the topol-ogy architectures of the DELTA robot and Tsaismanipulator, respectively, which have three translationalDoFs. In the design, the three actuators are arrangedaccording to the Cartesian coordinate system, which meansthat the actuating directions are normal to each other, andthe joints connecting to the moving platform are located onthree sides of a cube, for such reason we call this type ofmanipulator the parallel cube-manipulator. The kinematicsproblems, singularity, workspace, compliance characteristicof the manipulator are investigated in the paper. Theanalysis results show that the manipulators have theadvantages of no singularities in the workspace, relativelymore simple forward kinematics, and existence of acompliance center. The parallel cube-manipulator can beapplied to the elds of micro-motion manipulators, remotecenter compliance (RCC) devices, assembly, and so on.spatial parallel manipulator with two translational DoFs andone rotational DoF, which has high mobility. They havebeen applied widely to the elds of motion simulator, force/torque sensor, packaging, micro-motion manipulators,medical devices, compliance devices and machine tools. Inthese designs, parallel manipulators with three translationaldegrees of freedom have been playing important roles in theindustrial applications,which is covered by a family of 36 patents.especially, the DELTA robot,911 912Generally, most of these manipulators suffer from bothsingular congurations within the workspace and multiplesolutions of the direct geometric model. The objective of thepaper is to design a three translational DoFs parallelmanipulator which avoids these drawbacks and which canbe well adapted to the applications of micromotionmanipulators, remote center compliance (RCC) devices, andprecision assembly machines. In the design, the threeactuators are arranged according to the Cartesian coordinatesystem, which means that the actuating directions arenormal to each other, and the joints connecting to themoving platform are located on three planes being perpen-dicular to each other too; hence, we call this type ofmanipulator a parallel cube-manipulator. The kinematicsproblems, singularity, workspace and compliance character-istics of the manipulator are investigated in the paper. Thekinematics analysis of the manipulator shows that thesolution for the inverse and forward kinematics is unique forthe reason of interference. The manipulators have theadvantages of high compactness and stiffness, no singular-ities in the workspace, relatively more simple forwardkinematics, and existence of a compliance center. Otheradvantages of this type of parallel manipulator will beinvestigated in the future work.KEYWORDS: Parallel manipulators; Singular congurations;Compliance; Kinematics; Workspace.1. INTRODUCTIONAfter a motion simulator with parallel kinematics chains1was introduced in 1965, parallel manipulators receivedmore and more attention because of high stiffness, highspeed, high accuracy, compact and high carrying capability.And more and more parallel manipulators with speciednumber and type of degrees of freedom (DoFs) have beenproposed. Behi described a 6-DoF conguration with three2legs where each leg consists of a PRPS chain. Hudgens andTesar investigated a device with six inextensible legs where3each leg is driven by a four-bar mechanism mounted on the2. PROPOSAL OF THE PARALLEL CUBE-MANIPULATORbase. Romiti and Sorli introduced a 6-DoF parallel4manipulator named TuPaMan with three legs, each of whichis composed of a double parallelogram, one sliding joint, the5connecting bar, and a ball joint. Austad mentioned a hybridarchitecture with 5 DoFs based on two parallel mechanisms.Pierrot and Company presented a new family of parallel6manipulators with 4 DoFs, which are 3 translations and 17rotation. Kim and his colleague proposed a 6-DoF parallelmechanism named Eclipse-II, which has the advantage ofenabling continuous 360-degree spinning of the platformIn the eld of parallel manipulators, an interesting problemis to nd a method to design a mechanical architecture fora parallel manipulator being given its number and type ofdegree of freedom. After Gough established the basicprinciples of a mechanism with a closed-loop kinematicsstructure in 1947, many other parallel manipulators withspecied number and type of degrees of freedom have alsobeen proposed. Fig. 1 is the general architecture of 6-DoFparallel manipulators. Theoretically speaking, the arrange-ment of the six legs of the manipulator could be at will,* Corresponding author: xinjunl中国科技论文在线646A three translational DoFs parallel cube-manipulatorFig. 4. The Pierrots manipulator.Fig. 1. A general 6-DoF parallel manipulator.spatial 3-DoF 3-RPS parallel manipulator presented byHunt in the early of 80s. The output of the manipulator is16the complex motion, which are one translation and tworotations with continuously changed axes.17 For suchreason, the manipulator has less good applications exceptfor the micro-motion device.18 The similar manipulatorincludes CaPaMan in Italy,19 which has complex DoFs aswhich will lead to some potential 6-DoF parallel manip-ulators, such as a manipulator as shown in Fig. 2, where thelegs are arranged as 3-2-1 style. This architecture has the13application advantage in micro system. The arrangementdisposal of six legs, as shown in Fig. 3, will make themanipulator move freely along a specied direction, whichwell. When we consider three translational parallel manip-ulators, Tsais parallel manipulator11 is worth mentioning.is very useful for the application in industry.14Letting every two legs of the six legs of the manipulator,as shown in Fig. 1 be parallel to each other will lead to a6-DoF parallel manipulator similar to that with revoluteAlthough Tsais manipulator has translations identical withthat of DELTA, this manipulator is not the version ofDELTA. Tsais manipulator is the rst design to solve theproblem of UU chain. There is also another 3 translationalDoFs parallel manipulator, Star, which is designed by Hervbased on group theory.10 Such a kind of parallel manipulatorhas wide applications in industrial world, e.g. pick-and-place application, parallel kinematics machines, andmedical devices.12 In the family of spatial 3-DoF parallelmanipulators, the manipulators with three rotational DoFslactuators presented by Pierrot shown in Fig. 4.15Thenumber of DoFs of the manipulator will be different ifinputs of the two parallel legs are identical. This is actuallya topology mechanism of the DELTA with linear actuators.Similarly, the manipulator shown in Fig. 4 can also beevolved into the DELTA robot. The fact that the outputs oftwo nearby revolute actuators in Fig. 4 are always same toeach other will result in the different output of the movingplatform. Actually, this is the design of the well-knownDELTA robot, as shown in Fig. 5.received much more attention.2023 They have been appliedto the elds of camera-orienting and haptic devices.24,25Another type of 3-DoF parallel manipulator is that themoving platform is connected to the base through four legs.For such a mechanism, it usually consists of 3 identicalactuated legs with 6 DoFs and one passive leg with 3 DoFsconnecting the platform and the base, i.e. the degree offreedom of the mechanism is dependent on the passive legsdegree of freedom. One can improve the rigidity of this typeof mechanism through optimization of the link rigidities toApart from the DELTA robot, there are also many otherparallel manipulators with three DoFs. For example, thereach a maximal global stiffness and precision. This type26of mechanism has been applied to the design of a hybridmachine tool. There are few 3-DoF fully parallel manip-27ulators that can combine the spatial rotational andtranslational DoFs and be further with denite motion(being opposite to the complex motion) except for that ofHALF with three non-identical legs. All these spatial8Fig. 2. The manipulator with 3-2-1 arrangement.Fig. 3. The Hexaglide manipulator.Fig. 5. The DELTA robot.中国科技论文在线A three translational DoFs parallel cube-manipulator647Fig. 6. The three translational DoFs parallel cube-manipulators.parallel mechanisms have some disadvantages in common,i.e. singularity existing in the workspace, more complexforward kinematics problem, and no compliance center,which are very important for some applications. This paperattempts to present a three translational DoFs parallelmanipulator which avoids these drawbacks.The supposed design conceives for the above-mentionedmanipulators can not only make us to understand themanipulators easily, but provide us new conceive to designa manipulator as well. For example, the 6-DoF parallelmanipulators described in references 28,29 can be taken asthe topology architectures of the manipulator shown inFig. 1 by rearranging the six legs. This inspires us to designnew parallel manipulators by rearranging the three legs ofjoints is denoted as Bi (i=1,2,3). And the center of theinterval between the two spherical joints connecting themoving platform for each chain is denoted as Pi(i=1,2,3),which is in one of three sides of the cubic moving platform,respectively. Bi and Pi are the centers of the revolute jointsin each leg for the design of Fig. 6(b). A xed globalreference system :oxyz is located at the intersectionpoint of three axes of actuated prismatic joints with the z-axis and the y-axis directed along the rst and thirdactuation directions, respectively, as shown in Fig. 7.Another reference system :oxyz is located at thecenter of the cubic moving platform. The z-axis and y-axisdirected along P1o and P3o, respectively, as shown inFig. 7. Related geometric parameters are oPi=r andBiPi=L, where i=1, 2, 3.DELTA and Tsais parallel manipulator, which are shown9 11in Fig. 6. In Fig. 6(a), the moving