Design, Simulation and Implementation of a 3-PUU Parallel Mechanism for a Macro/mini Manipulator Zheng Ma, Aun-Neow Poo, Marcelo H. Ang Jr , Geok-Soon Hong, and Feng Huo,  Abstract— Parallel mechanisms have the advantages of high involved continuous contact between the robot end-effector rigidity, high precision and fast movement in its workspace. It is and the workpiece, and the simultaneous control of the force at a most suitable mechanism to serve as the mini manipulator in a the point of contact. Such force/position controlled operations macro/mini manipulator as the mini manipulator needs to have include high-precision edge and surface finishing operations fast response and high resolution in positioning. In this paper, often encountered in the precision engineering, aerospace, and the design of a 3-PUU parallel mechanism to be used as such a marine industries. mini is presented. Failures are encountered during the process of simulation and implementation of the parallel mechanism. Since an adequate workspace and a sufficient Causes of the failures are analyzed and solutions are proposed to payload-carrying capacity are required in the performance of overcome these. Based on the lessons from building the first their tasks, industrial robots are often designed with long and prototype, improvements were made to the second prototype large arms. With its large mass and inertia [1], it is thus which effectively removed the shortcomings resulting in a mini difficult to control such a single robotic arm in applications which met the requirements for its intended application. which require position, force or force/position control and achieve high accuracy with a fast response simultaneously. I. INTRODUCTION A proposed solution is to implement a compact The development and application of robotics has made end-effector with a small limited workspace which can have a much progress since the first programmable industrial robotic high bandwidth and high accuracy in positioning and have this arm, the Unimate, was invented in 1961. Compared with carried by a larger but slower robotic arm. This configuration human operators, industrial robots have the advantages of high is commonly referred as a macro/mini manipulator, where the precision, repeatability and speed of motion, and high large robotic arm is referred to as the “macro”, and the smaller dexterity. They can also work in environments hazardous or and faster end-effector referred to as the “mini”. The unsuitable for human beings and, with large robots, are capable macro/mini manipulator has the advantages of a large of carrying and moving, with higher speeds and accuracy of workspace provided by the macro robotic arm, as well as a fast motion, heavy workpieces. In addition, except for downtime and high-accuracy response provided by the mini [2]. for maintenance, they are 24/7 workers who do not need rest or holiday leaves and can thus improve productivity and speed of Considerations which need to be taken in the design of a production. mini manipulator depend on what tasks it is being developed for. In this paper, a mini manipulator designed for polishing When used appropriately, industrial robots can reduce the and deburring tasks is discussed. The normal forces that need need, not only of unskilled labourers but also skilled workers, to be applied by the polishing or deburring tool on the in industry. As a result, they have found widespread workpiece are estimated at up to 100 N and a few Newtons for applications in repetitive operations such as material handling polishing and deburring respectively. The optimum exerted and assembly, welding and spray painting. To date, most of the force depends on the type of operation, the material of the applications of industrial robots are for non-continuous contact workpiece and the type of tool used. A rough type of operations, operations which do not require the robotic sanding/polishing operation using a sanding/polishing pad end-effector to be in continuous contact, and with a controlled which has a large area of contact with the workpiece surface level of contact force, with the workpieces. will require a large exerted force whereas a small exerted force Recent advances in robotics technology have allowed the will be needed for a fine finishing operation with a smaller development of robotic arms with increased speeds and polishing pad. precision of motion and with greater build-in intelligence. The profile of the surface of the workpiece that is to be There is now increasing interest in developing and employing operated on is assumed not to have sudden rapid changes such these devices for more challenging tasks, including those that a workspace in the form of a sphere with a diameter of labour-intensive and low-productivity operations which 40mm will be sufficient for the mini end-effector. During a polishing or deburring operation, the macro manipulator *Research supported by SIMTech-NUS Joint Laboratory and A*STAR. carries the mini manipulator (end-effector) along a desired Zheng Ma is with the Advanced Robotics Center and the SIMTech-NUS reference path parallel to and at a small distance away from the Joint Laboratory (Industrial Robotics), National University of Singapore, surface to be polished or from the edge of the workpiece to be Singapore, 117580. (Corresponding author. Phone: +65-91188562; Email: deburred. For optimum operation, the orientation of the mpemz@nus.edu.sg). end-effector should have a predefined orientation with respect Aun-Neow Poo, Marcelo H. Ang Jr, Geok-Soon Hong and Feng Huo are with the Department of Mechanical Engineering, National University of to the surface, or edge, of the workpiece. While being moved Singapore, Singapore, 117576. (Emails: mpepooan@nus.edu.sg, along this reference path by the macro, the mini moves in such mpeangh@nus.edu.sg, mpehgs@nus.edu.sg and huofeng@nus.edu.sg). FinE-R 2015 Page 42 IROS 2015, Hamburg - Germany The path to success: Failures in Real Robots October 2, 2015 a way as to exert the desired normal force on the workpiece. prismatic joints move in a direction perpendicular to the base Since the mini is always in contact with the surface or edge of platform and are attached symmetrically at 120 degrees apart at the workpiece, and as long as there are no sudden and large Ai , where i  1,2,3 , to the base platform. As shown in Fig. 1, change to the surface or edge of the workpiece, the workspace of the mini will not need to be large to perform the polishing or two universal joints (universal joints) connect the end of each deburring task. prismatic joint to the top platform. The axes of the two universal joints are parallel to each other and perpendicular to Based on the aforesaid considerations and using feedback the prismatic joint. According to the Chebychev-Grübler– from users with experience in polishing and deburring Kutzbach criterion [3], the number of degrees-of-freedom is operations, a 3-DOF PUU(Prismatic-Universal-Universal) given by: parallel mechanism, inspired by the Delta robot was selected j for the mini manipulator. This 3-DOF translational parallel  M  3(N 1 j)   fi   mechanism (TPM) has only pure translational motions and was i1 designed to have a cylindrical workspace with a diameter of where N is the total number of links, j the total number of 40mm and a height of 30mm. joints, and fi , ( i  1,2,3 ) the degrees of freedom of link i . For In the design process, solid models were first created to the mechanism shown in Fig. 1, the total number of links simulate and to analyze the motions, and to evaluate the (including the base link) is N  8 , the total number of joints stresses and deformations in the various links and components is j  9 , and the degree of freedom is fi  1 for the prismatic when it is subjected to the maximum design applied forces and joints and fi  2 for the universal joints. Thus torques. During the simulation study of its motions, unexpected motions with extra degrees of freedom were  M  3(8 1 9)  31 6  2  3   observed which caused the mini manipulator to take on and the mechanism shown in Fig. 1 has three postures in which the platform on the mini end-effector was degrees-of-freedom with all being translational motions as will not purely translated but was rotated from its starting position. be elaborated on in the next section. This ensures that the top A kinematic analysis based on the 3-DOF translational motion platform is always parallel to the base platform. fails to explain these unexpected motions since the assumptions made in the kinematic analysis does not hold top platform U‐ joint when the mechanism is not in parallel with its starting position. B3 B2 P3 O’ To reduce the overall cost and time, the universal joint U‐ joint P2 components are directly ordered off the shelf for implementation. The parallel mechanism appears to have B1 Prismatic notable backlash. The resulting precision of the mechanism is joint poor and cannot serve as the mini manipulator which supposed base platform P1 A3 A2 to have high accuracy in positioning. The mechanism is modified eventually to overcome the O backlash problem and retains the same kinematics as previously designed. As a result, the working range and mobility of the mechanism meets the requirement. Together with a proper control algorithm, the mechanism can be used to serve as the mini manipulator which has a fast response and A1 high precession in positioning. In this paper, the 3-PUU parallel mechanism is first Figure 1. Structure of the 3-PUU parallel mechanism. described and a standard kinematic analysis is derived under assumptions. Unexpected motions in simulations are shown, with a brief analysis of the reason why it happens. Problems of backlash and positioning accuracy encountered in implementation is discussed with an analysis of an off-the-shelf universal joint structure. Improvements of the mechanism architecture and joint options are presented which overcomes the failure from the simulation as well as the real implementation. II. MECHANISM DESCRIPTION AND KINEMATIC ANALYSIS A. A 3-PUU Parallel Mechanism The structure of the 3-PUU parallel mechanism designed is shown in Fig. 1 with three identical limbs connecting the base platform to the top platform. Fig. 2 shows the structure for one of the limbs. From the figures, it can be noted that the three Figure 2. One of the limbs of the 3-PUU parallel mechanism. FinE-R 2015 Page 43 IROS 2015, Hamburg - Germany The path to success: Failures in Real Robots October 2, 2015 B. Kinematic Analysis of 3-DOF Translational Motion  z i   L2  ( x  xi ) 2  ( y  yi ) 2  z   With knowledge of the 3-DOF translational mobility, the kinematic model of the parallel mechanism can be derived [4]. In the same way, the forward kinematics can be obtained The top view of the base and top platform is shown in Fig. 3, by applying the same constraint equation. where Ai and Bi are the locations where the prismatic joints and the universal joints are mounted to the base and the top III. FAILURES IN SIMULATION AND IMPLEMENTATION platform respectively. Coordinate Frame O and Frame O’ are With the kinematic model obtained, the parameters R, r and respectively attached at the centre of the base and the top L were chosen to meet the workspace criteria. Solid models platform. The distance from the center of the platforms to Ai were then established for motion and stress analysis, the and Bi are R and r respectively. Let the displacement of the ith former to confirm the translational motions of the top platform prismatic joint attached at Ai be zi. All the universal joints are within the specified workspace and the latter for sizing the passive. components for strength and stability. Since the parallel mechanism are constrained to have only translational motions, the transformation matrix for rotation During simulation, some unexpected results were observed from frame O’ to frame O is an identity matrix. Let the position when the top platform moved away from being parallel to the vector of Frame O’ in Frame O be base platform. Unacceptable motion performance was also obtained with the first prototype developed using off-the-shelf  [ c ]O  ( x y z )T   universal joints. These will be discussed in the following A2 sections. B2 A. Extra DOF observed in Simulation R Solid models of the parallel mechanism were created using r the software SolidWorks®. Motion studies were done A3 B3 simulating motion at the three prismatic joints. This caused the three lower universal joints, P1, P2, and P3 in Fig. 1, to move vertically. Various combinations of linear motions for the three prismatic joints were used to study the movement of the top platform relative to the base platform, as well as to verify the B1 size of workspace of the parallel mechanism. A1 The top platform was expected to remain parallel to the base platform at all times since the design of the mechanism Figure 3. Top view of base platform(left) and top platform(right). constrained it to have only 3-DOF translational motion. However, it was noted that for some motion combinations of According to the mechanism structure shown in Fig. 1 and the prismatic joints, the top platform does not always remain the geometric conditions shown in Fig. 3, the inverse and parallel to the base platform but moved into a non-parallel forward kinematics of the parallel mechanism can be obtained. mode of motion after remaining parallel for some time. Fig. 4 By assuming the top platform has only translational motion shows an example of how the roll-pitch-yaw angles of Frame with respect to the base platform, position vector Bi in frame O’ with respect to Frame O change with time for one such instance. From the figure, it can be seen that the top platform O’ is moves with only translational motion for about 11s after which [ Bi ]O '  (r cos i r sin  i 0)T , it has rotational motions.    1  30 , 2  150 , 3  90 Therefore the position vector Bi in frame O is  [ Bi ]O  (r cos i  x r sin  i  y z )T   and the position vector Pi in frame O is  [Pi ]O  (R cosi R sini zi )T   For all three limbs, if the distance between the two universal joints, Bi to Pi is L. The constraint equation can then be written as  [Bi  Pi ]O  L   After substituting Bi and Pi into (7), we have ( x  xi ) 2  ( y  yi ) 2  ( z  zi ) 2  L2 ,    xi  ( R  r ) cosi , yi  ( R  r ) sin i Figure 4. Roll-pitch-yaw angles oftop platform for non-paralle motion. The inverse kinematics thus can be obtained as FinE-R 2015 Page 44 IROS 2015, Hamburg - Germany The path to success: Failures in Real Robots October 2, 2015 To explain the unexpected rotational motion, the a hole to accommodate the external shaft and a dowel pin is assumption of pure translational motion was reviewed. A used to hold the shaft to the joint as shown in the figure. typical drawing of a universal joint is shown in Fig.5. Ux Uy Figure 6. Universal joint(double) [7]. Link side UzP Figure 7 shows the first prototype of the mini manipulator Platform UzL mechanism using these universal joints. Three linear actuators, side labeled with 0, 1 and 2, are used for the prismatic joints. Each link connecting the prismatic joint to the top platform is made up of a circular shaft with a universal joint at each end. The universal joint at one end of each link is fixed to a linear actuator and the other end to the top platform. Figure 5. Rotational axis of a universal joint. Consider one of the three universal joints attached to the top platform as shown in Fig. 5. With the other end, Pi, of the link fixed, there will be no rotation about the axis UzL, The universal joint can only rotate about the Ux and Uy axes, enabled by the cross component in the joint. With only two degrees-of-freedom, there will not be any rotation about the axis UzP, and thus no rotation of the platform [5]. Since there are three universal joints attached to the top platform, therefore no rotation of the platform is allowed about three axes. When these three axes are linearly independent in 3 , the top platform will lose all the rotational motion and Figure 7. Translational parallel mechanism using U-joints. its 3-DOF motions will be purely translational. Based on this analysis, the rotational motion of the top platform during When the three linear actuators are fixed in any position, simulation as shown in Fig. 4 is thus unexpected. i.e. not moving, the top platform should also remain in a fixed position parallel to the base platform. However, it was found This rotational motion observed in simulation is suspected that with the actuators fixed in their positions, the horizontal to be caused by the loss of independence among the three axes slack of the top platform was 4 to 5 mm, which is unacceptably UzPi. When two or more axes become linearly dependent, the large, together with unacceptably large angular rotations. parallel mechanism will be in a singular position. Unlike the Investigations showed that these unacceptably large motions, singularities in serial-link robots, instead of losing degrees of or “backlash”, are due to the clearances used in the mobility, a parallel mechanism gains extra degrees of freedom manufacture of the mechanical components used. While pure at a singular position [6]. translation motion of the top platform was observed in In Fig. 4, it is likely that the parallel mechanism reached a simulation for which perfect dimensions of the various singular position at about 11s, gained an extra degree of components are used in computation, such perfectly formed rotational mobility and the top platform became non-parallel to parts are not available in practice, thereby resulting in the the base platform. Thereafter, the motion of the mechanism unacceptable results. A close examination of the first prototype was no longer constrained to be purely translational. showed that the exhibited backlash phenomenon is due almost entirely to clearances in the off-the-shelf universal joints used. Referring to the Chebychev-Grübler–Kutzbach criterion, the mechanism should have three degrees-of-freedom when it The universal joint, also known as a Hooke's joint, is a joint is not in a singular position. It is likely that the motion of the or coupling which is commonly used to transmit rotary motion mechanism after passing through the singular position is a from one rigid shaft to another rigid shaft when the axes of the combination of three degrees of motion with both rotation and two shafts are at a small angle to each other. The rotary motion translation. Further investigation will be needed explain and to transmitted is usually in one direction only. Because there is no understand this unexpected simulation result. change in direction of the transmitted rotary motion, the small clearances designed into them for ease of manufacture does not B. Backlash in Implementation cause any backlash problem. The universal joints used in the construction of the first The universal joints used in the TPM mechanism in the prototype were off-the-shelf good quality joints the schematic work here serve a different purpose. They serve as joints of which is shown in Fig. 6. Each side of the universal joint has providing two degrees of freedom (rotary motion) constraining FinE-R 2015 Page 45 IROS 2015, Hamburg - Germany The path to success: Failures in Real Robots October 2, 2015 the motion of the parallel mechanism as required from the are used for their typical functions of transmitting rotary structure shown in Fig. 1. Referring to Fig. 5, the universal motion between two shafts. joints used should rotate only about axes Ux and Uy to cause The first prototype failed to meet the requirements for its the top platform of the TPM mechanism to move. There should intended application and a review of the design, and where it be no rotation about axis UzL or UzP. However, when one side failed, was carried out to come up with the second prototype. of the U joint, say the link side, is fixed and not allow to rotate about its axis UzL, it is observed that the other side has freedom IV. LEARNING FROM THE FAILURES to rotate, about axis UzP, to some significant degree. This is due to manufacturing clearances designed into the joints, in In the process of developing and building the first particular at the four ends of the cross component in the joint. prototype, two valuable lessons were learned. One is the The resulting free-play or backlash is accentuated due to the unexpected results during simulation studies and the other is short lengths of the two rods forming the cross component in the poor performance in the fabricated mechanism due to the joint. The off-the-shelf U joints thus did not have sufficient manufacturing clearances and backlash in the off-the-shelf stiffness along the Uz axes and are not suitable for the TPM universal joints used. mechanism. It is noted that that the top platform of the mechanism does Another significant cause of the free-play or backlash not remain parallel to the base platform under all problem in the motion of the TPM mechanism is due to circumstances. Rather, when starting from a parallel position, clearance applied during the fabrication of the mechanism. As the top platform may move into a mode, or region of its mentioned earlier and with reference to Fig. 6, dowel pins were workspace, where it gains rotational motions after passing used to connect the external shaft to each end of the U joints. through a singular position. This problem occurred during Ideally, the two holes in the U joint and the one in the shaft to simulation when it is put all possible motions within its total accommodate the dowel pin should all be of exactly the same workspace. In practice, this problem can easily be overcome diameter, corresponding to the diameter of the dowel pin, with by constraining the motions of the three actuators such that its their centers perfectly aligned. However, as the holes were workspace clearly does not contain any singular positions. drilled at different times, if they were to be made of the same diameter with very little clearance, the centers of the holes The first prototype has unacceptably poor accuracy in its need to be perfectly aligned in order for the dowel pin to be motion and positioning. The top platform has some degrees of inserted. Alignment of the holes, when drilled separately, is not mobility, of about 5 mm due to backlash when the actuators are easily done. As such, the fabricator introduce some clearance fixed in their positions. This mobility is not acceptable as the and made the hole in the shaft larger (Fig. 8) than that of the mini manipulator is required to have high stiffness and holes in the U joint, which is of the same diameter as the dowel precision. It is clear that this problem is caused by the pin. While this allowed for the insertion of the dowel pin even manufacturing clearances in the off-the-shelf universal joints if there is some slight misalignment of the holes during used. To overcome this problem, while still using lower-cost manufacture, it caused significant rotational free-play or off-the-shelf components, other type of joints which has the backlash between shaft and the universal joint. Here again, the same motion properties as universal joints but do not suffer rotational backlash is accentuated by the small diameter of the from the same backlash problem was investigated as shaft, and thus the length of the hole in it. replacements. The mechanical structure to replace the link with its pair of universal joints is shown in Fig. 9. It is composed of four ball joints connected in a way to form a parallelogram. B A D C Figure 8. Clearamce between dowel pin and the external shaft connected to the U-joint. Figure 9. Improved parallel mechanism with ball joints. The unsatisfactory motion of the first prototype of the According to the property of an ideal parallelogram, the mechanism is largely due to the clearances in the off-the-shelf opposite sides of the parallelogram will always be parallel. universal joints and the limited machining accuracy of the Therefore, the side AB will always be parallel to the side CD in fabricated parts. Information on clearances for off-the-shelf Fig. 9. Since the side CD is mounted parallel and fixed to the base platform, the side AB will also always be parallel to the universal joints are not readily available from manufacturers base platform. As there are three limbs in the TPM mechanism, as such information may not have been important when they FinE-R 2015 Page 46 IROS 2015, Hamburg - Germany The path to success: Failures in Real Robots October 2, 2015 there are three parallelogram with three sides AB attached to resolved. Further research will be done to determine the exact the top platform. cause of the rotational motions of the 3-PUU parallel These three parallelogram limbs are attached to the top mechanism during simulation. platform such that the three sides AB all lie in a plane and the Unacceptable free play and backlash was exhibited by the top platform is parallel to this plane. Since all the three sides first prototype. This was not evident in the simulation AB are parallel to the base platform, the plane formed by them experiments which are based on perfectly manufactured will be parallel to the base platform. Therefore, the top components. Investigations showed that this problem was due platform will also always be parallel to the base platform. With to inaccuracies in the dimensions of the components used. The the top platform constrained to be parallel to the base platform, main cause was the free play in the off-the-shelf universal and the base platform is fixed and immobile, the motion of the joints used for the first prototype. To overcome this problem top platform will be constrained to be translational only. the universal joints were replaced by off-the-shelf ball joints If there is free play or backlash in the ball joints at A, B, C, forming a parallelogram structure for the three limbs of the or D in Fig. 9, then the parallelogram formed will not be an mechanism. The kinematic model of the mechanism remains ideal parallelogram. In this case, the sides AB may become the same but the free play problem was effectively eliminated non-parallel to the side CD. The amount of non-parallelism and the second prototype exhibits high stiffness and depends on the amount of free play in the ball joints and the length of the sides AB and CD, the longer the sides are, the positioning accuracy. smaller the degree of non-parallelism. Lessons were learned from unexpected outcomes and failures during the simulation experiments and in For the typical applications they are intended for, good implementation. Properly designed simulation experiments quality ball joints have almost no free play or backlash. The may produce results not predicted by theoretical studies as length of the sides AB and CD of the parallelogram are also much longer than the length of the cross component in the these studies are normally based on certain simplifications universal joints. As such, the use of ball joints with a and assumptions, which cannot be completely replicated in parallelogram structure for the three limbs of the TPM simulation experiments. mechanism effectively eliminated the free play and backlash Furthermore, straightforward simulation experiments problem. The resulting second prototype is rigid and has high which are based on perfect physical properties of the precision in positioning. With the actuator fixed in their component parts may not show up possible inadequacies in positions, there is no measurable backlash in the top platform. the design. These inadequacies may show up only in the The backlash found in the first prototype had been effectively prototypes built due to unavoidable imperfections in the eliminated and this second prototype will be suitable as the physical components making up the whole system. mini in a macro-mini manipulator to be used for finishing and deburring applications for which both position and force/position control are required. Unlike a serial-link robot, ACKNOWLEDGMENT the parallel structure of this robotic device gives it the high The authors acknowledge the support from the Collabora- rigidity and thus the capability of exerting large forces on the tive Research Project under the SIMTech-NUS Joint Labora- workpiece in force-controlled polishing applications tory (Industrial Robotics). This work was also supported in part by the Science and Engineering Research Council V. CONCLUSIONS (SERC) A*STAR Industrial Robotics Program Grant 12251 A parallel mechanism, based on the structure of the Delta 00008. robot, was designed and implemented to serve as a mini REFERENCES manipulator, acting as an end-effector, in a macro-mini manipulator configuration for polishing and deburring [1] O. Khatib, "Inertial properties in robotic manipulation: an objective-level framework," The International Journal of Robotics Research, vol. 1, no. applications. 13, pp. 19-36, February 1995. Kinematic models of the mechanism were first obtained [2] Z. Ma, G. S. Hong, M. Ang and A. N. Poo, "Mid-ranging control of a and applied to fulfil the given criteria. Solid models were macro/mini manipulator," in IEEE International Conference on Advanced created to simulate and analyze the resulting motions and Intelligent Mechatronics, Busan, 2015. workspace of the mechanism which was design. Unexpected [3] J. Angeles and C. 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