IROS2019国际学术会议论文集1526

A Mobile Extendable Robot Arm: Singularity Analysis and Design* Seiichi Teshigawara and H. Harry Asada, Member, IEEE1 AbstractInspection and maintenance of equipment inside buildings, such as exit signs, bared pipelines, air vents, and fi re alarms often requires a robot to reach high, hidden, or confi ned areas that are diffi cult for humans to access. Even though these tasks are easy and repeatable, they are still not automated. The Mobile Extendable Robot Arm (MERA) is a movable robot arm with a novel 2-DOF scissor mechanism for reaching a high place and positioning an end-effector. MERA is composed of a locomotion vehicle with a rotation table and a 4-DOF extender arm, itself made of two layers of the 2-DOF scissor mechanism arranged in series. Placing the end-effector at an arbitrary point in space, the 4-DOF arm possesses two degrees of redundancy, allowing access to a point from various directions and enabling obstacle avoidance. In this paper, we present the design and analysis of the 2-DOF scissor mechanism. The 2-DOF scissor mechanism has two rotary actuators for driving the base links individually; consequently, the mechanism can elongate the entire body and tilt at the center of the base shaft. However, we found that the 2-DOF scissor mechanism had a singularity; after analyzing the singularity, we propose two novel solutions to the problem. I. INTRODUCTION Inspection and maintenance workers working inside large buildings, such as factories, hospitals and schools, are fre- quently tasked to access narrow spaces. For example, older buildings often have many bared pipelines and air ducts, especially on the ceilings of basements, and these often stretch in various directions in a complex manner. Workers can access these pipelines from below by using a ladder. However, because maintenance tasks like this can often result in worker injury and decreased productivity, facility staff should not perform every required task manually. Thus, an effective technology is needed to automatically perform easily repeatable but high-risk tasks, such as the inspection of exit signs, bared pipelines, air vents, fi re alarms and the insides of fl uorescent light covers, in order to maintain the safety of users of these buildings. One solution is QuicaBot 1, a quality inspection and assessment robot that can autonomously scan an entire room using cameras and laser scanners to pick up building defects, such as hollowness and cracking, and measure evenness, alignment, and inclination. This technology is usable for inspection of fl oors, walls, and ceilings. However, it is diffi cult to use in confi ned areas, and the detection accuracy relies on the resolution of the cameras and scanners. Other solutions are drones 2 and wall-climbing robots 34. They can easily access higher places, but these robots *This work has been supported by NSK Ltd. 1 The authors are affi liated with the dArbeloff Laboratory for Information Systems and Technology in the Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. seiichi, have a low payload capacity and unsafe for usage inside buildings. Zipper type 56 and chain type 78 mech- anisms possess high rigidity and a high rate of expansion. However, these extendable mechanisms extend only directly upward. Therefore, it is diffi cult to access confi ned areas with complex structure. On the other hand, TSE (Triple Scissor Extender) 9, TSERA (Triple Scissor Extender Robot Arm) 10 realized a high payload capacity and multiple degrees of freedom. However, because these robots are base-mount type and have a singularity in their scissor mechanisms, their workspace is limited by their geometric design. To address this limitation, we propose the Mobile Extend- able Robot Arm (MERA) (see Fig. 1). MERA is composed of a locomotion vehicle with a rotating base and a 4-DOF extender arm, itself made of two layers of 2-DOF scissor mechanisms arranged in series. Each scissor mechanism layer has one revolute and one prismatic degree of freedom. The fi rst layer is high power and long range; on the other hand, the second layer is small and short range, in order to be able to access a confi ned area easily. As the 4-DOF extender arm moves in one plane, 2 degrees of freedom are redundant; this allows access to a target point from above, avoiding obstacles such as pipelines (see Fig. 2). Fig. 1.The Mobile Extendable Robot Arm (MERA) has two layers of 2-DOF scissor mechanisms. The fi rst layer is high power and long range, and the second layer is small and short range, so as to be able to access confi ned areas. In this paper, we present the design, kinematics and singularity analysis of the 2-DOF scissor mechanism that is the key component of the MERA. We found that the 2- DOF scissor mechanism has a singularity; specifi cally, it is impossible to elongate the mechanism directly upward. After analyzing the singularity, we propose a novel solution to the problem. 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 978-1-7281-4003-2/19/$31.00 2019 IEEE5131 Fig. 2.Inspection of a pipeline using MERA. MERA is able to reach the upper side of the pipeline and access a confi ned space with its small extendable arm. II. PROTOTYPE OF THE2-DOFSCISSOR MECHANISM The main benefi t of using a scissor mechanism is its characteristically large expansion rate. Typically, scissor mechanisms are used as lifters that provide portability and accessibility. However, since the traditional scissor mecha- nism can only extend in a direction perpendicular to its base, the work space is limited. The 2-DOF scissor mechanism has two rotary actuators for driving the base links individually; the mechanism can both elongate the entire body and tilt at the center of the base shaft (see Fig. 3). Fig. 3.Prototype for the 2-DOF scissor mechanism. Actuation of the two different DOF, prismatic and revolute, is shown at right. If the two base links rotate in opposite directions, the mechanism extends or contracts. If the base links rotate at the same speed in the same direction, the mechanism rotates around the base shaft, maintaining its length. This driving method has a major advantage for torque and extensional speed of the robot arm. When the arm rotates, the two motors rotate the links to the same direction. Thus, the rotation torque of robot arm is double the torque of one motor. On the other hand, when the arm only expands, the motors drive the links at equal speeds and opposite directions. In this case, the relative rotation speed between the linkages is double the speed of one motor. As a result, the arm can expand and contract very quickly. This driving method is known as ”coupled drive” 11. III. KINEMATICS In this section we show the kinematics of the 2-DOF scissor mechanism. A. Forward kinematics First, we will analyze the forward kinematics. Forward kinematics refers to the computation of the position of the end-effector from joint displacements. A coordinate system is set around the rotation shaft of the base link as shown in Fig. 4. The forward kinematics equations are shown below: xn= 1 2L(cosq1 +cosq2)(1) yn= 1 2L(sinq1 +sinq2)(2) Here, L is defi ned as L = 2li, the total length of one series of links and the theoretical maximum extension length. Fig. 4.Cartesian coordinate model of an ideal n-stage 2-DOF scissor mechanism B. Inverse kinematics Next, we will calculate the inverse kinematics. Inverse kinematics makes use of the system geometry to determine the joint displacements that provide a desired position for each of the robots end-effectors. The inverse kinematics equations are shown below: q1= atan2(yn,xn)cos1 p x2 n+y2n L ! (3) q2= atan2(yn,xn)+cos1 p x2 n+y2n L ! (4) 5132 IV. MODELING FOR SINGULARITY ANALYSIS We implemented the 2-DOF scissor mechanism in a prototype (see Fig. 3), and attempted to extend it upward. However, only the bottom links extended, and only slightly; the middle and the upper links cannot be extended, as if the mechanism were locked (see Fig. 5). We expected that this is due to a mechanical singularity for several reasons. Primarily, the angle of the links is close to 180 degrees, the singular angle of an ideal scissor linkage. Additionally, we considered how structural non-idealities, specifi cally the defl ection of the each link and the clearance of each joint can contribute toward singular behavior. Fig. 5.Demonstration of an attempt to extend the initial 2-DOF scissor mechanism prototype. It is diffi cult for the scissor to expand upward, even when only loaded by self-weight; specifi cally, upper segments of the scissor effectively lock, even when lower segments move slightly. In this section, we detail the modeling of the 2-DOF scissor mechanism for singularity analysis. There are many papers which analyze scissor mechanisms in order to opti- mize their deployment as actuators 121314. However, these papers did not focus on singularity analysis because commercial 1-DOF scissor lifts avoid the singularity by supplementing the scissor mechanism with a high-power linear actuator. We based our model on that developed by Chikahiro et. al. 15. However, their model did not account for clearance at the joints; thus, we modifi ed it to include this phenomenon and predict its effects. Our simulation model can calculate the motor torque needed to drive the scissor mechanism, the load at each joint, the defl ection of the whole structure, and the infl uence of the clearance of each joint. A. Calculation of the forces added each joint A free-body diagram (FBD) for a single scissor segment is shown in Fig. 6; the length of each member is l1+l2, and the inclination angle of the scissor is measured from the vertical direction. This scissor structure was designed by using the equilibrium equations for the FBD. The equilibrium equations for each external force in the x- and y-directions are as follows: H : FA1x+FB1x+FD1x+FE1x= 0 (5) V : FA1y+FB1y+FD1y+FE1y= 0 (6) Fig. 6.Free-body diagram (FBD) for a single segment of the 2-DOF scissor mechanism For the intersecting members, two equilibrium equations can be obtained for the moments at Point C, MC(BD)and MC(AB): MC(BD): 1FB1x+1FB1y+2FD1x2FD1y = 0 (7) MC(AB): 1FA1x+1FA1y2FE1x2FE1y= 0 (8) Where, 1= l1cos, 2= l2cos, 1= l1sin and 2= l2sin. First, consider the case of a cantilever model that has pinned support at Points A1and B1. The matrix equation shown in (9) is directly constructed from the equilibrium equations (5)(8). Equation (10) shows a block-vector ab- breviation of (9). 1010 0101 1100 0011 FA1x FA1y FB1x FB1y = 1010 0101 0022 2200 FD1x FD1y FE1x FE1y FC1x FC1y 0 0 (9) L1 ? FA1FB1 ?T = R2 ? FD1FE1 ?T ? FC10 ?T (10) Where, L1,R2 R4x4 Next, we consider the modeling of the entire 2-DOF scissor mechanism, including the tip and base links (see Fig. 7). In this problem, it is possible to treat the external forces as the left and right segments of internal forces operating on the hinges like at Points Dn1Anand En1Bn. These relationships can be expressed as (11). Equation (12) shows a block-vector abbreviation of (11). FDn1x FDn1y FEn1x FEn1y = FDn1Anx FDn1Any FEn1Bnx FEn1Bny FAnx FAny FBnx FBny (11) ? FDn1FEn1 ?T = ? FDn1AnFEn1Bn ?T ? FAnFBn ?T (12) 5133 Fig. 7.Model of the Entire 2-DOF Scissor Mechanism Moreover, the section forces for each segments can be calculated in a manner similar to that for the single-segment scissor problem. These relationships can be expressed as (13). The equations (12) and (13) can be applied repeatedly to each segment, from segment-(n-1) to segment-1. As the result, we can obtain the load at each joint. ? FAn1FBn1 ?T = L1 n1Rn ? FDn1FEn1 ?T L1 n1 ? FCn10 ?T (13) Fig. 8-(b) shows the FBD of the tip links. From this FBD, we can derive the equilibrium equation as follows. ? FAnFBn ?T = L1 n Rn ? FCn0 ?T (14) Fig. 8.FBD for (a) Base links and (b) Tip links Represented as inputs Anand Bn, the loads at the points D0and E0, can be obtained from (12) and (13). We show the FBD of the base links in Fig. 9-(a). From this fi gure, we can derive the equilibrium equation as follows, in (15). Fox Foy 1 2 =R1 FDox FDoy FEox FEoy ? Fo ?T = R1 ? FDoFEo ?T (15) From (15), we can obtain the motor torque needed to drive the scissor mechanism. When we perform the simulation, the self-weights of components are modeled as concentrated loads. Specifi cally, the self-weights of links are assigned to points Di1Aiand Ei1Bi, (i = 1, 2, ., n), and the self- weights of joints are assigned to points Ci, Di1Aiand Ei1Bi, (i = 1, 2, ., n). The payloads (external forces Wx, Wy) are assigned to point Cn, represented as the force FCn. B. Calculation of the deformation of each link Next, we show the defl ection modeling for each link using mechanics of materials. The load at each joint can be obtained as per the above equation and calculation. As a result, we can estimate the defl ection of each link. First, we calculate the load perpendicular to the link. Fig. 11 shows one segment for clarifi cation and simplicity. The load for each link PDn1, PEn1can be obtain as follows. ? PDn1 PEn1 ? = ? cossin00 00cossin ? FDn1x FDn1y FEn1x FEn1y (16) Fig. 9.FBD for calculating the deformation of one segment of the linkage. Each crossing link is modeled as an overhanging beam, shown at right. Next, we selected the model of an overhanging beam, as shown in Fig.9. The defl ection (Dn1, En1) of the beam can be obtained as per (17). E (N/mm2) and I (mm4) correspond to the Youngs modulus and second moment of area. This model holds for all segments except for the base link. Instead, we modeled the base link as a cantilevered beam (see Fig.10). 5134 The defl ection (D0, E0) of the beam can be obtained as per (18). Dn1= PDn1l2 n(ln1+ln) 3EI En1= PEn1l2 n(ln1+ln) 3EI (17) D0= PD0l3 1 3EI ,E0= PE0l3 1 3EI (18) Fig. 10.FBD for calculating the deformation of the base links. Each crossing link is modeled as a cantilevered beam, shown at right. C. Calculation of new joint positions As is mentioned above, each link is defl ected by a self- weight and external forces, and which causes the defl ection of the whole scissor structure. The deformation due to the link defl ection on the XY plane can be determined by (17) or (18), and the following equation. Dn1x Dn1y En1x En1y = cos0 sin0 0cos 0sin ? Dn1 En1 ? (19) Moreover, when we simulate the displacement of each joint position, we must consider the ”clearance” that contains various tolerances, gaps, and deformations in real mechanical joints. For example: Radial internal clearance of ball bearings: This factor depends on the kind of ball bearings. We can obtain this value from data sheets; a standard miniature ball bearing used in our 2-DOF extendable arm has a clearance between 5 (m) and 10 (m). Deformation of ball bearings depending on an added load: Though this factor is generally smaller than radial internal clearance, it should be considered in the case of a large load. The tolerance between the ball bearing and its housing The tolerance between the shaft and the ball bearing Ideally, every clearance parameters must be estimated in the calculation; however, we simplify by setting one clearance parameter, Ga, and using this parameter to describe the clearance of every joint of the 2-DOF scissor mechanism. Because this clearance holds for each joint, there will be a displacement between the center positions of each joint between a back-link and a forward-link, as shown in Fig. 11. Furthermore, the direction of the clearance Gadepends on the load direction at each joint. The direction at Dn1 and En1can be obtained as per (20). By using the , the clearance on the XY plane can be obtained using (21), and as mentioned above, this parameter is applied to all joints. Fig. 11. The direct infl uence of a clearance Gaat a joint. There arises a positional deviation of magnitude Gain the same direction as the joint contact force. =tan1 Fy Fx (20) Gx=Gacos Gy=Gasin(21) The deformation of the entire 2-DOF scissor mechanism on the XY plane is determined by the defl ection of each link and the clearance of each mechanical joint. Therefore, the new position of each joint is calculated as follows. D0=D(Dx,Dy)+tD(Dx+Gx,Dy+Gy)(22) E0=E(Ex,Ey)+tE(Ex+Gx,Ey+Gy)(23) Similarly, the calculation is performed for all scissor segments, and all points are redrawn from the base joint to next joint. This is illustrated in Fig. 12. Fig. 12.Redrawing the joint positions of the linkage after link deformation and joint clearance deformation are taken into account 5135 V. SINGULARITYANALYSIS In this section, we show the singularity analysis of the 2- DOF scissor mechanism. First, we expect that the cause of singularity is the angle of base link, 170 (deg) as it close to the angle of the theoretical singularity posture, 180 (deg). To verify this, we simulated the necessary motor torque to extend the fully contracted scissor mechanism. The simulation parameters are shown as follows. Material: Aluminum 6063-T5 Density: 2690 (kg/m3) Youngs modulus: 68600 (MPa) Cross-section: square pipe (outer dimension: w=20 (mm), h=20 (mm), inner dimension: wi=16 (mm), hi=16 (mm) Joint parts weight: 21 (g) Number of segments: n = 8 Lengths of links: l1, l2, l3,., l7, l8= 125 (mm) Link angle q1=5 (deg), q2= 175 (deg), (fully com- pressed condition) External force: concentrated load Wy= 0 (N) or 9.8 (N) In this simulation, the self-weight of each link is assigned to the corresponding central point Ci, represented as a concentrated load. We show th