Kinematic Analysis of a 5 DOF Upper-limb Exoskeleton with a Tilted and Vertically Translating Shoulder Joint

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1 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) Wollongong, Australia, July 9-12, 2013 Kinematic Analysis of a 5 DOF Upper-limb Exoskeleton with a Tilted and Vertically Translating Shoulder Joint Yeongtae Jung, Student Member, IEEE, and Joonbum Bae, Member, IEEE, Abstract In this paper, an upper-limb exoskeleton with a tilted and vertically movable shoulder joint is proposed. By analyzing the biomechanics of the shoulder, the motion of the upper limb is approximated by including one degree of freedom (DOF), namely vertical translation of the glenohumeral joint, in addition to the three DOFs that are conventionally employed to analyze the motion of the shoulder. Also, the shoulder joint is tilted to avoid singularity problems in the workspace; by tilting the shoulder joint, the singularity position was placed outside of the normal range of motion. This configuration was analyzed using forward and inverse kinematics methods. Because the shoulder elevation affects all the joint angles, the angles were calculated by applying an inverse kinematics method in an iterative manner. The performance of the proposed upperlimb exoskeleton and analysis methods have been verified by simulations. I. INTRODUCTION Exoskeleton systems have been the subject of growing research interest for applications in rehabilitation and powerassistance [1] [5]. Because exoskeleton systems are worn by a human user, careful exoskeleton design is required so that it moves with the natural motion of the user, and does not compromise their safety. Exoskeleton systems are typically designed based on the skeletal system of the human body. However, it is not necessarily possible to mimic the motion of the user s internal joints using the same number of degrees of freedom (DOF) in the articulation of the joints of the exoskeleton. The problem is further complicated by the limited locations at which the actuators can be attached. Thus, exoskeleton systems have been designed based on an abstract skeletal model, which aims to mimic the main motions of a human body rather than the design of the joints. Some demonstrations of lower-limb exoskeletons have actuators only in the sagittal plane while the other joints are passively actuated or even neglected [1] [4]. In lower-limb exoskeletons, simplified designs based on an abstract skeletal model with reduced degrees of freedom may be appropriate since the main motions of the lower limb required for walking or running are in the sagittal plane. However, in upper-limb exoskeleton applications, it may not be possible to limit the DOFs in such a manner because the human arm typically requires multiple degrees of freedom to access and manipulate objects in the workspace. This work was supported by the Global Frontier R&D Program on <Human-centered Interaction for Coexistence> funded by the National Research Foundation of Korea grant funded by the Korean Government(MSIP) (NRF-2012M3A6A ). Y. Jung and J. Bae is with the Bio-Robotics and Control (BiRC) Laboratory, School of Mechanical and Advanced Materials Engineering, UNIST, Ulsan, Korea {ytjung, jbbae}@unist.ac.kr GH AC SC Fig. 1: Illustration of the skeletal structure of the shoulder [8] Various configurations have been proposed for upper-limb exoskeleton systems, but many design issues in ergonomics and kinematics remain [5] [7]. In this paper, a upper-limb exoskeleton system, that employs 5 DOF in order to mimic the complicated motions that arise from the shoulder structure 5 DOF upper-limb exoskeleton system, is proposed. The shoulder is modeled as a 4 DOF joint by adding the shoulder elevation as a vertical movement, and the elbow is modeled as a 1 DOF hinge joint. In order to avoid the singularity problem, the shoulder joint is tilted so that the singularity position is outside of the workspace of the human arm. The performance of the proposed upper-limb exoskeleton, i.e., whether it can reach all points in the normal range of motion, is analyzed in the framework of forward and inverse kinematics. Because shoulder elevation is considered in this system, which affects the positions of all joints, an inverse kinematic problem is solved in an iterative manner. The remainder of this paper is organized as follows. Section II describes the design of the 5 DOF upper-limb exoskeleton system by considering shoulder joint movement and singularity problems. The forward and inverse kinematics analysis is presented in Section III. The simulation results are presented in Section IV, and conclusions and future work are drawn in Section V. II. DESIGN OF THE 5 DOF UPPER-LIMB EXOSKELETON A. Anatomical Analysis of the Shoulder The human arm has been modeled using several different kinematic methods. Due to the complexity of the problem, it is usually modeled in a 7-DOF kinematic system by imposing some simplifications to the arm joints and segments. The shoulder joint can be considered as a ball-and-socket joint with 3 DOFs: flexion-extension, abduction-adduction, and medial rotation. The elbow can be modeled as a single-axis hinge joint with 1 DOF, and the wrist as a ball-and-socket joint with 3 DOFs /13/$ IEEE 1643

2 TABLE I: Change of θ SC θ AC by shoulder elevation [8] θ SC (deg) θ AC (deg) 0 θ < θ 0 30 θ < θ θ < θ θ < θ From an anatomical point of view however, the shoulder joint should be modeled by more than 3 DOF, as many muscles and bones are involved with movement of the shoulder. The shoulder joint is composed of three bones: the clavicle, scapula, and humerus, as shown in Fig. 1, and the movement of the shoulder results from the combined motion of each bone. The main rotation of the shoulder occurs at the glenohumeral (GH) joint of the scapula and the humerus. However, the center of the GH (CGH) moves as a result of motion of the acromioclavicular (AC) joint as well as the sternoclavicular (SC) joint. The CGH can be described by the angles of the SC and AC joints as follows [8]: X CGH = (l c cos(θ SC 90 ) l s sin(θ AC +θ SC )) h h ref (1) Z CGH = (l c sin(θ SC 90 )+l s cos(θ AC +θ SC )) h h ref (2) wherel c andl s is the effective length of Clavicle and Scapula to the shoulder joint. Since the magnitude of the shoulder motion is dependent on the body size, the height of the user, h, is added as a scaling factor; h ref = 180cm was used as a reference value. The relationship between the AC and SC angles and the net shoulder elevation angle, θ, is shown in Table I. Using the relationship in Table I, θ SC and θ AC are obtained from the shoulder elevation angle, θ. Then, the position of CGH, X CGH and y CGH, is calculated by using (1) and (2) as follows: X CGH = X CGH (θ) X CGH (0) (3) Z CGH = Z CGH (θ) Z CGH (0) = d 1 (4) As the shoulder elevation changes from 0 to 180, the variation of the CGH is -22.6mm in the x direction and 117mm in the z direction for a 170cm-tall adult, as shown in Fig. 2a. The corresponding angle, θ, is expressed as dots in the figure. Since the lateral change is relatively small compared with the vertical change, the CGH motion can be approximated by a vertical displacement, as shown in the figure. In this paper, only the vertical movement of the CGH is considered in the design of the upper-limb exoskeleton. The relationship between the vertical movement of the CHG and the shoulder elevation angle is shown in Fig. 2b. After this anatomical analysis of the shoulder, one DOF was added to account for the vertical movement of the CGH. The 5 DOF upper-limb exoskeleton is shown schematically in Fig. 3. θ 1, θ 2, and θ 3 describe the shoulder rotation, (a) CGH change by arm lifting (b) Relationship between the vertical movement of the CGH and the shoulder elevation angle Fig. 2: Variation of the CGH by arm lifting θ 4 describes the elbow rotation, and d 1 describes the CGH elevation B. Singularity of the Upper-limb Exoskeleton In the design of mechanical system, singularities should be avoided since the mechanical system cannot move to a certain direction at the singular position [9]. This is especially important in exoskeleton systems because the user may be injured without appropriate control at the singular position. With the configuration shown in Fig. 3, the upper-limb exoskeleton is in a singular position when the arm is straight forward, i.e., θ 2 = 90. In this position, the rotation axes of θ 1 andθ 3 are collinear; thus, shoulder adduction or abduction 1644

3 TABLE II: Shoulder range of motion [11] Adduction / Abduction Anterior / Posterior elevation External / Internal rotation Max. range (deg) 50 / / / 90 Fig. 3: Initial configuration of the upper-limb exoskeleton (a) Step 1 (b) Step 2 Fig. 4: Tilting of the shoulder joint motions cannot be achieved. Systems employing redundant DOFs have been proposed to deal with such singularity issues. However, a system with redundant DOFs may result in control issues since more than one set of actuations may result in transforms between given co-ordinates [10]. In this paper, the shoulder joint is tilted so that the singularity position occurs outside of the normal range of motion of the arm. The normal range of motion of the arm is specified in Table II. The shoulder is tilted in two steps: the first is a rotation of the exoskeleton around x 0 by α, as shown in Fig. 4a; the second is a rotation about z 0 by β, as shown in Fig. 4b. In this paper, both α and β were set to 50 considering the workspace. The final configuration of the upper-limb exoskeleton with the tilted shoulder is shown in Fig. 5, and it is compared with the original configuration in Fig. 3. In this configuration, the singularity, which happens when the arm is in the straight forward position with the configuration in Fig. 3, happens when the arm pointing to left-up side, which is outside of the workspace. Tilting the shoulder joint to avoid the singularity problem in the workspace has been proposed previously [5]; however, variation of the shoulder elevation has not been considered simultaneously with the tilted shoulder joint. Note that the shoulder elevation is 117mm for a 170cm adult while θ is changed from 0 to 180. Without considering the shoulder elevation, natural motion through the upper-limb exoskeleton is not possible III. KINEMATICAL ANALYSIS OF THE 5 DOF UPPER-LIMB EXOSKELETON The proposed 5 DOF upper-limb exoskeleton with a tilted and vertically translating shoulder joint analyzed by forward and inverse kinematics methods in this chapter. That is, whether the proposed exoskeleton is able to reach any points in the workspace, is checked. A. Forward Kinematics Analysis: DH Parameter The kinematics of the proposed 5 DOF upper-limb exoskeleton is analyzed by the DH (Denavit-Hartenberg) parameters [9]. The coordinate I is the initial coordinate, the coordinate 0 is vertically moved coordinate from the coordinate I, and the coordinate 0 is the tilted coordinate, which is rotated from 0 by α and β. The rest coordinates are specified in Fig. 5. By using the relationship between coordinates in the figure, the DH parameters in Table III are listed. The transformation matrices by the DH parameters were used to calculate joint angles, θ 1, θ 2, θ 3, and θ 4. B. Iterative Inverse Kinematics Given an arbitrary end-effector position (the wrist position in this configuration), the corresponding joint angles can be calculated using inverse kinematics. The coordinates of each joint are specified in Fig. 5; L u and L l are the lengths TABLE III: DH parameters of the proposed configuration Trans. Matrix α i 1 a i 1 d i θ i T I0 0 0 d 1 0 T 00 α 0 0 β T θ 1 T θ 2 T L u 180 +θ 3 T θ

4 Then θ 4 can be obtained by ρ as follows: θ 4 = π ρ (8) Once the elbow is determined from the infinite number of possible solutions to the inverse kinematics problem that arise by considering the physical limitation of the elbow, the transformation of coordinate 4 relative to coordinate I can be specified. Also, the transformation matrix from I to 0, T I0, is determined by the shoulder elevation, d 1, and the tilting angles, α and β, as follows: cosβ sinβ 0 0 cosαsinβ cosαcosβ sinα 0 T I0 = sinαsinβ sinαcosβ cosα d 1 (9) Fig. 5: Final configuration of the upper-limb exoskeleton Since the transformation matrices T I4 and T I0 are determined, the transformation matrix from coordinate 0 to coordinate 4 is calculated as follows. T I4 = T I0 T 0 4 (10) T 0 4 = T 1 I0 T I4 (11) Suppose the transformation matrix from0 to4is obtained as follows: x 41 y 41 z 41 x e T 0 4 = x 42 y 42 z 42 y e x 43 y 43 z 43 z e (12) Fig. 6: Geometric relationship of coordinates used for the inverse kinematics of the upper and the lower arms, and the positions of the wrist and the elbow are given by p w = (x w,y w,z w ) and p e = (x e,y e,z e ), respectively. p 0 = (x 0,y 0,z 0 ) is the position of the CGH after the shoulder elevation, d 1, which is determined from the shoulder elevation in Fig. 2b. Since the shoulder elevation affects the positions of all joints, the joint angles were calculated iteratively. First, the initial value of d 1 is set to 0. The angles, ρ, φ and θ, in the figure were calculated by using the laws of cosines with the geometric relationships shown in Fig. 6 as follows: ρ = cos 1 ( L2 u +L 2 l p 0 p w 2 2L u L l ) (5) φ = cos 1 ( L2 u+ p 0 p w 2 L 2 l ) 2L u p 0 p w (6) θ = 90 (φ sin 1 z w z 0 ( )) p 0 p w (7) The rest angles,θ 1,θ 2 andθ 3, are calculated by comparing T 0 4 which is from the DH parameters. Then, all joint angles are calculated as follows: θ 2 = sin 1 ( y e L u ) (13) θ 3 = sin 1 ( z 42 ) (14) cosθ 2 x e θ 1 = sin 1 ( ) (15) L u cosθ 2 Note that the above inverse kinematics problem is solved by assuming d 1 = 0, i.e., with zero shoulder elevation. After calculating all joint angles with this initial (zero) shoulder elevation, the shoulder elevation is updated using the relationship in Fig. 2b. Using this new value, p 0 is updated, and the inverse kinematics problem is solved again. This iterative procedure continues until the following convergence criterion is satisfied: d 1 (i) d 1 (i 1) < ε (16) where i is the iteration index, and ε is a specified tolerance. In the simulation, it was set to 0.001mm. 1646

5 IV. PERFORMANCE VERIFICATION BY SIMULATION The proposed 5 DOF upper-limb exoskeleton and the kinematic analysis methods have been verified by simulations. A linear path trajectory of the end effector was specified in a normal workspace. The user s height h was set to 170cm, the length of Clavicle, l c, was set to 149.4mm and the length of Scapula, l s, was set to 66.8mm. The length of upper arm L u and the length of lower arm L l were both set to 285mm. Both kinematic models, i.e., with and without shoulder elevation, were tested. Figure 7 shows the arm motions of each model for the given end-effector trajectory. Both simulated data sets indicated smooth motion; however, the kinematic model with shoulder elevation better approximated human arm motion. Figure 8 shows the joint angles of the kinematic model when shoulder elevation was included. All joint angles were calculated using the iterative inverse kinematics method. The average number of iteration of each point was about 3.8, which means that the proposed analysis methods can be applied in real time. Note that the shoulder elevation for the end-effector motion was about 50mm, which represents a significant deviation from the conventional model where the elevation of the shoulder joint is fixed. V. CONCLUSION In this paper, a 5 DOF upper-limb exoskeleton with a tilted shoulder joint that could be vertically translated was proposed and analyzed. The biomechanics of the shoulder joint were studied, and the shoulder joint movement was approximated to a vertical motion. In addition, the shoulder joint was tilted to have the singularity position outside of the arm workspace. Thus, total 5 DOF upper-limb exoskeleton with 4 DOF shoulder joint and 1 DOF elbow joint was proposed. In order to verify that the proposed system was able to reach all points in the workspace, forward and inverse kinematics were applied. Since the joint positions changed with the shoulder elevation, the joint angles were calculated iteratively. The simulated data showed that the full range of motion was accessible using our proposed upper-limb exoskeleton geometry. As a future work, the proposed upper-limb exoskeleton will be actually implemented and verified by experiments. Even the configuration of the upper-limb exoskeleton was proved in this paper, design and control of an actuation module and mechanism will be researched for the implementation of the proposed upper-limb exoskeleton. (a) Simulation of the kinematic models without shoulder elevation REFERENCES [1] A. Zoss, H. Kazerooni, and A. Chu, Biomechanical design of the berkeley lower extremity exoskeleton (BLEEX), IEEE/ASME Trans. Mechatronics, vol. 11, pp , [2] R. Riener, L. Lunenburger, S. Jezernik, M. Anderschitz, G. Colombo, and V. Dietz, Patient-cooperative strategies for robot-aided treadmill training: first experimental results, IEEE Trans. Neural Syst. Rehabil. Eng., vol. 13, pp , [3] S. K. Banala, S. H. Kim, S. K. Agrawal, and J. P. Scholz, Robot Assisted Gait Training With Active Leg Exoskeleton (ALEX), IEEE Trans. on Neural System Rehabilitation Engineering, vol. 17, pp. 2 8, (b) Simulation of the kinematic models with shoulder elevation Fig. 7: Simulation of the kinematic models with and without shoulder elevation 1647

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