Proceedings of the 32nd ISR(International Symposium on Robotics), 19-21 April 2001

HUMAN FACTOR FOR KINEMATIC DESIGN OF A HAPTIC DEVICE Keehoon Kim, Doik Kim, WanKyun Chung and Youngil Youm

Abstract

lems expressing the high stiffness and controlling under a big load. To overcome these defects, parallel type devices are introduced, and they can be used in a precision task due to their high resolution. The representative parallel mechanisms used as the haptic device are the Stewart platform type[3], the pantograph type[5][17], the fivebar type[4], and other hybrid mechanisms[6][15]. However, a major drawback of parallel mechanism is its small workspace. Since all types of haptic devices have merits and demerits, criteria are needed to design it. Human force factors, which can be a reference to design force-reflecting haptic interfaces, have been studied[7][12]. The result can be used to select proper actuators for a haptic device suitable for displaying the tactile sensing. However, human kinematic factors have not been considered deeply since they are very complex. If operator’s workspace can be predicted, a compact haptic device can be designed. In this paper, the workspace of human is calculated through the analysis of human motion. The motion of a human arm can be classified into two motion. The first is for a coarse motion and the second is for a fine motion. When a human manipulates an object, the fine motion is needed. The three-finger grasping haptic motion is considered here. In order to calculate the workspace, coordinate systems are attached to the bones and the poses of the coordinates are found out. Finally, the workspace is calculated by utilizing the developed model. This paper is organized as follows: section 2 classifies the motion of human during manipulating an object and defines “Three-Finger Grasping Haptic Manipulation” which is usual precision grasping. In section 3, the kinematics of the hand is shown from the view point of anatomy. In section 4, the motion range of “Three-Finger Haptic Manipulation” is calculated and section 5 concludes this paper.

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In designing a haptic device, human kinematic properties should be regarded for the sake of cost and workspace. This paper deals with 3-finger precision grasping to define “haptic manipulation” from the view point of anatomy. In this case, the manipulation can be defined by the movement of carpals, metacarpals and phalanges whose properties are mainly determined by constraints of the thumb and the wrist. Since the thumb is considered as a constrained 4 D.O.F. serial manipulator, the kinematic properties can be calculated easily in the range of “haptic manipulation” under the fact that human bone to bone bony ratio is fixed. The result can be applied to design a haptic device.

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Robotics and Bio-Mechatronics Lab., Dept. of Mechanical Engineering Pohang University of Science and Technology Hyoja-dong, Nam-ku, Pohang, Kyongbuk, Korea (E-mail : {khk,doiki,wkchung,youm}@postech.ac.kr)

1. Introduction

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When humans manipulate objects in virtual reality, a haptic device is able to carry the sense of touch to the operator. The device can be used to simulate the tasks which are dangerous or difficult to realize. The haptic interface consists of a control algorithm and a physical device. The control algorithm plays a role of a bridge connecting information of a virtual situation and an operator. Generally, the algorithm maps the force and the velocity between an operator and a virtual environment. On the other hand, the haptic device enables an operator to interact with the environment generated by computer. Therefore, the haptic device should reflect a human motion well in order for a proper interaction between the operator and the virtual environment. In the need of such appliances, various haptic devices have been developed. Berkelman, Butler, and Hollis[1] developed a haptic interface based on the Lorentz magnetic levitation. Since there is no linkage, it can be controlled without consideration of disturbance of the device in actuation and sensing. However, this type has small workspace and low stiffness. Sarcos Inc.[13] introduced a manipulator which is worn around the user’s arm while it is not an exoskelaton type. Massie and Salisbury[2] developed a serial type device which can be controlled by the distal part of a finger. Virtex Inc.[14] made a haptic interface for the entire hand. Until now, many serial type haptic devices have been developed and used in the field of virtual reality and tele-operation. While these types have a large workspace, they have prob-

2. Haptic Manipulation First of all, for the kinematic design of a haptic device the region of operator’s motion should be predicted. However, a haptic device does not have to cover the whole workspace of the human arm since the part for the haptic manipulation is constrained in a small area. In this section, a motion for the haptic manipulation is defined. There are two typical grasping methods when a human

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works with an instrument. The power grasping is used in the operation which needs high force. On the other hand, the precision grasping is used in the manipulation which needs high resolution. The power grasping decreases the dexterity because fingers are over-constrained by an object. If fingers are over-constrained, the ability of manipulation decreases since the absolute force control resolutions of the PIP(ProximalInterPharangeal), the MCP(MetaCarpal Pharangeal), and the wrist are higher than those of the elbow and shoulder [7]. Therefore, the precision grasping is focused for a haptic manipulation. Among the precision grasping, this paper deals with the three-finger grasping which is usually used in writing, soldering and surgery. When an object is manipulated by the three-finger precision grasping, there are three motions. The first one is and “Approach” action. During this action, the motion of shoulder and elbow and the wrist rotation is used as shown in Fig.1. The next is a “Finding the stable gripping” action in Fig.2. In this action, the motion of the wrist and fingers are executed for an easy manipulating motion. Finally, an object is manipulated or felt as shown in Fig.3. This motion uses fingers and wrist mainly. The most important actions for manipulating an object precisely are the second and the third motion.

Figure 4: Anatomy of a right hand ( A : Distal pharanges, B : Middle phalanges, C : Proximal pharanges, D : Metacarpals, E : Trapezium, F : Trapezoid, G : Scaphoid, H : Capitate, I : Hamate, J : Triquetral, K : Lunate, L : Pisiform )

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Figure 5: (a) : extension and flexion, (b) : abduction and adduction(radial-ulnar deviation), (c) : Wrist rotation

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Figure 1: Approach

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Figure 2: Finding the stable gripping

Figure 3: Manipulation

Thus, the precision haptic motion uses only fingers and the wrist. the elbow and the shoulder are not used in precision manipulation by the reason why the resolution of a manipulator is dependent on the joint of the worst resolution. Therefore, in order to distinguish the fine haptic motion from the other motion, the “Three-Finger Grasping Haptic Manipulation” is defined as follows. Definition 1 (Three-Finger Grasping Haptic Manipulation) The three-finger grasping haptic manipulation is a set of

motions which are composed of the movement of carpals, metacarpals, and pharanges and are constrained distal pharanges of thumb, index, and mid finger to manipulate an object. 3. Analysis of the Motion of the Three-Finger Grasping Haptic Manipulation If the workspace is measured through the experiment, its result is dependent on the experimenter’s criterion and the size of one’s hand. Therefore, the workspace of the TFG(Three-Finger Grasping) Haptic Manipulation is measured from the view point of anatomy. This approach is reliable under the fact that human bone to bone bony ratio is fixed[9]. If length of a bone like the distal pharanx of the thumb is known, the other lengths of bones in the hand can be calculated by the ratio. 3.1. Anatomy of Hand A hand consists of 8 capals, 5 metacarpals, 14 pharanges (Fig.4). The capal bones play a role in the motion of the radial-ulnar deviation (Fig.5.(b)) and the flexionextension(Fig.5.(a)). The metacarpals and pharanges help the hand manipulate an object. The hand is similar to a fine manipulator attached on the end of a coarse manipulator which

represents motion of the wrist rotation1 (Fig.5(c)), elbow, and shoulder. 3.2. Kinematics of the Wrist Youm, McMurtry, Flatt and Gillesp [10] studied the wrist motion, and the following results are adopted in this paper.

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Property 1 The trajectories of the hand during radial-ulnar deviation and flexion-extension, when they occur in a fixed plane, are circular and the rotation in each plane takes place about a fixed axis. The center of the rotation lies on the onequarter point of the capitate.

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Property 2 The carpal height, the distance from the base of the third metacarpal to the distal articular surface of the radius is constant during radial-ulnar deviation of the normal wrist.

Figure 6: Coordination of a right hand

From the above properties, the wrist motion2 is independent on the other motion of an arm and fingers. Thus, the motion of fingers can be calculated without considering the wrist motion. The workspace of the TFG Haptic Manipulation can be easily calculated by considering the finger and the wrist independently.

Since the index finger and the mid finger have mid pharanges, the index and the mid finger have a larger workspace than that of the thumb and always can cover the workspace of the thumb during the TFG haptic manipulation.

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3.3. Kinematics of the Thumb

Definition 2 (Medial plane) The Medial plane is a plane which includes the capitate and the third metacarpals and is orthogonal to the palmar plane.

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As shown in the previous section, since the motion of the fingers are not related to the wrist motion, this section derives finger motion independently. Especially, the motion of the thumb is the most important since the thumb constrains the motion of the other fingers in the TFG manipulation. Kapandji[11] suggested that the thumb has five degrees of freedom: two D.O.F. in the trapezo-metacarpal joint, two D.O.F. in the metacarpophalangeal joint and one D.O.F. in the interpharangeal joint. However, since the range of deviation of the metacarpophalangeal joint is much smaller than the range of the other joint motion, a metacarpophalangeal joint is assumed to have one D.O.F.. Assumption 1 The thumb has four degrees of freedom: two D.O.F. in the trapezo-metacarpal joint, one D.O.F. in the metacarpophalangeal joint and one D.O.F. in the interpharangeal joint. When an object is manipulated by the three fingers, the deviations of the index finger and the mid finger are very small in the TFG haptic manipulation. Moreover, since the third metacarpal represents the wrist motion, by the property 2 the thumb motion can be described with respect to the medial plane which is defined as:

Assumption 2 During the TFG haptic manipulation, the end of the distal pharanx of the thumb is on a plane3 parallel to the medial plane. On the plane the workspace of index and mid finger includes the workspace of the thumb. From the above two properties and assumption 1, seven frames can be attached from the wrist to the end of the thumb as shown in Fig.6. The zeroth and the first frame are on the one-quarter point of the capitate to represent the wrist motion and the zeroth frame is the world coordinate system. The second and third frame are on the trapezo-metacarpal joint and the second frame is the base of the thumb motion. The fourth and fifth frame are on the matacarpophalangeal joint and interpharangeal joint, respectively. The origin of the sixth frame is the contact point between the thumb and an object. 4. Workspace of the TFG Haptic Manipulation The motion range of fingers are mainly determined by the thumb motion as indicated in the previous section. This section derives the workspace of the thumb firstly, and the whole workspace of the TFG haptic manipulation by combining it with the workspace of the wrist motion.

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wrist rotation is not the motion of the wrist joint. This motion is operated by the radius bone and the ulnar bone. Therefore the wrist rotation is not included in the TFG Haptic manipulation 2 the extension-flexion and the radial-ulnar deviation

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plane is one of the planes parallel to the medial plane. It is determined by the size of a grasped object and the contact type between fingers and an object.

4.1. Derivation of the Range of Thumb

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By using Fig.6 and assumption 2, the workspace of the TFG Haptic manipulation can be considered as the motion of a serial manipulator which has 4 links and 6 rotary joint with several constraint as shown in Fig.6. There are two constraints in the thumb motion: the joints have limits and the origin of the sixth frame, O6 is always on a plane parallel to the x1 -y1 plane(medial plane) . More consideration on the orientation of the second frame, O2 − x2 y2 z2 , is needed. Fig.7(a) shows the pose of the thumb with respect to the palmar plane, OABC, and the medial plane, OCF G, when the thumb is on the neutral position4 . OE which includes the metacarpal of the thumb and OH which includes the second metacarpal are on one plane in the neutral position. The y2 -axis is orthogonal to the plane 4OEH and the x2 -axis is on the line OE in Fig.7(a). The arrangement of ligaments attached at the base of the first metacarpal makes the first metacarpal be in the pose of Fig.7(a) at the neutral position. Especially, since a ligament attached to the second metacarpal is on the frontal plane, a plane 4OEH in Fig.7 is on the frontal plane of the thumb at the neutral position. The angle ∠BOC is 40◦ from Fig.7(b). The angle ∠F OC is 35◦ from Fig.7(c). The angle ∠HOC is 20◦ from Fig.7(d).5 Using following geometry, we can find α, the angle between the plane 4EOH and 4BOH, and the angle β ∠EOH. let OC = 1

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=

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OH OB

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4OBH 4OEB   OB · sin ∠BOH −1 α = cos = 56.555◦ OE · sin β cos α =

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−37◦ −50◦ −30◦ −10◦ −70◦ −80◦

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= Rz (θ0 )Rx (90◦ ) = Rz (θ1 )T (l0 , −l2 , −l1 )Ry (20◦ ) Rx (−α)Ry (β) = Rz (θ2 )Rx (90◦ ) = Rz (θ3 )T (l3 , 0, 0)Rx (−90◦ ) = Rz (θ4 )T (l4 , 0, 0)Rx (−10◦ ) = Rz (θ5 )T (l5 , 0, 0)Ry (90◦ )Rz (90◦ )

(12) (13) (14) (15) (16) (17)

Here, the limit of joints are adopted from [10][11], and are

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position of rest of the thumb muscles measured values are different from people. However, we can assume that the angles are close to these values for normal humans.

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Now, all of the transformation matrices are known.

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(OE · cos β − OH)2 + (OE · sin β)2 = EH (8) ! 2 2 2 OE + OH − EH β = cos−1 = 44.667◦ (9) 2OE · OH

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Figure 7: The neutral position of the thumb

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tan ∠HOC = tan20◦ = 0.364 tan ∠BOC = tan40◦ = 0.839 tan ∠F OC = tan35◦ = 0.700 q 2 2 2 BC + OC + CF = 1.152 q 2 (BC − HC)2 + BE = 0.846 1 = 1.064 cos ∠HOC 1 = 1.305 cos ∠BOC

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HC BC CF

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< θ0 < θ1 < θ2 < θ3 < θ4 < θ5

< 20◦ < 45◦ < 45◦ < 20◦ < 0◦ < 0◦

(18) (19) (20) (21) (22) (23)

4.2. Workspace of TFG Haptic Manipulation without the Wrist Motion Using the above transformation, the workspace of TFG haptic manipulation without the wrist motion can be calculated6 . Fig.8 shows the positions of the transformation matrix 1 T6 with l0 = 0.818, l1 = 1.182, l2 = 0.833, l3 = 2.09, l4 = 1.37, l5 = 1.007 and z = −l1 . In this case, θ0 = θ1 = 0 since there is no wrist motion. 6 The 7l

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workspace is calculated numerically by simulation to l4 are from [9] and l0 to l2 are data from the x-ray picture of a man

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Figure 10: The workspace of TFG Haptic Manipulation

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Figure 8: The workspace of the thumb on the plane, x1 − y1 , and z1 = −l1

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Figure 9: The normalized workspace of thumb

Figure 11: The workspace during flexion(50◦ ) and ◦ extension(45 ) of the wrist

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The origin in Fig.8 is the point (0, 0, −l2 ) of the first frame, O1 − x1 y1 z1 and the plane is parallel to the medial plane. The center of the trapezo-metacarpal joint,i.e., the origin of the second and the third frame, O2 and O3 is on the (l0 , −l2 ) in Fig.8. As indicated in section 3, the thumb motion is occurred at a plane parallel to the medial plane. If the length of the bone is normalized, the size of the workspace of any human hand can be calculated. The values in Fig.9 are normalized by the distal pharanx of the thumb. If the length of the distal pharanx of a thumb is determined, the workspace can be always found for different people by using the bony ration. 4.3. Motion Range of the TFG Haptic Manipulation

Fig.9 shows the workspace of the TFG haptic manipulation without the wrist motion. By using this workspace, the workspace of the whole grasping motion including the wrist motion can be calculated since this workspace is independent of the wrist motion by property 1. The whole workspace of the TFG haptic manipulation can be found by adding the wrist motion to the thumb motion, i.e , the frame 0 T1 is added to the thumb and the angles θ0 and θ1 are not fixed, in this case. The result is shown in Fig.10 by using the calculated workspace in Fig.9. The plane 4OAB in Fig.10 is parallel to the medial plane. The plane of Fig.8 is 4OAB in Fig.10. Fig.11 shows the TFG haptic motion on the plane 4OAB in Fig.10, and represents the workspace of the TFG haptic manipulation during the flexion and the extension in

Fig.5(a). The plane 4O0 CDis parallel to the palmar plane and includes the line X − X 0 in Fig.9. X is the farthest point from O0 in Fig.10 when there is no wrist motion. Fig.12 show the TFG haptic motion on the plane 4O0 CD in Fig.10 during the wrist devition in Fig.5(b). The center of rotation in Fig.12 is on the on quarter point of the capitate. Finally Fig.13 and Fig.14 are the normalized workspace viewed at point E and F in the Fig.10, respectively. 5. Conclusion The human kinematic factors should be considered in designing a haptic device. Humans use a specific part of arm for haptic manipulation. In this paper, TFG haptic manipulation is defined and showed that it represents a precision haptic

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Figure 12: The workspace during wrist deviation: abduction(20◦ ) and adduction(37◦ )

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[4] K.Y. Woo, B.D. Jin, D.S. Kwon,“A 6DOF ForceReflecting Hand Controller Using the Five bar Parallel Mechanism,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp.1597-1602, 1998

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Figure 13: The workspace of the TFG haptic manipulation(front view): The size normalized to the distal pharanx of the thumb are M G = 2.91, M H = 1.43 and AB = 9.37.

[6] D.A. Lawrence, L.Y. Pao, M.A. Salada, A.M. Dougherty, “Quantitative Experimental Analysis of Transparency and Stability in Haptic Interfaces,” Proc. ASME Dynamic Systems and Control Division, DSC-Vol. 58, pp.441-449, 1996

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[5] G.L. Long, C.L. Collins,“A Pantograph Linkage Parallel Platform Master Hand Controller for Force-Reflection,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp.390-395, May, 1992

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[3] A. Rubio, A. Avello and J. Florez,“On the use of Virtual Springs to avoid Singularities and Works,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp.26902695, April, 2000

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[7] H.Z. Tan, M.A. Srinivasan, B. Eberman and B. Cheng, “Human factors for the design of force-reflecting haptic interfaces,” Proc. ASME Dynamic Systems and Control, DSC-Vol.55-1, pp.353-359, 1994

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[8] D.A. Lawrence, L.Y. Pao, M.A. Salada, A.M. Dougherty and Y. Pavlou “Rate-Hardness:A New Performance Metric for Haptic Interfaces,” IEEE Trans. on Robotics and Automation, Vol.16, No.4, Aug., 2000

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Figure 14: The workspace of the TFG haptic manipulation(rear view): The size normalized to the distal pharanx of the thumb are N G = 2.91, N H = 1.43, AB = 9.37, N L = 0.64, N K = 1.62 and IJ = 5.67.

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motion well. To solve the workspace of TFG haptic manipulation, an analytic approach is used from the viewpoint of anatomy. This approach is reliable since bone to bone bony ratio is fixed. The motion of the thumb is important to solve the workspace of TFG Haptic Manipulation. The characteristics of joint and the pose of thumb is found by separating the wrist motion. The workspace of TFG Haptic Manipulation is calculated numerically by computer simulation. The calculated pose of the thumb can be used not only for the workspace of the TFG Haptic Manipulation but also for the workspace of the other grasping motion if constraints are well defined.

[9] Y. Youm, M. Hoden and K. Dohrmann,” Finger Ray Ratio Study”, Technical Report on Wrist Project No.10, The Univ. of Iowa, Iowa City, Iowa, 1977 [10] Y. Youm, R.Y. McMurtry, A.E. Flatt and T.E. Gillespi,“Kinematics of the wrist”, The Journal of Bone and Joint Surgery, Vol. 60-A, No. 4, pp423-431, June 1978 [11] I.A Kapandji,The Physiology of the Joints: Upper Limb, Vol.1, Churchill Livingstone, Edinburgh London Melbourne and New York, 1982 [12] T.L. Brooks,“Telerobotic response requirements,” Proc. of IEEE Int. Conf. on Syst., Man and Cybern., Los Angeles, CA, November, pp.113-120, 1990

References

[13] http://www.sarcos.com

[1] P.J. Berkelman, Z.J. Butler, and R. L. Hollis,“Design of a Hemispherical Magnetic Levitation Haptic Interface Device,” ASME IMECE, (Atlanta, GA), DSC-Vol. 58, pp.483-488, 1996

[14] http://www.virtex.com

[2] T.M. Massie and J.K. Salisbury,“The PHANToM Haptic Interface: A Device for Probing Virtual Objects,” The 3rd Annual Symp. Haptic Interfaces for Virtual Environment and Teleoperator Systems, (Chicago, IL), DSC-Vol 1, pp.295-301, 1994

[15] http://intron.kz.tsukuba.ac.jp [16] http://www.aeat.co.uk [17] http://www.cs.utah.edu/ tthompso/haptics.html