Design, Fabrication, and Evaluation of a New Haptic
Device Using a Parallel Mechanism
Jungwon Yoon and Jeha Ryu, Member, IEEE
Abstract—This paper presents design, fabrication, and
evaluation of a new 6-DOF haptic device for interfacing with virtual reality by using a parallel mechanism. The mechanism is composed of three pantograph mechanisms that are driven by ground-fixed servomotors, three spherical joints between the top of the pantograph mechanisms and the connecting bars, and three revolute joints between the connecting bars and a mobile joystick handle. Forward and inverse kinematic analyses have been performed and the Jacobian matrix is derived. Performance indexes such as global payload index, global conditioning index, translation and orientation workspaces, and sensitivity are eval-uated to find optimal parameters in design stage. The proposed haptic mechanism has better load capability (low inertia, high bandwidth, etc.) than those of the pre-existing haptic mechanisms due to the fact that motors are fixed at the base. It has also wider orientation workspace mainly due to a RRR-type spherical joint. A control method is presented with gravity compensation and with force feedback by a force/torque (F/T) sensor to compensate for the effects of unmodeled dynamics such as friction and inertia. Also, dynamic performance has been evaluated for force charac-teristics such as maximum applicable force, static-friction force, minimum controllable force, and force bandwidth by experiments. Virtual wall simulation with the developed haptic device has been demonstrated.
Index Terms—Dynamic performance, gravity compensation,
haptic device, pantograph, parallel mechanism, performance indexes, RRR-type spherical joint.
I. INTRODUCTION
V
IRTUAL REALITY (VR) application is widely spreading in the areas of engineering, medical operation, teleoper-ation, welfare, and entertainment with the rapid development of computer technology. Haptic devices which feedback kinesthetic or tactile sensation to interactive users are also becoming indispensable to enhance the feeling of immersion in a VR system [1]. For kinesthetic sensation, many researchers have proposed different types of haptic devices such as a tool type, exoskeleton type, and serial robot type. Among these, a tool type device on the desk has been more widely accepted than the other types because of large bandwidth, safeness, and compactness.An ideal haptic device is required to have large workspaces, low inertia, high stiffness, low friction, and high control band-width and so on. It is, however, almost impossible to construct a
Manuscript received April 15, 2000; revised February 28, 2001. This research was supported in part by the Brain Korea21 research fund from the Korean Min-istry of Education. Recommended by Guest Editor N. Xi.
The authors are with the Department of Mechatronics, Kwangju Institute of Science and Technology (KJIST), Kwangju 500-712, Korea (e-mail: [email protected]).
Publisher Item Identifier S 1083-4435(01)08140-6.
haptic device satisfying all these requirements. Therefore, every effort must be made on optimally designing haptic devices by reducing moving inertia, by enlarging workspaces, and so on. Moreover, a device developer should provide users with evalu-ated kinematic and dynamic performance of the haptic device so that users may take care of the limitations of the haptic device for their specific application.
Parallel mechanisms have been used for tool type haptic de-vices because they have the characteristics of low inertia, high rigidity, compactness, and precise resolution compared with se-rial mechanisms. However, some of the haptic devices based on parallel mechanisms that have been developed so far still have disadvantages such as large inertia, difficult forward kinematics, and small workspaces. Long and Collins [2] and Iwata [3] pro-posed 6-DOF tool type haptic devices with a parallel mecha-nism which has three pantograph linkages, each of which is at-tached to a midpoint of an equilateral base triangle through a passive revolute joint. Woo et al. [4] made a similar force feed-back device for telesurgery. This device has five bars instead of pantograph linkages, for easier construction. In the above two devices, the top of each pantograph and five bar mechanism is connected to one vertex of a mobile platform through a 3-DOF ball-and-socket joint. These devices, however, have important disadvantages of large inertia because the rotary motors are not fixed to base, and small orientation workspace due to restricted rotation range of spherical joints. Tsumaki et al. [5] developed a 6-DOF haptic device that has an orientation gimbal mechanism on top of a 3-DOF modified DELTA mechanism. This device has compact size and wider orientation workspace but still has the problem of large motor inertia because three motors are lo-cated above the DELTA mechanism. Millman et al. [6] devel-oped a Stewart platform type device with 4-DOF motion, which has 3-DOF translation and 1-DOF roll angle orientation motion. This device has good resolution and high stiffness due to the ad-vantage of the parallel mechanism, but cannot make tilt angles that are important for versatile VR application.
Some researchers presented dynamic performance evaluation of various haptic devices. Howe and Kontarinis [7] have used a 2-DOF vertical planar device, with a force bandwidth exceeding 100 Hz over a 5-N range, in teleoperation experiments. Adel-stein and Rosen [8] developed a 2-DOF spherical mechanism which can be controlled with high fidelity up to 48 Hz at a sus-tained tip force of 20 N. Ellis et al. [9] developed a 2-DOF planar haptic device and presented experimental evaluation methods of dynamic performances. Their mechanism has maximum output force of 56 N, passive static-friction force of 1.7 N, minimum force of 0.4 N, and force bandwidth of 80 Hz at forces ex-ceeding 50 N. Moreyra and Hannaford [10] suggested a method 1083–4435/01$10.00 ©2001 IEEE
Fig. 1. Proposed haptic device based on parallel mechanism.
to characterize and experimentally measure the dynamic perfor-mance of haptic display devices. They introduced a dimension-less measure of structural deformation ratio (SDR) to quantify some aspects of the high frequency performance. Carignan and Cleary [11] pointed out that the quality of haptic devices can be measured in terms of impedance accuracy and resolution (or fidelity) and investigated several control methodologies for im-proving dynamic quality. Colgate and Brown [12] suggested the dynamic range of achievable impedance ( -width) as a measure of performance.
This paper presents design, fabrication, and evaluation of a new 6-DOF haptic device for interfacing with VR by using a parallel mechanism. The mechanism is composed of three pan-tograph mechanisms that are driven by ground-fixed servomo-tors, three spherical joints between the top of the pantograph mechanisms and the connecting bars, and three revolute joints between the connecting bars and a mobile joystick handle (see Fig. 1). The low moving inertia gives better dynamic bandwidth as compared to the existing devices and the RRR-type spherical joint assures a wider orientation workspace. Forward and in-verse kinematic analyses have been performed and the Jacobian matrix is derived. Static performance indexes such as global payload index (GPI), global conditioning index (GCI), transla-tion and orientatransla-tion workspaces, and sensitivity (S) are evalu-ated to find optimal geometric parameters at the design stage. This paper also presents a control method and experimental
evaluation of dynamic performances such as minimum control-lable force, static-friction force, force bandwidth, and maximum applicable force. In addition, stable ranges of virtual wall pa-rameters such as maximum achievable stiffness and damping coefficients are obtained by virtual wall simulation with the de-veloped haptic device.
This paper is organized as follows; Section II presents kinematic analyses including inverse, forward, and Jacobian analyses. Section III presents design analyses for optimal design of the parallel mechanism. Rearrangeability of the mechanism is also discussed for more versatile usage. Sec-tion IV compares kinematic performance indexes of the proposed device with those of the existing devices. Section V presents a control system with gravity, friction, and inertia compensation. Section VI presents evaluation of dynamic performance. Section VII shows virtual wall simulation results and Section VIII presents conclusions and discussions of the current research.
II. KINEMATICANALYSES
A. Mechanism Description
The proposed haptic device with a parallel mechanism is shown in Fig. 1. The new mechanism is composed of three pantograph mechanisms that are driven by six base-fixed servomotors that stand perpendicularly to the base plate, three RRR-type spherical joints between the top of the pantograph mechanism and the connecting bars, and three revolute joints between the connecting bars and a mobile platform. Since each pantograph mechanism is confined to a fixed vertical plane due to motors fixed at the base plate, the revolute joints between the base and the pantograph mechanisms in the pre-existing devices [2]–[4] should be moved to the locations between the top plate and the connecting bar, which is the main characteristics of the new haptic mechanism.
In order to analyze the proposed mechanism, kinematic pa-rameters are shown in Fig. 2. The fixed global reference frame ( , , ) is located at the bottom center of the base plate. The mobile reference frame ( , , ) is located at the top center of the top plate, where the -axis is in the plane of the top plate and is directed toward the first revolute joint. Each pantograph local reference frame ( , , ) is lo-cated at an active revolute joint, where the -axis is directed perpendicular to each pantograph plane. The axisymmetric po-sition of pantographs on base plate with radius are given by the angles (0, , and rads), which specify the rota-tion angles about -axis from -axis. Note that each panto-graph has 2-DOF motion on the – plane. Notice also that even though the spherical joints look to be located on the top of pantograph mechanisms (see Fig. 2) in the following kine-matic analyses, actual center of a spherical joint is located in an offset distance ( in Fig. 1). However, the following kine-matic analyses assume that the center of spherical joint is just on the top of a pantograph mechanism because the offset distance does not affect the kinematic analyses results if the base radius is replaced by . Lower links of pantographs are denoted by and upper links by . A connecting bar length
Fig. 2. Kinematics model.
is denoted by . Circle radius of the top plate is defined by . The points , , and denote the positions of active, spher-ical, and revolute joints, respectively. The three revolute joints are attached to the top plate and centered on a circle of radius with the angle (0, , rads), which specifies ro-tation angles about the -axis from the -axis.
B. Inverse Kinematic Analysis
The inverse kinematics computes the active joint angles and of the pantographs given the position and orientation ( , , , , , ) of the top plate. The position of a spherical joint can be represented by using (4 4) homogeneous matrices in the global reference frame ( , , ) as
(1) where ( , , ) specifies translation of the top plate origin and ( , , ) is the orientation matrix of the top plate, which is described by three successive Euler angles. Note in (1) that includes unknown revolute joint angle at position. Since
position must be on the pantograph – plane, the fol-lowing constraint equations of the plane – should be sat-isfied:
(2) Note, geometrically that the points are obtained by the inter-section of the circle of radius from revolute joint with the
pantograph plane . Thus, inserting and
com-ponents from (1) into (2) gives an equation with the unknown revolute joint angle in a closed form.
Then, by calculating (1) with the computed , it is possible to find inverse kinematics of A 2-DOF pantograph as follows. From Fig. 2, the distance between and is expressed as
(3)
The spherical joint positions with respect to the pantograph local frame ( , , ), can be derived as
(4) where the angles (0, , and rads) specify the rotation from the global reference frame to the pantograph local frame. From Fig. 2, the intermediate angles and are then given by
(5) Finally, active joint angles are given by
(6)
C. Forward Kinematic analyses
Forward kinematic analysis determines the position and ori-entation of the ( , , ) frame with respect to the ( , , ) frame given actuated angles and . The first thing for solving forward kinematics is to find revolute joint angels at points. These angles can be obtained by the fact that the distances between points in the global reference frame and the distances between points in the mobile reference frame are the same. The following steps are taken for forward kinematics.
1) In the global reference frame, the points should be calculated by using pantograph forward kinematics given the active joint angles ( and ) as
(7) Then, in the mobile reference frame, points that include unknown revolute joint angle, , can be repre-sented by
(8) 2) To solve the unknown angle , the following three
equality conditions are used:
(9) Nonlinear (9) can be solved for the variable by using the Newton–Raphson’s numerical method.
3) Using the computed angle, , the following vectors can be derived in the mobile reference frame ( , , ). From Fig. 2, the unit vector defining the direction of the axis expressed in the ( , , ) frame is given as
In addition, the axis that is normal to the plane de-fined by the three points , , can be found by the
vector cross product between and
(11) Then, the third axis is given by
(12) Thus, the intermediate transformation matrix from the mobile frame ( , , ) to the spherical joint frame ( , , ) can be described as
(13)
Similarly, the intermediate transformation matrix from the base frame to the spherical joint frame ( , ,
) is computed.
4) The (4 4) homogeneous transformation matrix from the base to mobile reference frames is obtained as
(14) Then, forward kinematic solutions are derived as
(15) where is the , th component of the matrix .
D. Derivation of Jacobian
The Jacobian matrix can be easily derived by using the con-cept of reciprocal screws [13], [14]. For each right subchain of the pantograph mechanism, the top platform twist is a linear combination of the joint screws
(16) where is the active joint rate, and are the rates of the passive revolute joints, and is a twist about the spherical three-system. From (16), the angular velocities of the passive joints are eliminated by the concept of the reciprocity stated as follows.
Two screws and are said to be reciprocal if
(17)
where is defined as when
and is the transpose of
Fig. 3. Reciprocal screws.
a screw . Let be the unit screw that is reciprocal to all the joint screws excluding the screw. In general, since the other five screws , , and are linearly independent, is uniquely specified. The reciprocity relationship yields by taking the virtual product of with (16)
(18)
Similarly, for each left subchain, is given by
(19)
Rearranging the expressions for and into a
single transformation, we obtain
(20)
where , and is a (6 6)
matrix which represents inverse kinematic Jacobian. When
and represents and ,
respec-tively, is described as
(21)
The reciprocal screw is a zero pitch screw passing through the spherical joint position and acts along the line of intersection of the -plane which contains point and
axis of , with the -plane which contains point
and axis of , (see Fig. 3). Let be a unit
normal vector defined by the cross product of and to -plane. Then,
And, let be a vector normal to -plane. Then
(23) So, a unit vector along the direction of the screw axis is represented by
(24)
Then, a screw that is reciprocal to all screws except is given as
(25) Similarly, a screw that is reciprocal to all screws except is obtained as
(26)
Inserting and into (21), therefore,
com-pletes the derivation of Jacobian.
Note that singular configurations are generated when and are reciprocal to and . Some of the singularities which have been found so far occur when the pantograph mech-anisms are either lowered down to the base plate plane or are vertically erected, and when all the connecting bars are perpen-dicular to pantograph planes.
III. DESIGNANALYSES
In haptic device design, there are many mechanical design requirements such as small inertia, large stiffness, small back-lash, and compactness in order to achieve good static and dy-namic characteristics such as workspace, force transmissibility, isotropy of the force and motion, backdrivability, high force bandwidth, and high force dynamic range [15]. In order to ful-fill these requirements, this chapter presents design analyses to obtain an optimum mechanical architecture with respect mainly to such static performances as the larger workspace, larger force transmissibility, better isotropy, and smaller sensitivity with re-spect to articular variable noises. In addition, we will discuss rearrangement of our design for more versatile usage for dif-ferent situations.
A. RRR-type Spherical Joint Design
The proposed parallel mechanism has three spherical joints. However, a conventional ball-and-socket-type spherical joint has rotational limitation as well as difficulties in connecting three bars (two links and one link). Therefore, it is necessary to design a spherical joint that allows largest possible rotations and easy installation. A spherical joint satisfying these requirements is a RRR-type joint shown in Fig. 4(a). As shown in Fig. 4(b), however, this joint does not allow full rotation about the -axis. It is, therefore, necessary to maximize this
Fig. 4. RRR-type spherical joint modeling. (a) Spherical joint detail. (b) Spherical joint rotation abouty-axis.
rotational angle for larger workspace without sacrificing other performance indexes which will be discussed in Section III-B.
From Fig. 4(b), is expressed as
(27) Using the relationship and sine formula, is rep-resented by
(28)
where is assumed to be less than .
As becomes small, the rotation range of the link increases, which in turn increases the constant orientation workspace projected in the – plane as shown in Fig. 5. It turns out, however, that if the angle is smaller than 20 , the RRR-type spherical joint does not significantly increase the constant orientation workspace, while degrading other per-formance indexes that are presented in the following section. Therefore, the angle is designed to be 20 by appropriately selecting , , and parameters in (28).
B. Parameter Design for Optimal Static Performance
Using the performance indexes such as GPI[16], GCI[17], [18], and constant orientation workspace (COW), optimum geo-metric design parameters can be found for the proposed mecha-nism. The COW is defined as the 3-D region that can be attained by an end-effector point when the mobile platform is kept at a constant orientation. Therefore, large values of COW will give wide range of motion.
Fig. 5. Constant orientation workspace variation with respect to angle. (a)
= 30 . (b) = 20 . (c) = 10 .
When the input motor torques have unity magnitude, the ex-treme values of the payload at the end-effector are
(29) where and represent the largest and the smallest sin-gular values of the inverse Jacobian matrix. Then, global pay-load index (GPI) is defined as
(30) where is the area of the constant orientation workspace of the robot. This GPI index represents force transmission capability. Therefore, the larger GPI, the bigger force transmission in the end-effector.
The global conditioning index (GCI) is define as
(31)
where is the condition number of a manipulator Jacobian at a manipulator configuration. This index represents the isotropy of manipulation over the entire workspace. Therefore, the closer the GCI to unity value, the more even feel through the workspace.
S of endpoint position with respect to perturbations in artic-ular variables is defined as the sum of the absolute values of all Jacobian elements in a single row over the COW. For the first row of the Jacobian, for example, sensitivity in -coordinate di-rection is defined as
(32) This index may be an important measure of kinematic perfor-mance because amplification of uncertainty in articular vari-able is undesirvari-able from the precision standpoint. Therefore, the lower the S, the better the attenuation of actuator perturbations at the end-effector.
The variations of performance indexes with respect to design variable changes are summarized in Table I, in which the ranges of design parameters are
mm In this table, the upward arrow indicates increase of geometric parameters (or ratio) or increase of performance indexes. From this table, we concluded that the conditions on the optimum
pa-rameters are; , , ,
value for . With this design, the constant orientation workspace is larger than 300-mm diameter circle in the – plane, the maximum payload is over 40 N, and the maximum tilt angle is over 50 .
C. Rearrangements of the Proposed Mechanism
Even though we arrange the designed mechanism as shown in Fig. 1, this arrangement can be changed drastically to different arrangements (see Fig. 6) with only reorienting actuators, with a minor change of upper revolute joints, and/or by removing some of the links. This is possible because all passive joints of the proposed parallel mechanism are revolute joints and the di-rection of the revolute joint can be changed arbitrarily. Further-more, some links can be taken out of the existing structure to make a simpler architecture (cases 1 and 2) with 3-DOF. Using these properties, other arrangement such as case 3 can be as-sembled by change of direction of the pantographs and upper revolute joints from the original mechanism. Note that in cases 2 and 3 the upper revolute joints have changed their rotation di-rections in the rearranged installation. In addition, a pantograph with 2-DOF motion can be changed simply to a five-bar mech-anism (case 4). These rearrangements of the proposed mecha-nism are good for more versatile usage of a haptic mechamecha-nism in different situations where different performance is required.
TABLE I
VARIATIONS OFPERFORMANCEINDEXES
Fig. 6. Possible rearrangements. (a) Case 1. (b) Case 2. (c) Case 3. (d) Case 4.
IV. STATICPERFORMANCECOMPARISON WITHEXISTING DEVICES
In order to compare static performances of the proposed mechanism with the existing haptic mechanisms of similar architecture, workspaces, GPI, GCI, and S are compared. KAIST master and UCI hand controller are selected for comparison (see Fig. 7). They are composed of three five bar mechanisms or three pantographs which are connected to the top plate with spherical joints and which are connected to the base with passive revolute joints. Therefore, motors are not fixed to the base plate, which results in large COW and large moving inertia. For fair comparison, the geometric parameters of each mechanism are adjusted to maintain equal height of the end-effecter, and equal base and top plate radii.
A. Workspace Comparison
The COW was determined numerically with an inverse kine-matics search algorithm in which joint rotation limits are taken
Fig. 7. Comparison of haptic mechanisms.
into account. A typical ball-and-socket type spherical joint is as-sumed to have 60 degree of cone angle. The constant orientation workspaces of the KAIST master and the UCI hand controller that have the spherical joint range of 60 are about twice as lare than that of the proposed mechanism, due to the fact that the pantographs and five bars are rotating from the base plate. On the other hand, the translational motion of the proposed mech-anism is determined mainly by the upper parts between the top plate and the pantographs, which results in smaller COW. Note that the COW shapes of KAIST master and UCI controller are very different from those in [4] and [2] because of limited rota-tion angle of the ball-and-socket type spherical joint. The larger the spherical joint angle, the closer the shapes to that of the pro-posed mechanism (see Fig.8).
Another kind of workspace is the orientation workspace that is defined as the set of all attainable orientations of the mo-bile platform about a fixed point. The analysis of the orienta-tion workspace may be based on the use of a modified set of Euler angles [19]. Fig. 9(a) shows the orientation workspaces in a cylindrical coordinate system. It was found that UCI hand con-troller and KAIST master have similar shape and size of orien-tation workspace due to limiorien-tation of spherical joint angle. The projected orientation workspace defined as the set of possible directions of the approach vector (represented by two tilt angles , ) of the mobile platform may also be obtained [19]. Fig. 9(b) shows samples of projected orientation workspaces. The orien-tation workspaces of the existing mechanisms are about 40% smaller than that of the proposed mechanism mainly due to the spherical joint type.
B. Other Performances Comparison
Other performance indexes that have been compared are the GPI, the GCI, and the S. These have been analyzed over the
constant orientation workspace ( , , ) for each
mechanism. In Table II, GPImax, GPImin, and GCI are shown for three mechanisms. The GPI of the proposed mechanism is about twice as large as that of the others. Therefore, the proposed mechanism can support double payloads compared to others. However, the GCI of each mechanism is very similar. On the other hand, the proposed mechanism is the least sensitive to the actuator perturbations at each direction.
Fig. 8. Constant orientation workspace of top plate center-point ( = 0, =
0, = 0). (a) New haptic device. (b) KAIST master. (c) UCI hand controller. V. HAPTICDEVICECONTROL
A. System Hardware
All links of the haptic device are made of light aluminum frames in order to reduce link inertia. Rotary motors are directly connected to lower bars of pantographs without reduction gears. This direct drive can achieve low friction and high bandwidth and eliminate backlash so that the haptic device is easily back-drivable by the operator. This construction is possible due to the fact that all six motors are fixed at the common base, which allows use of high power motors without increasing moving in-ertia. In addition, in order to reduce joint frictions miniature ball bearings are inserted at every revolute joint.
We used a 6-axis motor controller which is connected through an ISA slot to the Pentium III-450 PC which performs haptic rendering algorithm with a C program, in which calculations of forward kinematics and Jacobian, communication, and feed-back control are performed at the rate of 600 Hz. Through the motor controller, the commanded torque is changed to voltage by D/A converter and this value is fed to the ac servomotor (maximum output torque of 0.951 N m) with pulse width mod-ulation (PWM) amplifier. Motion of a motor is sensed by an en-coder that gives 2048 pulse in one revolution. We used the
As-Fig. 9. Orientation workspace at a nominal position (O = 0, O = 0, O =
230 mm). (a) Orientation workspace in cylindrical coordinates [(1) New haptic
device, (2) UCI hand controller]. (b) Projected orientation workspaces [(1) New haptic device, (2) UCI hand controller].
surance Technologies mini-40FT model, a 6-axis force/torque sensor with 16bit A/D conversion in increments of 0.02 N ( -and -axis) -and 0.14 N ( -axis). This sensor can detect up to N ( - and -axis) and N ( -axis). This sensor is used to determine the differential force between the mechanism and the human operator so that a feedback loop could be used to compensate for unmodeled components of the device dynamics.
B. Gravity Compensation
In order to precisely transfer the simulated force from the VR to the operator, the haptic device should have negligible gravity force, friction, and inertia. Since the weight of the proposed haptic device is about 300 g, which is heavy according to the pilot study [9], an operator may feel fatigue after 30-min opera-tion. Therefore gravity effect must be compensated in the haptic device control.
The motor torques required for compensating gravitational forces of the haptic mechanism can be obtained from the deriva-tives of the gravitational potential energy term that is repre-sented as (33) where , , , , , , ,
and where , , , , are weights of the mobile
platform, pantograph lower bar, pantograph upper bar, small connection bar in Fig. 4(a), and the connecting bar ,
TABLE II
GPI, GCI, SENSITIVITYCOMPARISON
Fig. 10. Step input responses. (a) Open-loop step response. (b) Closed-loop step response.
respectively, and where , are center-of-gravity heights of the platform and the connecting bar, respectively. The distance between the and points in Fig. 2 is computed from the following quadratic equation:
(34) Equation (33) can be simplified as
(35) Therefore, the motor torques from the gravitational forces of the haptic mechanism are computed as
(36)
where is computed in a closed
form from partial derivatives of the (34). Once the forward kine-matics in Section II-C are solved numerically, the other partial
derivatives in (36) may be computed approximately by a finite difference method as
(37)
C. Friction and Inertia Compensation
To control force precisely, the friction and inertia of the haptic device as well as external disturbances from unmodeled oper-ator’s dynamics, should be compensated by the force/torque sensor in the feedback loop. The total control torque input in this case can be represented by
(38) where is the Jacobian matrix and is the desired force from VR simulation.
D. Step Input Responses
Two step input responses in the -direction, with and without force sensor feedback, were measured so as to investigate the open- and closed-loop performance of the haptic device. In this experiment, a step input of 2 N in the -axis is commanded to the haptic device while an operator grasped the haptic device handle firmly in order not to move the handle (i.e., zero velocity at the grasped position). An open-loop step input response in a gravity compensation plus feed-forward control in Fig. 10(a) shows that a constant force was maintained close to the desired force within about 15% error that is caused by variation of human hand force. A closed-loop step input response in Fig. 10(b) is shown with a
PD feedback ( , ; gains are obtained
empir-ically by tuning process for minimizing steady state and over-shoot errors) plus feed-forward control. The overover-shoot and the steady-state error were relatively small compared to those of the open-loop response. Note that even though the hand force of an operator was varied, the differential force between the op-erator and the haptic device maintained a constant force, which showed disturbance rejection effect of the force feedback. Since the open-loop step response is not far worse than the closed-loop step response, the open-loop impedance control by using only
the gravity compensation plus the feed-forward loop may be ap-plied to some applications which do not need high fidelity of force control. An open-loop control can lower significantly the price of a haptic device by removing an expensive force/torque sensor.
VI. DYNAMICPERFORMANCEEVALUATION
Until now, experimental performance evaluations of only a small number of 6-DOF haptic devices has been reported [9]. We have evaluated experimentally dynamic performance of force characteristics such as force bandwidth, static-friction breakaway force, and extremum controllable forces. Ellis et al. [9] suggested two constraint conditions in the general task of free and unimpeded motion of the wrist in the plane for haptic device design: human operator constraints and mechanical constraints. As for the human operator constraints, maximum and minimum values of the controllable motion of a human operator are: workspace of 15 cm 15 cm, minimum force of 1 N, peak force of 40 N, and force bandwidth of 50 Hz. As for the mechanical constraints arising from considerations of the mechanical interaction of the human with the device, any haptic device: 1) should keep low apparent mass and inertia for less operator fatigue; 2) must have an internal friction level of at most 5% of the peak force; 3) should have high native mechan-ical stiffness; and 4) should have no kinematic singularities in the operating workspace. We will evaluate the performance of our haptic device with respect to these constraint conditions even though the human operator constraints studied by Ellis et
al. are for planar free wrist motion.
For force characteristics, we evaluated maximum applicable force, static-friction breakaway force, and minimum control-lable force. The maximum applicable force was measured by the force sensor attached to the handgrip when the computer com-manded a constant force in an open-loop control mode, while the operator keeps the handle unmoved. The static-friction break-away force is defined as the minimum open-loop force incre-ment when the change of the end-effector position was posi-tion resoluposi-tion of the end-effector. This force is measured by incrementally increasing command force when the haptic de-vice stands alone by the gravity compensation control without the human operator. The minimum controllable force was mea-sured by commanding a closed-loop proportional controller to maintain a zero differential force on the operator handle. This procedure was to move the device by voluntary hand motion, and record the resulting force and position.
Force bandwidth in haptic device is affected by a number of factors such as stiffness, inertia, damping, friction, actuator lim-iting, contact, sensor/actuator collocation, gains, and operator impedance [20]. The dynamic bandwidth of the proposed mech-anism is expected to be higher than that of the UCI controller and the KAIST master because moving inertia is significantly reduced by the base-fixed motor design even though the mech-anism stiffness may be somewhat decreased due to more links and joints in RRR-type spherical joint design. The force band-width was measured by the device response, while the human
Fig. 11. Minimum controllable force: (a) ForceF x, F y, F z. (b) Torque T x,
T y, T z. (c) Position x, y, z. (d) Orientation , , .
Fig. 12. x-axis force bandwidth.
operator grasped the handle as they would when interacting with virtual environments. The computer commanded the de-vice to maintain an offset-sinusoidal differential force. Then, the peak-to-peak amplitudes were recorded at each frequency in the range of 1–120 Hz.
The experimental results for force characteristics were as fol-lows: a maximum applicable force was different for each axis. The maximum force in the axis is 40 N and the force in the -and -axis is 20 N. The static-friction breakaway force was 1.5 N in the -axis direction. Friction force, therefore, was within 5% of the maximum applicable force. Fig. 11 shows the min-imum controllable forces and torques. The force that induces the device motion is less than 0.4 N (in the -axis direction) and 0.3 N (in the -axis and -axis directions) as shown Fig. 11(a). The torques are less than 0.01 N m as shown in Fig. 11(b). The position and orientation are changing slightly during this min-imum controllable force test with the max speed of about 15 cm/s and 0.2 rad/s, as drawn in Fig. 11(c) and (d).
In Fig. 12, the force bandwidth of the -axis direction is shown to be about 70 Hz at the crossover frequency of 3 dB below the dc level. This response is fast enough for some haptic applications, satisfying the maximum force bandwidth
TABLE III
NEWHAPTICDEVICECHARACTERISTICS
Fig. 13. Control block diagram including virtual environment.
(50 Hz) from the pilot study[9] for the human wrist free motion. Table III summarizes the performance characteristics of the proposed device. Comparing to the constraints suggested by Ellis et al. [9], the proposed haptic device sufficiently achieved the human operator and mechanical constraints.
VII. VIRTUALWALLSIMULATION
This chapter presents a virtual wall simulation by using the developed haptic device to observe the closed-loop response of virtual environment simulation. Virtual wall simulation has been used as a representative task featuring both very high impedance (when in contact with the wall) and very low impedance (when out of contact) [21], [22]. The virtual wall can be modeled as an equivalent spring-damper system. The force from the wall can be written as
(39) where and are unilateral constraints, is the virtual wall spring constant, and is the virtual wall damper coefficient. The unilateral constraints and are given as
(40) The unilateral constraint , ensures that the force is exerted to the end-effector only when the handle penetrates the wall. Simi-larly, ensures that the damper exerts no force when the handle is being moved away from the wall.
Fig. 14. Virtual wall simulation results.
A total control block diagram is represented in Fig. 13. The difference between the position of the haptic device driven by a human operator, and reference value that is the posi-tion of a virtual wall is represented by . Then, the value of is used to generate a virtual wall reaction force by the (39) for the human operator. In this block diagram, the dotted box represents nonlinear kinematics/dynamics. In this virtual wall simulation system, both control of the haptic device and haptic rendering are performed by the haptic controller with Pentium III-450 pro-cessor which is equipped with 6-axis motor controller. The vir-tual wall environment that is modeled by the World Tool Kit (WTK) software is simulated in a Pentium II-dual 350 processor NT system with a high-speed graphic board. The rendering of the virtual environment is performed at the rate of about 40 Hz. Both computers are interfaced by a RS-232 communication at the rate of 57 600 bps.
Through this simulation we can find achievable wall impedance while keeping the system stable. We define in-stability as the situation in which vibration occurs at the boundary of a virtual wall during wall contact operation. The maximum achievable wall stiffness without inducing vibration
is measured to be about 400 N/m when no wall damping exists while the maximum achievable wall damping is measured to be about 1500 N/m s. If there are both stiffness and damping, the maximum achievable stiffness with a damping value of 1000 N/m s is increased to 600 N/m for a stable virtual wall simulation.
Fig. 14 shows results of a simulation of moving down along the virtual wall with the parameters ( N/m and
N/m s). In this simulation, an operator first approached the wall in the -direction while grasping the haptic device. After contacting the virtual wall, the operator moved down in the -di-rection while contacting the virtual wall [see Fig. 14(a)]. During this operation, the operator could maintain contact with the sur-face of the virtual wall due to the force feedback toward the operator through the haptic device (see Fig. 14(b)). At this ex-periment, the virtual wall feels like smooth mud as depicted in Fig. 14(c).
VIII. CONCLUSIONS ANDDISCUSSIONS
This paper proposed a new tool type haptic device based on a parallel mechanism for improving static and dynamic quality of haptic interface in VR simulation. This mechanism has small moving inertia because motors are fixed to the base plate and has larger orientation workspace because there is only small ro-tational limitation in the RRR-type spherical joint. Through an optimal design and kinematic analyses, it has been shown that the proposed haptic device has better static performances such as wider orientation workspace, lesser sensitivity with respect to actuator perturbations, and higher force transmission capability compared to the mechanisms of similar mechanical architecture. However, the constant orientation workspace is smaller. In ad-dition, possible rearrangements of the proposed mechanism are discussed for more versatile usage. This paper also presented control methods, performance evaluation, and virtual wall sim-ulation. It has been shown that open-loop gravity compensation plus feed-forward control may be good for less precise control because this device has low friction and small backlash as mani-fested by the result of the open-loop step input response. Mean-while, the force feedback control to compensate the effects of inertia and friction using a F/T sensor may be used for more pre-cise and stable control. By experiments, dynamic performance characteristics such as force bandwidth, minimum controllable force, and static-friction force have been evaluated. This new haptic device has force bandwidth of 70 Hz, the maximum force of 40 N in the -direction, minimum controllable force of 0.3 N in the and directions, and wide orientation workspace. Fi-nally, we demonstrated a virtual wall simulation using the pro-posed haptic device. The measured maximum achievable wall stiffness (about 600 N/m) may be low for applications requiring harder contact operation. This low wall stiffness may be in-creased by; higher sampling rate (currently 600 Hz) by superior PC, use of material with higher stiffness, higher rate of commu-nication, use of admittance control instead of impedance con-trol, and so on. Even though the proposed haptic device has not been designed for any specific application, users can choose it for their particular application by understanding the static and dynamic performances evaluated in this paper.
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Jungwon Yoon received the B.S. degree in precision
mechanical engineering from the Chonbuk National University, Chonju, Korea, in 1998, and the M.S. de-gree in Mechatronics from Kwangju Institute of Sci-ence and Technology (KJIST), Kwangju, Korea, in 2000, where he is currently pursuing the Ph.D. de-gree.
His research interests include the design, analysis, and control of parallel mechanisms with applications to virtual reality haptic devices and medical systems.
Jeha Ryu (M’00) received the B.S. degree in 1982
from the Seoul National University, Seoul, Korea, the M.S. degree in 1984 from the Korea Advanced Sci-ence and Technology (KAIST), Seoul, Korea, and the Ph.D. degree in 1991 from the University of Iowa, Iowa City.
From 1992 to 1994, he worked as a master en-gineer in the simulation lab of BMY Combat Sys-tems, York, PA. In 1994, he joined the Department of Mechatronics, Kwangju Institute of Science and Technology (KJIST), Kwangju, Korea, where he has been an associate professor since 1999. His research interests are kinematics, dynamics, and control of mechatronics systems such as robot manipulators, ve-hicle systems, and haptic joysticks for interfacing with virtual reality systems. He has published more than 40 international journal and conference papers.
Dr. Ryu is a member of the American Society of Mechanical Engineers. In 1999, he received a best-educator award from KJIST.