A Pan–Tilt Orienting Mechanism With Parallel Axes of Flexural Actuation

1100 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 3, JUNE 2013

A Pan–Tilt Orienting Mechanism With Parallel Axesof Flexural Actuation

Yi-Chiao Lee, Chao-Chieh Lan, Member, IEEE, Cheng-Yu Chu, Chih-Ming Lai, and Yi-Jie Chen

Abstract—This paper presents the design and prototype of acamera-orienting mechanism. Bioinspired actuators and mecha-nisms have been developed to pan and tilt a camera with com-parable characteristics as a human eye. To meet the stringentspace/weight requirement of robotic applications, a compact-orienting mechanism is proposed. We specifically aim at matchingthe size of a human eye. Through the arrangement of two par-allel placed actuators and flexible mechanisms, nearly uncoupledpan and tilt motions can be provided in a streamlined space. Theflexible mechanisms utilize the deflection of beams to replace thekinematic joints; thus, they have fewer parts and can be easilyadapted to a small and irregular design space. The optimal mech-anism configuration has linear input–output relation that makesdriving electronics very direct. Through verification and prototypeillustration, the novel orienting mechanism is expected to serve asan alternative for robotic vision applications.

Index Terms—Bioinspired robot eye, camera-orienting device,flexible mechanism, parallel mechanism.

I. INTRODUCTION

TO INCREASE the field of view while reducing the numberof cameras used, cameras are often required to be installed

on an orienting mechanism with more than one degree of ro-tation freedom. This mechanism needs to provide at least panand tilt rotation to mimic the movement of a human eye. Ap-plications of camera-orienting mechanisms include humanoidrobot head [1], vehicle guidance [2], security surveillance [3],inspection [4], animatronics [5], and surgical imaging [6].

Commercial camera-orienting mechanisms use two rotarymotors in a serial fashion to achieve two perpendicular axesof rotation. Although the two perpendicularly placed actuatorscan provide full rotation range, they require too much spaceand make the camera device bulky. To overcome this problem,alternative orienting mechanisms have been proposed. Among

Manuscript received September 21, 2011; revised January 3, 2012; acceptedApril 5, 2012. Date of publication May 14, 2012; date of current version January18, 2013. Recommended by Technical Editor G. Yang. This work was supportedin part by the Metal Industries Research and Development Centre, Taiwan.

Y.-C. Lee was with the Department of Mechanical Engineering, NationalCheng Kung University, Tainan 70101, Taiwan. He is now with Chroma ATEInc., Taoyuan 33383, Taiwan (e-mail: [email protected]).

C.-C. Lan, C.-Y. Chu, and C.-M. Lai are with the Department of MechanicalEngineering, National Cheng Kung University, Tainan 70101, Taiwan (e-mail:[email protected]; [email protected]; [email protected]).

Y.-J. Chen is with the Project Coordination and Liaison Section, Planningand Promotion Department, Metal Industries Research and Development Centre,Taipei 100, Taiwan (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2012.2195192

them, spatial parallel mechanisms [7], [8] have higher stiffnessand better dynamic properties. Their motions are coupled andhence require more sophisticated electronics to drive the cam-era. Compared with serial mechanisms, they have a relativelysmaller workspace and may have to deal with configuration sin-gularities. Parallel mechanisms with independent pan and tiltmotions [9]–[11] have been proposed to overcome the problemof axes coupling. Unlike other pan–tilt mechanisms that requiredifferent types of joints or even multi-DOF joints, sphericalmechanisms [12]–[14] provide pan and tilt motions by usingonly pin joints. The two axes are less coupled. Sensors can beplaced at separate joints to directly measure their respective panand tilt angles.

A challenge of camera orientation is how to design a mecha-nism that is comparable to human eyes in terms of workspace,speed, size, and reliability. A human eye is rotated by six ocularmuscles and is capable of 3-DOF motion. A normal eyeball hasa diameter of 2.5 cm and the center distance between two eye-balls is merely 6 cm. The equivalent pan and tilt angles are nearly±30◦ and each with velocity and acceleration up to 600 ◦/s and50000 ◦/s2 [15]. Although human eyes seem delicate, they arerobust against external shock and vibration. This is a crucialrequirement for a camera-orienting mechanism if images are tobe captured in a demanding environment (for example, vehiclemoving on a bumpy road). While previous research has focusedon emulating the workspace and speed of a human eye, fewer at-tempts have been made to emulate the size of a human eye. Thisis especially important when a camera-orienting mechanism isto be used for capturing stereo vision in a humanoid head (see,e.g., [16] and [17]), in which two orienting mechanisms need tobe placed side by side like human eyes.

Human eyes, like human wrists and other multi-DOF biolog-ical joints, are actuated by antagonistic muscle pairs that arenearly parallel to each other. The parallel actuation schemesare ideal because of its compact design for generating multi-DOF rotation. Of the previously discussed parallel and sphericalmechanisms, parallel mechanisms may achieve parallel actua-tion axes. Inspired by human muscle actuation scheme, tendon-driven mechanisms (see, e.g., [18] and [19]) have been proposed.The tendons emulate the ocular muscles to pull the eyeball in anantagonistic pattern. Since two actuator/tendon pairs are neededto drive each axis of rotation, mechanical complexity is a con-cern. Spherical motors provide another alternative. A sphericalrotor can be driven by a spherical stator (or vice versa) based onultrasonic [3], [4] or magnetic [5] principles. They achieve panand tilt motion without using any gears or linkages.

This paper aims at designing a camera-orienting mechanismwith characteristics comparable to a human eye. We focus on a

1083-4435/$31.00 © 2012 IEEE

LEE et al.: PAN–TILT ORIENTING MECHANISM WITH PARALLEL AXES OF FLEXURAL ACTUATION 1101

Fig. 1. Actuating scheme for camera orientation. (a) Two rotary motors withperpendicular actuation axes. (b) Two linear motors with parallel actuation axes.

Fig. 2. (a) Slider crank and (b) flexible mechanisms.

compact design that is suitable for binocular vision applications,while the workspace and speed are not compromised. Comparedwith existing camera-orienting approaches that use perpendicu-lar actuation, the proposed design employs parallel actuation toachieve perpendicular pan and tilt motion. Actuators are placedin parallel to save space, yet they can achieve nearly uncoupledmotion, which is direct and intuitive. In what follows, we beginby presenting the design concept of the orienting mechanism.This is followed by the formulation to find the optimal con-figuration of the pan and tilt mechanisms. After verifying theirkinematics and dynamics, a prototype will be illustrated withperformance discussed.

II. PROPOSED DESIGN

A. Choice of Actuator Placement and Transmission Mechanism

To achieve an orientation with two perpendicular rota-tion axes, parallel and serial mechanisms have been adopted.Fig. 1(a) illustrates the design of a typical serial mechanism.Since there must be two actuators, the common approach is toplace two rotary motors the axes of which are perpendicular toeach other. Motor 1 provides the pan motion, while Motor 2provides the tilt motion. As Motor 1 rotates, the space sweptby Motor 2 forms a sectorial plane that is perpendicular to theaxis of Motor 1. This scheme is intuitive. The motion is uncou-pled and the mechanism can be easily constructed. It has beenemployed in the design of many surveillance cameras. How-ever, its operation requires a larger space in order to house theperpendicularly moving Motor 2.

To provide the same orientation, an alternative scheme isshown in Fig. 1(b). The two motor axes are placed in parallel.Compared with that in Fig. 1(a), this scheme is more compactand consumes a smaller space. The two parallel actuators needto be linear type and require a mechanism, e.g., a slider crankmechanism, to transmit the linear motion to rotation motion.Fig. 2(a) shows one such diagram. However, the use of slidercrank mechanisms introduces many links and joints. We pro-

Fig. 3. Proposed orienting mechanism.

pose here a design in which the coupler of the slider crank isreplaced by a slender flexible beam, as shown in Fig. 2(b). Uponthrust from the linear motor, the deflection of the beam serves totransmit the linear motion to rotary motion. Flexible elementshave been used in parallel mechanism design [20]–[22] to re-place joints and achieve precise motion. Most of them adoptpivot-type flexible elements. For large-displacement applica-tions, stress concentration is a concern. The proposed slenderflexible beam can be designed to distribute the stress over theentire beam. Thus large displacements can be achieved withoutviolating stress limit. For other robotic applications of slenderflexible beams, refer to [23]–[27].

As displacement is not a limit, slender flexural beams are usedin the proposed orienting mechanism. Their merits over usingother linkages (such as slider-crank) are as follows.

1) A flexible beam integrates the functions of pin joints andrigid links into a single piece. The use of it greatly reducesthe number of parts and achieves the same motion in amuch smaller space. Since pin joints are avoided, the errorscaused by accumulated joint clearance are eliminated.

2) To achieve compact parallel actuation, we need to makethe best use of unoccupied design space. Flexible elementscan be easily designed to adapt to an irregular space with-out sacrificing its functionality. This facilitates the parallelactuation scheme.

3) Unlike rigid mechanisms, flexible mechanisms can be eas-ily designed such that the input–output relation is almostlinear, which makes the implementation of control elec-tronics much easier. During motion, they are also free ofmechanism singularities.

While the first merit is evident, the second and third meritswill be illustrated in Section IV.

B. Proposed Orienting Mechanism

Fig. 3 shows the CAD model of the proposed pan–tilt orient-ing mechanism. It consists of two identical ground-fixed linearstep motors (Haydon, size 8) that separately drive a flexiblemechanism. The pan motor actuates the pan mechanism to pro-vide input pan rotation. On top of the pan motor, the tilt motor


Fig. 4. Pan mechanism and the front view.

Fig. 5. Side view and the tilt mechanism.

actuates the tilt mechanism to provide the input tilt rotation. Thetwo rotation axes perpendicularly intersect at the origin of framex0y0z0 , in which pan is along the z0 and tilt is along the y0 axis.The two flexible mechanisms connect to a spherical mechanism.It has a front panel for mounting a camera. The mechanism canprovide ±35.54◦ pan range and ±32.97◦ tilt range. The overallsize is 42 mm× 43 mm× 116 mm, in which the mechanism partis about half. The whole mechanism can be enclosed by a tubewith center at the origin of frame x0y0z0 and radius 25.5 mm.The two motors are symmetric about the x0y0 plane and x0z0plane. Each motor weighs 50 g. The motors are the majority ofthe whole mechanism weight.

Figs. 4 and 5 show the detailed dimensions of the pan andtilt mechanisms. Both are in their neutral positions. In Fig. 4(a),the displacement Dp from the pan motor deflects the pan beamto rotate the pan joint with angle θ1 . The tilt mechanism rigidlyconnects to the top of the pan mechanism. Fig. 4(b) shows itsfront view while the front panel is not shown. The tilt motoractuates the tilt beam shown in Fig. 5(a) with displacement Dt

to rotate the tilt joint with angle θ2 . The yaw (θ3) and spin (θ4)joints in Fig. 5(b) connect the tilt joint to the tilt beam. The panand tilt beams are made of elastic plastics that are resilient tolarge deflection.

III. KINEMATICS OF THE SPHERICAL MECHANISM

The rigid-body portion of the mechanism forms an overcon-strained 2-DOF spherical mechanism. The skeleton diagram isshown in Fig. 6(a). The pan, tilt, yaw, and spin joints intersect atthe origin of frame x0y0z0 . The pan and tilt axes are rigid-bodyequivalents of the pan and tilt beams. Fig. 6(b) shows the coor-dinate system. The x0y0z0 frame is ground-fixed. Frame x1y1z1is fixed on the housing of the pan joint. Frames x2y2z2 , x3y3z3 ,and nsa are fixed on the shafts of the tilt, yaw, and spin joints,respectively. Except for the nsa frame, the origins of all otherframes coincide at the center of the mechanism. The relations

Fig. 6. (a) Spherical mechanism skeleton. (b) Coordinate system.

TABLE ID–H PARAMETERS

Fig. 7. Input and output angles.

among the frames are described by using D–H parameters inTable I.

Fig. 7 shows the input and output angle definitions. The anglebetween the x1 and –x0 axes is denoted as the input pan angleθp . Its rotation is induced by the deflection of the pan beam.The angle between the a and –x0 axes is denoted as the inputtilt angle θa . Its rotation is induced by the deflection of the tiltbeam. The output angles are θp and θt , where θt is the anglebetween –x1 and x2 . It is used to measure the actual tilt angle.The input and output angles are related to the joint angles by

θ1 = θp + π, θ2 = θt + π. (1)

Due to the special configuration of the spherical mechanism,calculation of inverse kinematics is greatly simplified. Throughstandard inverse kinematic analysis, the relation between theoutput tilt angle and input angle is obtained as

θt =± cos−1

⎡⎣ CpCa√

C2p + S2

p S2a

⎤⎦ for θa ≥ 0(+) and θa ≤ 0(−)

(2)where C and S are cosine and sine angles. For the special casewhere θp = 0, the output and input tilt angles are identical. Forother θp , the amount of output tilt angle will be increasinglylarger than the input tilt angle. The Jacobian matrix of interest


Fig. 8. Schematic of the pan mechanism design.

can be expressed as[

θp

θt

]=

[1 0

CaSpSa/(C2a C2

p + S2a ) Cp/(C2

a C2p + S2

a )

][θp

θa

]

(3)with singularity at θp = 90◦. The proposed spherical mechanismhas a kinematic relation same as that in [13]. The difference isthat we place the yaw joint at the center of the mechanism,in order to reduce the overall size. Although the camera to beoriented will slightly be away from the center, the inertia effectwill be shown in Section V-B to be negligible.

The specific design of the spherical mechanism offers twoadvantages. First, the output pan and tilt angles are nearly un-coupled within the operational range. Hence, controlling the panand tilt motion can be intuitive and energy efficient. Second, onlypin joints of the same bearing size are required. This simplifiesthe design and mass production. The direct measurements ofjoint angles are also facilitated.

IV. DESIGN OF PAN AND TILT FLEXIBLE MECHANISMS

As mentioned in Section II-A, a flexible beam is used toreplace the coupler and two pin joints of the slider crank mech-anism. The design of the pan and tilt mechanisms now relies onshape optimization of the flexible beams. Considering the panmechanism in Fig. 8, the flexible pan beam connects the panmotor to rigid Link 1, which is then connected to the pan joint.An input displacement Dp is specified at the slider. Accompa-nying the displacement is the required thrust Fp provided by thepan motor. As there is no other pin joints except for the one atnode n1 , the rotation of Link 1 relies on deflecting the pan beam.As a result, the shape and length of the pan beam is essentialto the range of rotation. In the following, we first consider thedesign of the pan and then the tilt mechanism.

A. Objectives and Constraints

The design aims to maximize the rotation of Link 1 (and thusthe pan angle) given a specified input from the pan motor. Theinput includes a positive and negative displacement Dp of thesame amount, in order to pan the camera in both directions.To make sure that maximal rotation is achieved while motionsin the two directions have comparable force and displacementproperties, we propose a multiobjective optimization aiming to

minimize the following weighted sum:

f = −|θp(Dp) − θp(−Dp)| + |θp(Dp) + θp(−Dp)|+ 2.5|Fp(Dp) + Fp(−Dp)| + 0.4|σm (Dp) − σm (−Dp)|.

(4)

The first term in (4) is used to maximize the output rotation. Thesecond term is used to equalize the range in the two directions, sothat the input–output relation can be made as linear as possible.The third and fourth terms are used to minimize the differenceof force and maximal stress in the two directions. As the lasttwo terms have units other than degrees, a different weightingfactor is used for each term. Since it is not sure at the beginningwhich direction has positive values, an absolute sign is given foreach term in (4).

The objective value in (4) mainly depends on the shape varia-tion of the pan beam. As the beam has a constant in-plane thick-ness w and out-of-plane thickness t, its shape variation refers tothe directional change along the neutral axis. To parameterizethe shape, we first divide the beam into five links with lengthsfrom L2 to L6 . The links are separated by six nodes (n2–n7),where slopes at the nodes are not necessarily continuous. Theundeflected shape of a link is then described by a shape functionη(u), where u∈[0 1] is a nondimensional arc length along thelink and η measures the angle of rotation (in radians) along u.Using an mth-order polynomial [28], the shape function of theith link is represented as

ηi(u) = ci0 + ci1u + · · · + cim um (5)

where coefficients ci0–cim decide the shape of the ith link.Shape functions with m = 0 and 1 refer to a straight line andarc, respectively. A shape becomes more complicated as theorder increases. Details of link deformation model and shapeparameterization are in given in Appendix A. Given an ηi func-tion and link length Li , a point [xi yi] on the ith link is expressedas

xi = xi(0) + Li

∫ u

0cos ηidu; yi = yi(0) + Li

∫ u

0sin ηidu

(6)where [xi(0) yi(0)] is the coordinate of ni described in framexpyp . By using (5) and (6), the shape of the pan beam nowdepends on the coefficients ci0–cim and length Li of each link.In addition to the beam, the shape of rigid Link 1 is also conve-niently described by a shape function η1 . Since no deformationis involved, only the first term c10 and length L1 are requiredto describe Link 1. Detailed formulation for the pan mechanismdesign is given in Table II.

There are six constraints in Table II to ensure convergenceand that the converged optimal shape is feasible. Constraint (i)confines the dimension of the pan beam by limiting the nodepositions to be within the design boundary. To further preventeach link from intersecting with others, constraints (ii) and (iii)ensure that all the five links stay within the adjacent boundaries.In addition, constraint (iv) limits the link lengths. The lowerlimit is to ensure that link lengths do not converge to zero. Theupper limit is to prevent lengthy links from exceeding the design


TABLE IIFORMULATION OF PAN MECHANISM OPTIMIZATION

TABLE IIIDESIGN PARAMETERS OF THE PAN MECHANISM

boundary. Constraint (v) avoids sharp corners that present fabri-cation difficulties. For constraint (vi), the maximal stress σm (inabsolute value) within a link cannot exceed the allowable stressσy /SF, where σy is the yield stress and SF is the safety factor.The deformation analysis required in the optimization process iscarried out by using the generalized (multiple) shooting method(GMSM) [28], [29]. This method is capable of accurate andefficient beam large deflection computation. The optimizationis realized by using fmincon() in MATLAB.

B. Optimal Beam Shape of the Pan Mechanism

Based on the formulation in Table II, we seek for the optimalshape and the corresponding relationship among θp and Dp .Table III lists the design parameters. We use polyoxymethylene(POM) as the material with elastic modulus E = 2 GPa andyield stress σy = 76 MPa. Consider the case of m = 1 (arc),the optimal initial shape of the pan beam is shown in Fig. 9.The design boundary and node positions (in circles) are alsoshown. The shown deflected shapes of θp =−32.00◦ and 32.00◦

correspond to Dp = 9 and −9 mm, respectively. The optimizedoutput pan angle and input displacement show very good linearrelation. When using a third-order (m = 3) shape function,the maximal pan angles further converge to θp = ±35.54◦, asshown in Fig. 10. The total pan range Δθp = 71.08◦ is sufficientfor camera orientation. Detailed numerical values of the designvariables are listed in Table VI of Appendix B.

Fig. 11 shows the thrust and maximal stress of the pan beam.Marks ◦ and� are finite-element analysis (FEA) results that willbe discussed in Section V-A. The maximal stress magnitudes inboth directions quite match and are below the limit of constraint

Fig. 9. Optimal initial and deflected shapes of the pan mechanism (m = 1).

Fig. 10. Optimal initial and deflected shapes of the pan mechanism (m = 3).

Fig. 11. Thrust and maximal stress of the pan beam (m = 3).

(iv). At Dp = 9 mm, the stress reaches σm = 50.6667 MPa,becoming the active inequality. To increase the pan range underthe same stress limit, the design domain size Xp must increase.This would require a larger mechanism dimension. Unlike themaximal stress, the use of asymmetric beam shape results inunmatched thrusts in the two directions. Negative Dp requiresless thrust to deflect the pan beam. Still, the maximal thrustrequired is small enough and can be adequately provided by thepan motor.

The optimal shape can be explained physically. First, Link 1appears to be short. This is because the objective in Table IIaims to maximize the rotation of Link 1 given the input Dp .Hence, a shorter Link 1 tends to magnify the rotation. Second,Links 4 and 5 form an S-shape. An S-shaped segment naturallyhas a linear compression and tension behavior. This allows therotation amount to be matched in both directions, when giventhe same amount of input displacement.

In Section IV-B, we use five links with m = 3 to sufficientlyprovide beam shape variation. As the formulation in Table II israther generic, extension to more involved shape variations canbe made.


Fig. 12. Schematic of the tilt mechanism design.

C. Design of the Tilt Mechanism

As shown in Fig. 12, the tilt mechanism employs a similardesign approach as the pan mechanism. The tilt motor actuatesto deflect the tilt beam. The tilt beam is divided into Links 3–6.The transmitted motion rotates (rigid) Links 1, 2, 7, and 8 withangle θa . Link 7 represents the distance from the origin to thetilt axis, which is required to accommodate the geometry of thespin and yaw joints. Since the tilt beam remains in the x0z0plane for all θp , the length of Link 7 is the same regardless ofthe rotation of the spin and yaw joints. The vertical bar at the endof Link 8 is used to attach a camera. A 50-g payload is appliedat n9 to emulate the weight (0.5 N) of the camera. Due to thesize of the two motors, the tilt input displacement must be offset11.5 mm from the tilt axis. Although this slightly increases thespace, the gained leverage makes the actuation easier than thepan mechanism.

Table IV lists the optimization formulation. The objective issimilar to that in (4), except that relatively more weighting is onthe second term that involves angle difference. This is requiredsince the input offset would inherently create a biased angle out-put. To design the tilt beam, Links 3–6 are further parameterizedby using the shape function in (5). The objective again dependson the coefficient c and length L that determine the shapes of thelinks and node positions. The constraints are similar to those inTable II. In particular, constraint (ii) ensures that the links mustfit in an irregular design domain caused by input offset. Thedomain is the union of two rectangular areas enclosed by f1–f4and f7–f8 . Constraint (v) prevents mutual interference of Links3–6 and Links 1 and 2 after deformation. This is necessarybecause the design domain of the tilt beam is much closer tothe rigid links, as compared with the pan beam design.

We optimize the tilt beam shape with parameters in Table V.Fig. 13 shows the optimal initial shape. Considering θp = 0,the initial θa due to the camera weight is a small 1.7860◦. A0.263-N thrust Ft is required to hold the camera. The followingθa ’s are calibrated so that the initial input tilt angle is zero. Thedeflected shapes at θa = −32.97◦ and 32.97◦ are also shown.They correspond to Dt = 9 and −9 mm, respectively. The com-puted optimal design variables are presented in Table VII ofAppendix B. Fig. 14 shows the thrust and maximal stress ofthe tilt beam. The maximal stress is 36.7243 MPa and maximalthrust is 1.7706 N at Dt = 9 mm. Both are much smaller thanthose of the pan beam. The input offset creates an inherent lever-age for the tilt beam, as compared with the pan beam that has no

TABLE IVFORMULATION OF TILT BEAM SHAPE OPTIMIZATION

TABLE VDESIGN PARAMETERS OF THE TILT MECHANISM

Fig. 13. Optimal initial and deflected shapes of the tilt mechanism.

Fig. 14. Thrust and maximal stress of the tilt beam.

offset. This explains why the tilt beam has a smaller thrust andstress. As there is no need to use the shape to form an artificialleverage, the tilt beam appears as a smoother line shape than thepan beam.

Considering the ability to maximize the tilt range, the mostimportant active inequalities are L1 = 4 mm, θ1 = π/2, θ2 =


Fig. 15. Pan and tilt angles versus input displacements.

3π/4, and that n4 lies on f7 . These constraints may be relaxed toachieve a larger tilt angle. However, this would induce a largerspace and possible interference between neighboring mechani-cal parts.

Similar to the pan beam, the positive Dt requires a larger thrustthan the negative Dt . In addition to Fp and Ft , deflection of theflexible beams will introduce unwanted side thrust normal to theactuation direction. The maximal side thrust on the pan motoris 0.2666 N in the yp direction and 0.5360 N for the tilt motorin the yt direction. Both are not too big and can be sufficientlyresisted by the linear motor bearings.

Fig. 15 shows the curves of pan and tilt angles with respectto the input displacements. They are linearly regressed as

GMSM : θp = −4.0297Dp (7a)

θa = −3.6973Dt. (7b)

The nonlinearities of pan and tilt are 1.2281% and 0.6371%, re-spectively. The nonlinearity is defined as the maximal deviationfrom the best-fit line, as percentage of the rotation range. The al-most linear curves make the control very direct from given stepmotor input. In contrast, if slider–crank mechanisms were usedinstead, it would be difficult to achieve the level of input–outputlinearity. This is especially obvious for the tilt mechanism, theslider offset of which would result in a skew relation betweeninput and output.

V. FINITE-ELEMENT VERIFICATIONS

A. Static Analysis

To verify the GMSM computation in Section IV, we furthercompare the results in Figs. 11, 14, and 15 with those obtainedby using the static FEA. The FEA is implemented in ANSYS,where pin joints are modeled by using MPC184 elements andflexible beams are modeled by using SOLID184 elements. Theproperties used for the pan and tilt beams are the same as those inSection IV. All other parts are modeled as rigid. The minimal el-ement size is 1.2 mm. Figs. 16 and 17 show the pan and tilt mech-anism simulation. Both are given a ±9-mm displacement input.The maximal stress occurs in the middle of Link 5 for the panbeam and in the middle of Link 4 for the tilt beam. The curvesof forces and maximal stresses are plotted in Figs. 11 and 14.In these figures, they match well with those computed by usingthe GMSM. The difference is primarily a result of modeling dis-

Fig. 16. FEA result of pan beam deflection.

Fig. 17. FEA result of tilt beam deflection.

Fig. 18. FEA result of extreme positions.

Fig. 19. FEA result of pan and tilt angles.

crepancy between line geometry and solid geometry; the FEAmodels use solid geometry, and hence, their results are moreaccurate. Fig. 15 further compares the pan and tilt angles, whichare critical to the motion. The FEA results match with GMSMand shows very good linearity. The FEA pan and tilt relationsare fitted as

FEA : θp = −4.0555Dp (8a)

θa = −3.7008Dt. (8b)

The coefficients in (8) are very close to those in (7). Thenonlinearities of the pan and tilt best-fit lines are 1.2441% and0.6897%, respectively.

Fig. 18 further shows the four extreme configurations whenboth axes are actuated. No interference is observed at thoseconfigurations when the camera is mounted on. Fig. 19 showsthe effect of pan angle on output tilt angle variation. When the


Fig. 20. Dynamic model of the pan flexible mechanism.

pan axis is given a ±9-mm displacement, the top-to-bottomcurves correspond to Dt at −9, −6, −3, 0, 3, 6, and 9 mm.Ignoring the payload weight, the FEA and analytical curvesare compared. The analytical curves are calculated by usingthe GMSM to obtain the deformation of tilt beam and (2) toobtain the inverse kinematics. The FEA values differ from theanalytical ones by at most 0.36◦. The difference is again causedby the modeling discrepancies between FEA and GMSM.

Fig. 19 also shows the joint workspace plot of the mechanism,which is very close to a rectangle with no irregular boundaries.Singularities are not observed in the operational range. Exceptfor the tilt curve of Dt = 0, the effect of pan motion makes thetilt curves to slightly increase from θp = 0 to ±36◦. At Dt =±9 mm, the increase is maximal with amount nearly 5◦. Thissmall amount of increase can often be ignored if not for accurateorientation applications. Hence, the proposed mechanism can betreated as if output pan and tilt angles are uncoupled.

B. Dynamic Analysis

One concern of the flexible mechanisms is their effect of high-speed dynamic behavior on the precise orientation, when com-pared with their rigid-mechanism counterparts. As the weightsof all movable components are less than 1 g, their dynamicaleffects can be ignored. The only one contributing is the iner-tia from the camera payload, which may vary from 10 to 50 g.Considering the pan mechanism in Fig. 20 as an illustration, itcan be regarded as a second-order system. The payload is mod-eled as a point mass with mass m. It has a moment of inertiaIp = mr2 with respect to the pan axis. The pan beam results ina rotational stiffness kp about the pan axis. It is a function ofcurrent pan position. To emulate a lightly damped pan joint, adamping coefficient 0.002 N·mm·s/◦ is assigned. It correspondsto a damping ratio of order 0.1.

To consider the effect of payload inertia, we perform a dy-namic FEA simulation. Without loss of generality, a high-speedprofile from the pan motor is given as follows:

Dp = −9 sin(2πt)mm, for 0 < t < 1

Dp = 0mm, for t > 1. (9)

Fig. 21 shows the response of the pan angle corresponding topayload mass 0, 50, and 250 g. The 0-g case refers to the staticcase. The responses of 0 and 50 g are almost identical, exceptthat the 50-g case has a negligible oscillation when the motionstops after t = 1. When the mass increases drastically to 250 g,the inertia of the payload makes the response to deviate fromthose of 0 and 50 g. As our design payload is an optimistic

Fig. 21. Effect of payload inertia on dynamic performance.

Fig. 22. Prototype of the orienting mechanism.

50 g, the results show that the stiffness of the pan mechanism ishigh enough for high-speed applications. The same conclusionis made for the tilt mechanism. Hence, the proposed orientingmechanism can be treated quasi-statically. Additional controleffort is not required to compensate the motion deviation causedby payload inertia.

VI. PROTOTYPE AND EXPERIMENTS

A. Prototype

Fig. 22 shows the orienting mechanism together with the panand tilt beams. The shapes of the pan and tilt beams were ma-chined exactly as the geometries designed in Section IV. Othermechanical parts were also fabricated based on the dimensionsdescribed in Section II-B, using POM as the material. Sincethe mechanism motion has been shown in Section V-B to bequasi-static for payload under 50 g, the following tests wereperformed without considering the payload. Without load, theFEA tilt curve in Fig. 15 has a best-fit line slightly changed to

θa = −3.7872Dt (10)

with nonlinearity 1.1029%, while the pan curve remains un-changed. Due to the sufficient stiffness of the tilt beam, theabsence of payload only slightly increases the best-fit linecoefficient.

Both pan and tilt motors have a 2-mm lead per revolution.They provide a 0.01-mm input displacement step. This convertsto 0.040◦ pan angle resolution and 0.038◦ tilt angle resolution.Compared with other types of linear actuators, the linear stepmotor, although has a small size, has a very large holding force(up to 45 N) due to the use of leadscrews. This is advantageoussince the orientation of the camera can be maintained under


Fig. 23. Measurement setup.

Fig. 24. Experimental pan and tilt curves.

applied external disturbance, even when the power is OFF. Sincethe pan and tilt beams only require a small thrust, the speed andacceleration can be increased by using motors with a larger lead(up to 8 mm).

Benefitted from the use of only pin joints, angle sensors canbe easily placed on the output pan and tilt joints to measure theactual orientation. We place an angle sensor (Murata SV01L,±2% nonlinearity) on the pan joint and two angle sensors on theoutput tilt joints to measure the output angles. To compare withthe input displacement, we measured the motor stroke usinga laser sensor (Keyence LK-081, ±0.1% nonlinearity). Fig. 23shows the measurement setup. The noncontact-type laser sensorhas a better accuracy than the contact-type angle sensor. For thepresent loading conditions, the input displacement measuredby the laser sensor is almost identical to the desired. Hence, thelaser sensor signal is used as a reference for the angle sensor. Theangle sensor, on the other hand, is less accurate and vulnerableto physical disturbance. Nevertheless, its tiny size allows it tobe directly installed on a moving joint (especially the tilt joint)without increasing the overall size. The tests in Sections VI-B–VI-E were conducted based on the prototype in Fig. 22 andsetup in Fig. 23.

B. Accuracy Test

By using the laser sensor to obtain the displacement and anglesensor to obtain the rotation, Fig. 24 shows the experimental panand tilt curves. Each curve is the average of five repeated testswhile the other axis is in its zero position. The experimental tiltcurve matches with the FEA curve (no payload weight) verywell, while the pan curve has a slight difference during thenegative input displacement. The maximal difference is 3.05◦

and occurs at Dp = −9 mm. Except for the angle sensor error,the discrepancies are caused by the fabrication and assemblyimperfections. For practical use, the experimental pan and tilt

Fig. 25. Pan resolution test.

Fig. 26. Tilt resolution test.

curves are linearly regressed as

Experiment: θp = −4.2045Dp (11a)

θt = −3.7113Dt (11b)

where the nonlinearities of the pan and tilt best-fit lines are2.98% and 0.79%, respectively. Note that θt replaces θa in (11b)and Fig. 24, as compared with (8b) and Fig. 15. In the accuracytest and the following tests, the tilt motion was performed withθp = 0. Hence, θt and θa are the same. We use θt to identify thatit is the actual output tilt angle measured by the angle sensor.

C. Resolution Test

Figs. 25 and 26 show the resolution test of the pan and tilt mo-tion, respectively. Both axes were given an input displacementwith 0.4-mm step size. This converts to 1.6818◦ angular panstep and 1.4845◦ tilt step. The laser sensor measured the inputdisplacement and the angle sensor measured the output rotation.The scales of displacements (Dp and Dt) and angles (θp , θt) areadjusted so that their ratios are exactly the coefficients obtainedin (11). By doing so, the displacement and angle curves shouldideally match, except for the minor nonlinearities. In Figs. 25and 26, clear stair-case profiles are observed for the displace-ment curves. The angle curves show stair-case profiles as well,but they are not as clear-cut as the displacements. The anglecurves also deviate from the displacement curves. The maximaldifference is less than 3◦. These nonmatching results are pri-marily due to the angle sensor accuracy and joint clearance.

D. Speed Test

Given an open-loop command from the motor, the pan andtilt were to complete a period of full range (±9 mm) motion.Figs. 27 and 28 show the speed response of the pan and tiltmechanisms, respectively. The laser sensor measured the inputdisplacement and angle sensor measured the output rotation.The given motion profile is almost identical to that obtained


Fig. 27. Speed response of the pan mechanism.

Fig. 28. Speed response of the tilt mechanism.

Fig. 29. Reliability test of the pan mechanism.

by the laser sensor and hence is not plotted. Again, the ratiosof the displacement scales and the angle scales match with thecoefficients in (11).

The pan mechanism completed one cycle in 1.898 s, whilethe tilt mechanism completed one cycle in 1.249 s. The averagespeed is nearly 80 ◦/s for the pan and 110 ◦/s for the tilt mech-anism. For the pan motion, the angle response closely matcheswith the displacement response. For the tilt motion, there aredead bands at the peaks. The dead bands are mainly results ofaccumulated joint clearance at the spin and yaw joints.

E. Reliability Test

Although the pan and tilt beams are designed to operate withintheir limit of yield stress, there is a need to test that the beamscan operate for many cycles without fatigue and failure. Of thetwo flexible beams, the pan beam suffers from much more thrustand stress than the tilt beam during the entire motion. Hence, itsreliability is of primarily concern. To investigate the reliability ofthe pan beam, we performed a test to see its motion characteristicassociated with cycles. The pan beam was to travel in the fullrange using the same speed profile in Fig. 27. Fig. 29 shows themaximal θp measured by the angle sensor. Ten thousand cycleswere continuously tested. As can be seen, the pan mechanismwas able to repeat its full range of motion. The small oscillationsafter 103 cycles are less than 1.5683◦. They are results of minormotor stall.

Fig. 30. Step responses.

Fig. 31. Frequency responses.

Fig. 32. Binocular vision.

F. Control Test

To demonstrate the ability to accurately align the pan and tiltangles in various conditions, two closed-loop PID controllers(one for each axis) were implemented on the mechanism. At10-kHz sampling rate, the controllers generate velocity signalsfor power drives (ST5-Plus, Applied Motion Products) to com-mand the two motors. The pan and tilt angle sensors providefeedback signal to match with the desired. Fig. 30 shows thestep responses of the pan and tilt mechanisms. With a step from–20◦ to 20◦, the rise time is 0.08 s for the pan and 0.1 s forthe tilt mechanism. These correspond to average angular veloc-ities exceeding 400 ◦/s. Fig. 31 shows the sinusoidal frequencyresponse of the mechanism. Both axes are asked to track a sinu-soidal wave with 20◦ amplitude. The responses of pan and tilt arevery similar. Both have a bandwidth of approximately 4.5 Hz.The bandwidth corresponds to achievable angular velocity of360 ◦/s.

VII. STEREO VISION APPLICATIONS

One major motivation of the proposed streamlined mecha-nism is to realize a compact integration of two mechanisms forbinocular vision applications. Fig. 32 shows three such configu-rations. Like human eyes, the two orienting mechanisms can beplaced side by side, 6 cm apart, without interference. The fouraxes in Fig. 32(a) are independently actuated. Depending on thespecific application, they may be reduced to three or two inde-pendent axes. To mimic human eye movement, the two tilt flexi-ble beams can be made into a single piece, as shown in Fig. 32(b).Thus, the two tilt axes can be jointly actuated. The two indepen-dently actuated pan axes can perform conjugate and vergenceeye movements [15]. For stereopsis applications, the pan flexi-ble beams are placed as mirror images of each other, as shown


Fig. 33. Deformation model of a flexible link.

in Fig. 32(c). They are jointly actuated to facilitate vergencecontrol. This further reduces the number of actuators to two.

VIII. CONCLUSION

This paper has presented the design and prototype of a mech-anism to pan and tilt a camera. Two linear motors are placed inparallel to drive their respective flexible mechanisms for nearlyuncoupled pan and tilt motions. The adaptive arrangement ofthe actuators and flexible mechanisms makes the overall sizevery compact and streamlined. As the mechanism portion onlyconsists of a small volume, the overall size is merely limited bythe choice of the camera and motors used. The dimension canbe reduced if smaller camera and motors are available.

The optimized pan and tilt axes provide linear input–outputrelations. Static and dynamic simulations showed that the weightand inertia of a payload under 50 g can be ignored. These goodproperties make the implementation of the driving electronicsvery easy and intuitive.

The performance tests demonstrated that the mechanism issufficient for various camera-orienting applications. As the de-sign is generic, we expect it can be extended to other applicationsthat may include surgical tools and haptic devices.

APPENDIX A

LINK DEFORMATION MODEL AND ITS SHAPE

PARAMETERIZATION

The pan and tilt beams are divided into multiple links asshown in Figs. 8 and 12. Each link has a rectangular crosssection with in-plane thickness w and out-of-plane thickness t.The length of the link is denoted as L; it flexural rigidity isdenoted as EI, where E is the elastic modulus and I = tw3 /12is the second moment of area. Fig. 33 shows the schematic ofthe link. The undeflected link is described by a shape (intrinsic)function η(u), where u∈[0 1] is a nondimensional arc lengthalong its neutral axis and η measures the angle of rotation (orslope, in radians) along u.

External loads change the shape of the link from the initialη(u) to deflected ψ(u). The link reacts with horizontal force h,vertical force v, and bending moment M to balance external loadsat the two ends (u = 0 and u = 1). The differential equationsgoverning the link deflection is derived by using the principleof minimal potential energy

[ψ ψ′ x y]′

=[ψ′ L2

EI(h sin ψ − v cos ψ) + η′′ L cos ψ L sin ψ

](12)

Fig. 34. Effect of using different number of polynomial terms.

where a prime denotes derivative with respect to u; [x y] isthe coordinate of a point on the link. Equation (12) can besolved by using the GMSM with proper formulation of boundaryconditions [28]. After solving (12), the bending moment andmaximal bending stress are calculated as follows

M = EId(ψ − η)

du(13)

σm =Ew

2L

d(ψ − η)du

. (14)

When the undeflected shape of the link is described by (5), ashape function of different order creates a different link initialshape. The effect of the number of polynomial terms in (5) onthe link shape is depicted in Fig. 34. When only one term (c0)presents, it corresponds to a straight link with slope tan(c0),as shown in Fig. 34(a). When considering both c0 and c1u,it describes an arc with radius of curvature L/c1 , as shown inFig. 34(b). When three terms present (m = 2), it is a curve with atmost one inflection point shown in Fig. 34(c). Similarly, higherorder polynomials can be further expected. For any coefficientcombination in (5), we have [x′ y′] = [Lcosη Lsinη] �= 0 for allu. Thus, links represented by the shape functions are naturallyfree of cusps. This is beneficial since the prevention of cusps andnear-cusp regions avoids stress concentration and manufacturingdifficulties. As the link shape depends on the coefficients of theshape function in (5) and length L, they are formulated as designvariables. The number of design variables is thus (m + 2) foreach link.

APPENDIX B

OPTIMAL DESIGN VARIABLES

TABLE VIOPTIMAL DESIGN VARIABLES OF THE PAN BEAM (m = 3)


TABLE VIIOPTIMAL DESIGN VARIABLES OF THE TILT BEAM (m = 2)

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Yi-Chiao Lee received the B.S. and M.S. degreesin mechanical engineering from National ChengKung University, Tainan, Taiwan, in 2009 and 2011,respectively.

He is currently with the Research and Devel-opment Substitute Service of Chroma ATE Inc.,Taoyuan, Taiwan. His previous fields of interestwere flexure-based mechanism design and bioin-spired robotics.

Chao-Chieh Lan (M’09) received the B.S. degreefrom National Taiwan University, Taipei, Taiwan, in2000, and the Ph.D. degree from the Georgia Instituteof Technology, Atlanta, in 2006, both in mechanicalengineering.

He is currently an Associate Professor in theDepartment of Mechanical Engineering, NationalCheng Kung University, Tainan, Taiwan. His researchinterests include flexure-based mechatronics sys-tems, robotics, multibody dynamics, and mechanismdesign.

Cheng-Yu Chu received the B.S. degree in mechan-ical engineering from National Cheng Kung Univer-sity, Tainan, Taiwan, in 2011, where he is currentlyworking toward the Graduate degree in the Depart-ment of Mechanical Engineering.

His current research interests include mechanismdesign, system dynamics, and robotics.


Chih-Ming Lai received the B.S. degree in mechan-ical engineering from National Central University,Jhongli, Taiwan, in 2010. He is currently workingtoward the Graduate degree in the Department ofMechanical Engineering, National Cheng Kung Uni-versity, Tainan, Taiwan.

His current research interests include feedbackcontrol systems, machine vision, and robotics.

Yi-Jie Chen received the M.S. and Ph.D. degreesin mechanical engineering from National ChengKung University, Tainan, Taiwan, in 2004 and 2008,respectively.

He is currently a Project Manager in the Metal In-dustries Research and Development Centre, Taipei,Taiwan. His research interests include robotics,mechanism design, and mechatronics systems.

A Pan–Tilt Orienting Mechanism With Parallel Axes of Flexural Actuation

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