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Mechanism, design and motion control of a linkage chewing device for food evaluation
Available online at www.sciencedirect.com
Mechanism and Machine Theory 43 (2008) 376–389
Mechanism and Machine Theory www.elsevier.com/locate/mechmt
Mechanism, design and motion control of a linkage chewing device for food evaluation W.L. Xu a
a,*
, D. Lewis a, J.E. Bronlund a, M.P. Morgenstern
b
Institute of Technology and Engineering, College of Sciences, Massey University, New Zealand b New Zealand Institute for Crop and Food Research Ltd., New Zealand Received 30 January 2007; received in revised form 12 March 2007; accepted 16 March 2007 Available online 27 April 2007
Abstract A linkage-based chewing device is proposed to perform standardised chewing for use in food evaluation. The linkage for chewing is firstly specified in terms of the trajectory of the first molar and the chewing force, according to the in vivo measurements of the human chewing ranging from grinding (or lateral chewing) to crunching (or vertical chewing). A fourbar linkage is synthesized to achieve the lateral chewing trajectory of the molar, and by adjusting the ground link length to achieve any trajectory between the lateral and vertical chewing. A six-bar crank-slider linkage is then designed to guide the molar teeth moving in a set orientation while still following the chewing trajectory produced by the four-bar linkage. The chewing device based on the six-bar linkage is constructed with inclusion of anatomically correct teeth for reducing the food particle size, a food retention device for collecting the food particles being chewed and a shock absorber for preventing excessive chewing force. The linkage chewing device is evaluated by simulations of kinematics and dynamics and actual measurements of the trajectory and chewing force. For the motion control of the actuator, the chewing velocity along the trajectory is also profiled for occlusal phase and opening/closing phase of the chewing, and the variations of the chewing for different foods are set in a GUI (graphical user interface) in Labview. The device is finally validated by chewing on a cereal bar and comparing the resulting particle size of the bolus with those by human subjects. 2007 Elsevier Ltd. All rights reserved. Keywords: Human chewing; Food evaluation; Chewing device; Adjustable linkage; Motion control
1. Introduction The human masticatory system is a complex system that comprises of an upper and lower jaw that have teeth located on them. It also includes a tongue, cheek and saliva production capability. When mastication is performed, the lower jaw (mandible) is moved by muscles that are attached between it and the upper jaw [1]. The chewing movement begins with the mandible opening thereby creating a space between the teeth located on skull and the mandible. The tongue then places food particles that need chewing on to the molars *
Corresponding author. Tel.: +64 9 414 0800; fax: +64 9 443 9774. E-mail address: [email protected] (W.L. Xu).
0094-114X/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2007.03.004
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on one side of the mouth. The mandible then closes and breaks up these food particles and then the particles fall off the teeth back on to the tongue for repositioning during the next cycle [2]. The opening of the mouth of the chewing cycle is approximately vertical [3]. The speed of the mandible in the opening phase initially starts slowly and increases as the mouth opens. When the mouth starts to close, the mandible moves laterally outward and initially closes quickly coming back towards the teeth and then slows for occlusion. The trajectories of the teeth during chewing vary substantially for different foods in the frontal plane, but, they are very close to a straight line in the sagittal plane [4]. This line may vary from a vertical line where the teeth come together at a 0 angle and a line where the teeth come together at a 30 angle. The trajectories used to chew different food particles differ depending on both the shape and the texture of the food particles, thus generating a different chewing action for different foods. If a vertical chewing motion is used, the teeth use their cusps to fracture the food particles. Where as if a more lateral chewing motion is used, the teeth use their sharp edges to function as blades and cut up the food particles [5]. As food properties affect the chewing trajectories, a considerable amount of work has been done to determine chewing movements in food sciences [4,6,7]. Measurements were made continuously over the masticatory process and included some of the following: frequency, length of chewing, tracking of jaw movement, force distribution, application of compression and shear forces on the food and particle size and structure of the bolus just prior to swallowing. These quantities vary between subjects (e.g. due to differences in jaw geometry, teeth shape, sensitivity to pain) and food texture (e.g. elasticity, hardness, adhesion especially to dentures, etc.). There are a variety of instruments or devices available for evaluating food properties. However, such devices usually use a simple straight motion (mostly food compression) and are not able to simulate the entire suite of complex functions and movements involved during mastication. Since the early 1990s there have been attempts in developing masticatory robots for food texture assessment [8–11]. While robotic chewing devices that possess multiple degrees of freedom (DOF) of motion are able to reproduce chewing behaviour in threedimensional space, a single DOF linkage device for chewing is pursued in this study. A linkage device is much simpler in structure and motion control and more reliable in operation. The presence of a straight line trajectory in the sagittal plane presents the opportunity to reproduce the chewing motion in 2D using a simple linkage. In this paper, the chewing linkage is specified to meet basic human chewing behaviours in terms of kinematic requirements and forces. Mechanism design is carried out using an atlas for the generation of trajectory, and the design also takes into account the set teeth orientation. To produce a range of chewing trajectories, the linkage is made with an adjustable ground link. The motion of the actuator is planned according to different velocity requirement in occlusal phase and opening/closing phase of the chewing, and the GUI (graphical user interface) in Labview facilitates the various chewing operations of the device. The validation of the device is performed by chewing on a real food. 2. Design specifications of a linkage chewing device Each mandibular tooth has its own trajectory while chewing, and a typical trajectory can be defined by vertical and lateral displacements and opening (exit) and closing (entry) angles, as illustrated in Fig. 1, as well as the time to complete them [2]. The trajectory of the first molar is simply a vertically compressed version of the incisor trajectories, while the entry and exit angles to and from occlusion are not greatly different [12]. The incisor trajectory can be measured but vary between lateral chewing (grinding) and vertical chewing (crunching), depending on the type of food being chewed. Due to the fact that chewing is performed on the molar teeth, the chewing device must follow the trajectories of the molar teeth. As no actual data is available, the trajectories of the molar teeth during chewing can be estimated by simulation from the trajectories of the incisor [12,13], as given in Table 1. To evaluate different foods the chewing device to be developed should be able to achieve any trajectory between lateral and vertical trajectories. The device should also meet cycle time and occlusal time. Therefore, the linkage for chewing can be specified by the set of parameters in Table 1. Furthermore, the forces applied on the teeth vary with the type of food being chewed. The force applied to a single tooth is also different to that of total force between all the contacting teeth during chewing. On foods such as biscuits, carrots and cooked
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Fig. 1. A tooth trajectory and its defining parameters.
Table 1 Values of the trajectory parameters for lateral and vertical chewing [12,13]
Closing angle () Opening angle () Total angle () Vertical opening (mm) Lateral displacement in opening (mm) Lateral displacement in closing (mm) Cycle time (s) Occlusal time (s) Opening/closing time (s)
Lateral chewing
Vertical chewing
46.6 113.1 66.5 14.6 1.1 4.0 0.77 0.12 0.65
72.5 78 5.5 15.1 0.4 3.1 0.7 0.16 0.54
meats forces range between 70 and 150 N on a single tooth [14]. Thus, the chewing force that the linkage can apply on food samples is specified as 150 N at maximum. 3. Basic linkage mechanism for the chewing device A four-bar linkage (Fig. 2) is a relatively simple mechanical mechanism and a point ‘P’ on the coupler can trace a 2D trajectory. The kinematic parameters for the linkage include crank link ‘a’, coupler link ‘b’, follower link ‘c’ and ground link ‘d’, as well as angle of ‘c’ and distance ‘BP’ for the coupler point ‘P’. A four-bar
Fig. 2. Kinematic parameters for a four-bar linkage [15].
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linkage in its standard form can only perform one set trajectory, and in the case where a range of trajectories are required to be reproduced, the ground link can be made adjustable manually. The Cedarville engineering atlas [15] was used to find a number of suitable trajectories that have entry and exit angles that closely match a lateral chewing cycle as specified in the above section. When a trajectory was found that matches the desired occlusal angles of a lateral chewing motion it was marked down as a possible solution. As vertical chewing motions are also required, this can be achieved by further changing the ground link length. Fig. 3 shows the final choice of the lateral chewing trajectory where the link parameters are shown at the top with varying ‘BP’ length. After the occlusal angles were examined, the final design chosen was Crank (link ‘a’) = 1, Follower (link ‘c’) = 3, Ground (link ‘d’) = 3.8–5 to achieve horizontal and vertical chewing motions, Coupler (link ‘b’) = 3.5, Coupler (distance ‘BP’) = 3, Coupler (angle ‘c’) = 60. These values are only ratios of the link lengths, relative to the Crank (a), and the actual links can be of any length as long as the ratios are obeyed. To make the actual linkage chewing device to be as compact as possible, a smallest feasible physical crank chosen is 10 mm long when its pivotal and joint bearings are taken into account. The chewing trajectories by the linkages were compared with those from real measurements of human chewing in Table 2. It can be found that in terms of the occlusal angles, the linkage can achieve a close match with the lateral chewing trajectory while still having reasonable trajectories for the vertical chewing; however, the linkage has larger vertical opening and lateral displacements. This should be acceptable as these aspects of
Fig. 3. Candidate trajectories of the four-bar linkage.
Table 2 Comparison between the trajectories by linkages and humans Lateral chewing
Closing angle () Opening angle () Total angle () Vertical opening (mm) Lateral displacement in opening (mm) Lateral displacement in closing (mm)
Vertical chewing
Human
Linkage
Human
Linkage
46.6 113.1 66.5 14.6 1.1 4.0
45 112 67 23 3 9
72.5 78 5.5 15.1 0.4 3.1
99 105 6 34 3 0
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the chewing trajectory do not impact on the food breakdown process as long as they are sufficient to clear the food between chewing cycles. The motor can be sped up during this part of the cycle to ensure representative masticatory behaviour is simulated.
Fig. 4. Three chewing trajectories by adjustable four-bar linkage.
Fig. 5. Construction of the adjustable four-bar linkage: (a) adjustable ground link; (b) adjustable four-bar linkage; (c) major parts chosen.
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Fig. 4 depicts three trajectories by the linkage at the ground length of 38 mm, 44 mm and 50 mm, respectively. It can be seen that the occlusal position shifts, the vertical opening displacement increases and the lateral displacement decreases as the length of the ground link gets smaller. This confirms that the linkage is able to reproduce various chewing trajectories. The chewing device to be constructed can adjust the occlusal position of the teeth by varying the distance between upper and lower teeth. Once the link lengths of the four-bar linkage were determined, the design of the mechanical device could commence. The basic designs of the crank, coupler and follower are straightforward only with the joint points of the links matching the lengths determined. The ground link needs to have a 12 mm adjustment that effectively changes the link length between 38 mm and 50 mm. Fig. 5 shows the final four-bar linkage constructed where the adjustable ground link was achieved using a threaded rod to move a block when the rod is turned. 4. Six-bar linkage mechanism for the chewing device 4.1. The six-bar linkage As discussed before, the adjustable four-bar linkage can produce the required trajectories. However, it cannot keep the mandible or teeth in same proper orientation over the entire trajectory. A simple way to resolve this is to add another two links (links 5 and 6 in Fig. 6) to the four-bar linkage, thus making it a six-bar linkage. The two links are connected by a sliding joint between them, and link 5 is attached onto the coupler by a revolute joint and link 6 onto the ground by another sliding joint. The set of teeth is mounted atop link 5, which is forced to move in a plane constrained by the two sliding joints. To produce the chewing trajectories in the sagittal plane of an angle ranging between 0 and 30 to the horizontal plane, the base of the six-bar linkage can be tilted manually. To have balanced dynamics to reduce the forces and impact, the chewing device was constructed symmetrically by placing two identical four-bar linkages on each side of the device (Fig. 6). The cranks of the two linkages were mounted on a single shaft driven by a single motor via a spur-gear train.
Mandible teeth attaching point
Link 5
Revolute joint Sliding joint
Link 6
Frame tilted for a saggital plane
4-bar linkages
Fig. 6. Design of a six-bar crank-slider linkage.
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While being constructed, the six-bar linkage was extended to include anatomical teeth with a quick attachment mechanism, a molar teeth repositioning table, a shock absorber that prevents excessive impact force and a simple food retention mechanism that collects chewed food particles. Food repositioning may be performed by the operator between chewing cycles. Fig. 7 shows a photograph of the built chewing device where the linkage is inverted with mandible teeth up and the maxilla teeth down for convenience of collecting chewed food particles. 4.2. Motion planning While the linkage can trace a desired chewing trajectory, the velocity along the trajectory still needs to be profiled. With respect to a chewing trajectory (Fig. 8), the molar teeth moves at constant velocity during the occlusion phase, and then speeds up from occlusal velocity to a maximum velocity and back down to occlusal velocity in a specified time. The occlusion starting and ending positions can be found by a horizontal line of 0.5 mm down from the maximum intercuspal position [13]. The linkage constructed was simulated for a lateral chewing trajectory in SolidWorks (Fig. 8). Each point on the trajectory corresponds to the crank shaft rotating 4.5 and the occlusal phase of 36 turn of crank shaft is found. As the time to complete this phase is specified as 0.12 s (Table 1), the occlusal velocity of the crank is 300/s. The start angle and final angle of crank are found 18 and 342 (Fig. 8a). Considering a 1:42 gear reduction between the motor and the crank, the occlusal velocity, start angle and final angle of the motor shaft are
Motor & control unit Crank Ground link
Coupler Link 6
Follower
Link 5 Handle for the adjustable sagittal plane
Handle for the adjustable ground
Quick teeth attachment mechanism Mandible molar
Shock absorber Food retention mechanism Maxilla molar Maxilla molar repositioning table
Handle for the adjustable maxilla
Fig. 7. The constructed chewing device.
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Fig. 8. Definition of the occlusal phase.
12,600/s, 756 and 14,364, respectively. The time taken to open and close the mouth is specified of 0.65 s (Table 1). Based on these values, a cubic trajectory of the motor shaft is found as [16] hðtÞ ¼ 756 þ 12; 600t þ 38; 471t2 39; 457t3 _ ¼ 12; 600 þ 76; 942t 118; 371t2 hðtÞ
ð1Þ
€ hðtÞ ¼ 76; 942 236; 742t
ð3Þ
ð2Þ
The above planned trajectory is for the lateral chewing. As the chewing device is intended for performing a variety of trajectories between the lateral and vertical chewing, the trajectory other than the lateral chewing will be different. An actual planned trajectory is decided by occlusal angle, occlusal time and opening/closing time (Fig. 8b), which can be set up in the motion control GUI (see Section 6). 4.3. Motor selection After the materials of the parts are specified for the linkage and a constant force of 150 N is applied vertically at the coupler point ‘P’, the linkage can be simulated in SolidWorks to find the driving torque required
Moment - Y (newton-mm)
2603
1578
552
-473
-1498 0.00 0.06 0.12 0.18 0.24 0.30 0.36 0.42 0.48 0.54 0.60 Time (sec)
Fig. 9. The torque required at the crank shaft.
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Table 3 Comparison of required and achievable specifications at the crank Parameter
Required
Estimated capability
Speed (rpm) Torque (N m) Acceleration (/s2)
100 2.6 190
190 3.82 414
at crank shaft. Fig. 9 shows a crank torque versus time plot when the crank runs at 300/s which is the occlusal speed of the crank. The maximum torque the crank requires to run the chewing device is 2.6 N m. Consequently, the output of the geared motor must be able to produce a minimum torque of 2.6 N m at 300/s (or 78 rpm) to achieve the desired chewing force of 150 N. In addition, the required acceleration is estimated at 190/s2 [12]. A brushless DC motor finally chosen could deliver 6.0 N m of torque continuously and 7.5 N m of torque for short periods. With the gear ratio of 1.57, the torque, speed and acceleration at the crank can be 3.82 N m, 190 rpm and 414/s2, respectively, which meets the required performance of the crank (Table 3). 5. Analysis of the linkage chewing device 5.1. Trajectory and force evaluation A simple way to compare the trajectories that the device can produce and the desired chewing trajectories is to use a pen to trace the trajectories achieved and overlay them. The pen used to trace the trajectories was modified so that the spring was used to push the nib out rather than retracting it. The pen was securely attached to the slider of the six-bar linkage and the card was setup in a vertical fashion so that the nib was
Fig. 10. The overlay of the achieved and desired trajectories (solid line = actual, dotted line = desired): (a) later chewing; (b) vertical chewing.
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in contact with the card. It was found from numerous measurements that the trajectories produced by the chewing device are close to the desired ones during the occlusion but slightly different in the opening/closing phases, as illustrated in Fig. 10. This minor difference is due to the play in the joints of the linkage, and insignificant to the entire chewing as it occurs only in the opening/closing free motion. The force testing was performed by the use of a load cell. This idea involves having the teeth attaching point (link 5) pressing down on the load cell to measure the force applied. The chewing device was set to run continuously and the force that the linkage can apply was measured. The results show that the chewing device could comfortably apply the desired 150 N chewing force and would stall at approximately 260 N. 5.2. Stress and deformation analysis The six-bar linkage can be simulated in COSMOS/Works to test if the device can withstand the forces that will be applied. When a force of 150 N was applied at the teeth attaching point, the stress analysis was performed at the occlusal position. Results show that there is no excessively large stress on the device, with the largest stress being concentrated where the linear bush of the link 5 of the four-bar linkage is (Fig. 11). This is due to the fact that the linear bush makes a relatively sharp edge in the structure. This stress concentration was expected when the structure was designed, and hence needs not to be avoided as the link 5 is strong enough to withstand that level of stress. The deformation of the device was also analysed to examine the buckling that occurs when the 150 N load was applied at the teeth attaching point. The results show that the deformation is 0.004 mm at the place where the linear bush meets the shaft that it slides on (Fig. 12). This can be considered negligible as this amount of buckling in the shaft will not cause the linear bush to jam.
Fig. 11. The stress analysis of the linkage.
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Fig. 12. Deformation analysis of the linkage.
6. Control system and software Because the chewing cycle time and occlusal time vary between people and foods being chewed, motion control of the motor is required. This control was implemented in National Instruments ‘Labview’ programming language to allow flexibility in subsequent prototypes. As the device was to be controlled from a Labview program it made sense to choose a control card that could easily be interfaced with Labview. The communication between the control card and the computer based software was done via a RS-232 serial interface. For the chewing device to function in a way that the human operation would be satisfied with, it is important to include all the functions that would be necessary for simple operation. These functions are as follows, which can be seen in GUI in Fig. 13: • Set to lower position – this function sets the chewing device to the occlusal position so that the teeth can be aligned when setting up the device. • Set to top position – this function sets the chewing device to the position where the teeth are maximum distance apart so that a food sample can be placed in it. This can be thought of as the mouth being open. • Start chewing – this will be used to make the device chew by making the device follow a velocity profile that matches that of a human chewing velocity profile. The number of chews will also be able to be set. • Single cycle – this function will be used as a quick select ‘one chew’ button and will only perform one chewing cycle. • Low speed manual control – the user will be able to use this control to make the chewing device move at a slow speed to check the occlusion once the teeth have first been set up. • Master stop – this will be used as a safety feature that allows the user to stop it at any time during any function. It should be cautious that this stop stops only the execution of those motion programs by setting the velocity of the motor to zero. To enhance the safety, an emergency button is still in order.
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Fig. 13. GUI implementing the operational functions.
Fig. 14. GUI for specifying the occlusion.
The operator may wish the chewing device to chew foods differently. To this end, the device has to allow different velocity profiles (Fig. 14). This can be implemented by changing the parameters for the velocity profiles in the controller. These control parameters are: • Occlusal time – the time the occlusal phase is to take. • Opening/closing time – the time it takes to return to the start of the occlusal phase. • Occlusal angle – this specifies the point where the occlusion begins and ends. 7. A chewing experiment The chewing device designed is to reproduce the trajectory of the molar teeth during human chewing cycles. It employs anatomically correct teeth geometries with accurate occlusion. The trajectory of the jaw can be adjusted to give a range of vertical and lateral movements so that different foods can be processed appropriately. The speed of the jaw can also be adjusted to simulate the motions observed during human chewing.
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Fraction passing through 1.4mm seive
90% 80% 70% 60% 50% 40%
Chewing device
2g sample 4g sample
30%
Chewing device
20% 10% 0% 0
2
4
6
8
10
12
14
Subject number
Fig. 15. Comparison of particle size between human subjects and the chewing device.
Validation of the device was performed by comparing the resulting particle size of the bolus produced by the chewing device with the particle size of a bolus produced by a human subject. The device was tested on a cereal bar by taking 1 g slices and placing them onto the teeth. The machine was made to undergo two cycles after which artificial saliva was added in the proportion measured during human chewing trials. The food particles were rearranged on the teeth and the device was made to carry out another 5 cycles. The particles were again rearranged on the teeth before chewing for another 5 cycles, repeating this pattern until the total number of chewing cycles was that observed in human chewing. The bolus was then collected and washed through 1.4 mm and 0.25 mm sieves and dried. The fraction of solid particles passing through the 1.4 mm sieve was then compared with the results collected from human subjects as a partial validation of the device. The results are seen in Fig. 15, where those in the shaded box is the particle size using the chewing device developed and the rest is that of human chewing on 2 g and 4 g food sample. It can be found that although there is some variability between the fractions passing through the 1.4 mm sieve in the device chewed samples, it is of a similar magnitude to that observed in the human subjects. While further validation is necessary it is believed that the device has enough flexibility to be developed into a routine laboratory apparatus for the purposes of pre-processing foods in a systematic and reproducible manner for subsequent nutritional analysis and for evaluation of the dynamics of food texture changes during chewing. 8. Conclusion The linkage chewing device for use in food evaluation was developed and the mechanism design, construction, motion control and simulation and experimental validation were described. The design specifications were derived from published in vivo measurements of human chewing. While the four-bar linkage was for chewing trajectory, the six-bar linkage was to keep the molar teeth moving in a set orientation. A variety of chewing trajectories were achieved by varying the ground link length. The motion of the actuator was planned to implement various chewing motions required for different foods. The operation of the device was made easy via GUIs programmed in Labview. While initial experiments show the promising results by the device, more validations of chewing are required before it becomes a routine laboratory apparatus for the purposes of pre-processing foods.
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Acknowledgements The work in this paper was supported by the Baking Industry Research Trust, New Zealand and by the NZ Foundation for Research, Science and Technology, through Innovative Foods contract C02X0401 (Lifestyle Foods for Energy Balance – The Carbohydrate Story). It is acknowledged that the validation data were provided by Kylie Forster and Christine Lawrence of Institute of Food, Nutrition and Human Health, Massey University, New Zealand. References [1] P.W. Lucas, The structure of the mammalian mouth, in: Dental Functional Morphology: How Teeth Work, Cambridge University Press, United Kingdom, 2004, pp. 13–54. [2] P.W. Lucas, How the mouth operates, in: Dental Functional Morphology: How Teeth Work, Cambridge University Press, United Kingdom, 2004, pp. 55–86. [3] F. Mongini, G. Tempia-Valenti, G. Benvegnu, Computer-based assessment of habitual mastication, Journal of Prosthetic Dentistry 55 (1986) 638–649. [4] K. Anderson, G.S. Throckmorton, P.H. Buschang, H. Hayasaki, The effects of bolus hardness on the masticatory kinematics, Journal of Oral Rehabilitation 29 (2002) 689–696. [5] P.W. Lucas, Tooth shape, in: Dental Functional Morphology: How Teeth Work, Cambridge University Press, United Kingdom, 2004, pp. 87–132. [6] M.A. Peyron, C. Lassauzay, A. Woda, Effects of increased hardness on jaw movement and muscle activity during chewing of viscoelastic model foods, Experimental Brain Research 142 (2002) 41–51. [7] K. Foster, A. Woda, M.-A. Peyron, Effect of texture of plastic and elastic model foods on the parameters of mastication, Journal of Neurophysiology 95 (2006) 3469–3479. [8] H. Takanobu, T. Yajima, et al., Quantification of masticatory efficiency with a mastication robot, in: Proceedings of the IEEE Internal Conference on Robotics and Automation 1998, pp. 1635–1640. [9] W.L. Xu, J. Bronlund, J. Kieser, A robotic model of human masticatory system for reproducing chewing behaviours, IEEE Robotics and Automation Magazine 12 (2) (2005) 90–98. [10] J. Torrance, J.-S. Pap, W.L. Xu, J. Bronlund, K.D. Foster, Motion control of a chewing robot of 6 RSS parallel mechanism, in: Proceedings of International Conference on Autonomous Robotics and Agents, Palmerston North, New Zealand, 12–14 December 2006, pp. 593–598. [11] J.-S. Pap, W.L. Xu, J. Bronlund, Design of a biologically inspired chewing robot, IEEE Transactions on Industrial Electronics, in press. [12] D. Lewis, A robotic chewing device for food evaluation, Master of Engineering Thesis, Massey University, New Zealand, 2006. [13] T. Ogawa, M. Ogawa, K. Koyano, Different responses of masticatory movements after alteration of occlusal guidance related to individual movement pattern, Journal of Oral Rehabilitation 28 (2001) 830–841. [14] D.J. Anderson, Measurement of stress in mastication, Journal of Dental Research 41 (1956) 175–189. [15] T. Thompson, How to use and interpret the coupler curve and centrode atlas, 1999. Available from:. [16] J.J. Craig, Introduction to Robotics, Mechanics and Control, third ed., Prentice Hall, 2004.
Mechanism and Machine Theory 43 (2008) 376–389
Mechanism and Machine Theory www.elsevier.com/locate/mechmt
Mechanism, design and motion control of a linkage chewing device for food evaluation W.L. Xu a
a,*
, D. Lewis a, J.E. Bronlund a, M.P. Morgenstern
b
Institute of Technology and Engineering, College of Sciences, Massey University, New Zealand b New Zealand Institute for Crop and Food Research Ltd., New Zealand Received 30 January 2007; received in revised form 12 March 2007; accepted 16 March 2007 Available online 27 April 2007
Abstract A linkage-based chewing device is proposed to perform standardised chewing for use in food evaluation. The linkage for chewing is firstly specified in terms of the trajectory of the first molar and the chewing force, according to the in vivo measurements of the human chewing ranging from grinding (or lateral chewing) to crunching (or vertical chewing). A fourbar linkage is synthesized to achieve the lateral chewing trajectory of the molar, and by adjusting the ground link length to achieve any trajectory between the lateral and vertical chewing. A six-bar crank-slider linkage is then designed to guide the molar teeth moving in a set orientation while still following the chewing trajectory produced by the four-bar linkage. The chewing device based on the six-bar linkage is constructed with inclusion of anatomically correct teeth for reducing the food particle size, a food retention device for collecting the food particles being chewed and a shock absorber for preventing excessive chewing force. The linkage chewing device is evaluated by simulations of kinematics and dynamics and actual measurements of the trajectory and chewing force. For the motion control of the actuator, the chewing velocity along the trajectory is also profiled for occlusal phase and opening/closing phase of the chewing, and the variations of the chewing for different foods are set in a GUI (graphical user interface) in Labview. The device is finally validated by chewing on a cereal bar and comparing the resulting particle size of the bolus with those by human subjects. 2007 Elsevier Ltd. All rights reserved. Keywords: Human chewing; Food evaluation; Chewing device; Adjustable linkage; Motion control
1. Introduction The human masticatory system is a complex system that comprises of an upper and lower jaw that have teeth located on them. It also includes a tongue, cheek and saliva production capability. When mastication is performed, the lower jaw (mandible) is moved by muscles that are attached between it and the upper jaw [1]. The chewing movement begins with the mandible opening thereby creating a space between the teeth located on skull and the mandible. The tongue then places food particles that need chewing on to the molars *
Corresponding author. Tel.: +64 9 414 0800; fax: +64 9 443 9774. E-mail address: [email protected] (W.L. Xu).
0094-114X/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2007.03.004
W.L. Xu et al. / Mechanism and Machine Theory 43 (2008) 376–389
377
on one side of the mouth. The mandible then closes and breaks up these food particles and then the particles fall off the teeth back on to the tongue for repositioning during the next cycle [2]. The opening of the mouth of the chewing cycle is approximately vertical [3]. The speed of the mandible in the opening phase initially starts slowly and increases as the mouth opens. When the mouth starts to close, the mandible moves laterally outward and initially closes quickly coming back towards the teeth and then slows for occlusion. The trajectories of the teeth during chewing vary substantially for different foods in the frontal plane, but, they are very close to a straight line in the sagittal plane [4]. This line may vary from a vertical line where the teeth come together at a 0 angle and a line where the teeth come together at a 30 angle. The trajectories used to chew different food particles differ depending on both the shape and the texture of the food particles, thus generating a different chewing action for different foods. If a vertical chewing motion is used, the teeth use their cusps to fracture the food particles. Where as if a more lateral chewing motion is used, the teeth use their sharp edges to function as blades and cut up the food particles [5]. As food properties affect the chewing trajectories, a considerable amount of work has been done to determine chewing movements in food sciences [4,6,7]. Measurements were made continuously over the masticatory process and included some of the following: frequency, length of chewing, tracking of jaw movement, force distribution, application of compression and shear forces on the food and particle size and structure of the bolus just prior to swallowing. These quantities vary between subjects (e.g. due to differences in jaw geometry, teeth shape, sensitivity to pain) and food texture (e.g. elasticity, hardness, adhesion especially to dentures, etc.). There are a variety of instruments or devices available for evaluating food properties. However, such devices usually use a simple straight motion (mostly food compression) and are not able to simulate the entire suite of complex functions and movements involved during mastication. Since the early 1990s there have been attempts in developing masticatory robots for food texture assessment [8–11]. While robotic chewing devices that possess multiple degrees of freedom (DOF) of motion are able to reproduce chewing behaviour in threedimensional space, a single DOF linkage device for chewing is pursued in this study. A linkage device is much simpler in structure and motion control and more reliable in operation. The presence of a straight line trajectory in the sagittal plane presents the opportunity to reproduce the chewing motion in 2D using a simple linkage. In this paper, the chewing linkage is specified to meet basic human chewing behaviours in terms of kinematic requirements and forces. Mechanism design is carried out using an atlas for the generation of trajectory, and the design also takes into account the set teeth orientation. To produce a range of chewing trajectories, the linkage is made with an adjustable ground link. The motion of the actuator is planned according to different velocity requirement in occlusal phase and opening/closing phase of the chewing, and the GUI (graphical user interface) in Labview facilitates the various chewing operations of the device. The validation of the device is performed by chewing on a real food. 2. Design specifications of a linkage chewing device Each mandibular tooth has its own trajectory while chewing, and a typical trajectory can be defined by vertical and lateral displacements and opening (exit) and closing (entry) angles, as illustrated in Fig. 1, as well as the time to complete them [2]. The trajectory of the first molar is simply a vertically compressed version of the incisor trajectories, while the entry and exit angles to and from occlusion are not greatly different [12]. The incisor trajectory can be measured but vary between lateral chewing (grinding) and vertical chewing (crunching), depending on the type of food being chewed. Due to the fact that chewing is performed on the molar teeth, the chewing device must follow the trajectories of the molar teeth. As no actual data is available, the trajectories of the molar teeth during chewing can be estimated by simulation from the trajectories of the incisor [12,13], as given in Table 1. To evaluate different foods the chewing device to be developed should be able to achieve any trajectory between lateral and vertical trajectories. The device should also meet cycle time and occlusal time. Therefore, the linkage for chewing can be specified by the set of parameters in Table 1. Furthermore, the forces applied on the teeth vary with the type of food being chewed. The force applied to a single tooth is also different to that of total force between all the contacting teeth during chewing. On foods such as biscuits, carrots and cooked
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Fig. 1. A tooth trajectory and its defining parameters.
Table 1 Values of the trajectory parameters for lateral and vertical chewing [12,13]
Closing angle () Opening angle () Total angle () Vertical opening (mm) Lateral displacement in opening (mm) Lateral displacement in closing (mm) Cycle time (s) Occlusal time (s) Opening/closing time (s)
Lateral chewing
Vertical chewing
46.6 113.1 66.5 14.6 1.1 4.0 0.77 0.12 0.65
72.5 78 5.5 15.1 0.4 3.1 0.7 0.16 0.54
meats forces range between 70 and 150 N on a single tooth [14]. Thus, the chewing force that the linkage can apply on food samples is specified as 150 N at maximum. 3. Basic linkage mechanism for the chewing device A four-bar linkage (Fig. 2) is a relatively simple mechanical mechanism and a point ‘P’ on the coupler can trace a 2D trajectory. The kinematic parameters for the linkage include crank link ‘a’, coupler link ‘b’, follower link ‘c’ and ground link ‘d’, as well as angle of ‘c’ and distance ‘BP’ for the coupler point ‘P’. A four-bar
Fig. 2. Kinematic parameters for a four-bar linkage [15].
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linkage in its standard form can only perform one set trajectory, and in the case where a range of trajectories are required to be reproduced, the ground link can be made adjustable manually. The Cedarville engineering atlas [15] was used to find a number of suitable trajectories that have entry and exit angles that closely match a lateral chewing cycle as specified in the above section. When a trajectory was found that matches the desired occlusal angles of a lateral chewing motion it was marked down as a possible solution. As vertical chewing motions are also required, this can be achieved by further changing the ground link length. Fig. 3 shows the final choice of the lateral chewing trajectory where the link parameters are shown at the top with varying ‘BP’ length. After the occlusal angles were examined, the final design chosen was Crank (link ‘a’) = 1, Follower (link ‘c’) = 3, Ground (link ‘d’) = 3.8–5 to achieve horizontal and vertical chewing motions, Coupler (link ‘b’) = 3.5, Coupler (distance ‘BP’) = 3, Coupler (angle ‘c’) = 60. These values are only ratios of the link lengths, relative to the Crank (a), and the actual links can be of any length as long as the ratios are obeyed. To make the actual linkage chewing device to be as compact as possible, a smallest feasible physical crank chosen is 10 mm long when its pivotal and joint bearings are taken into account. The chewing trajectories by the linkages were compared with those from real measurements of human chewing in Table 2. It can be found that in terms of the occlusal angles, the linkage can achieve a close match with the lateral chewing trajectory while still having reasonable trajectories for the vertical chewing; however, the linkage has larger vertical opening and lateral displacements. This should be acceptable as these aspects of
Fig. 3. Candidate trajectories of the four-bar linkage.
Table 2 Comparison between the trajectories by linkages and humans Lateral chewing
Closing angle () Opening angle () Total angle () Vertical opening (mm) Lateral displacement in opening (mm) Lateral displacement in closing (mm)
Vertical chewing
Human
Linkage
Human
Linkage
46.6 113.1 66.5 14.6 1.1 4.0
45 112 67 23 3 9
72.5 78 5.5 15.1 0.4 3.1
99 105 6 34 3 0
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the chewing trajectory do not impact on the food breakdown process as long as they are sufficient to clear the food between chewing cycles. The motor can be sped up during this part of the cycle to ensure representative masticatory behaviour is simulated.
Fig. 4. Three chewing trajectories by adjustable four-bar linkage.
Fig. 5. Construction of the adjustable four-bar linkage: (a) adjustable ground link; (b) adjustable four-bar linkage; (c) major parts chosen.
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Fig. 4 depicts three trajectories by the linkage at the ground length of 38 mm, 44 mm and 50 mm, respectively. It can be seen that the occlusal position shifts, the vertical opening displacement increases and the lateral displacement decreases as the length of the ground link gets smaller. This confirms that the linkage is able to reproduce various chewing trajectories. The chewing device to be constructed can adjust the occlusal position of the teeth by varying the distance between upper and lower teeth. Once the link lengths of the four-bar linkage were determined, the design of the mechanical device could commence. The basic designs of the crank, coupler and follower are straightforward only with the joint points of the links matching the lengths determined. The ground link needs to have a 12 mm adjustment that effectively changes the link length between 38 mm and 50 mm. Fig. 5 shows the final four-bar linkage constructed where the adjustable ground link was achieved using a threaded rod to move a block when the rod is turned. 4. Six-bar linkage mechanism for the chewing device 4.1. The six-bar linkage As discussed before, the adjustable four-bar linkage can produce the required trajectories. However, it cannot keep the mandible or teeth in same proper orientation over the entire trajectory. A simple way to resolve this is to add another two links (links 5 and 6 in Fig. 6) to the four-bar linkage, thus making it a six-bar linkage. The two links are connected by a sliding joint between them, and link 5 is attached onto the coupler by a revolute joint and link 6 onto the ground by another sliding joint. The set of teeth is mounted atop link 5, which is forced to move in a plane constrained by the two sliding joints. To produce the chewing trajectories in the sagittal plane of an angle ranging between 0 and 30 to the horizontal plane, the base of the six-bar linkage can be tilted manually. To have balanced dynamics to reduce the forces and impact, the chewing device was constructed symmetrically by placing two identical four-bar linkages on each side of the device (Fig. 6). The cranks of the two linkages were mounted on a single shaft driven by a single motor via a spur-gear train.
Mandible teeth attaching point
Link 5
Revolute joint Sliding joint
Link 6
Frame tilted for a saggital plane
4-bar linkages
Fig. 6. Design of a six-bar crank-slider linkage.
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While being constructed, the six-bar linkage was extended to include anatomical teeth with a quick attachment mechanism, a molar teeth repositioning table, a shock absorber that prevents excessive impact force and a simple food retention mechanism that collects chewed food particles. Food repositioning may be performed by the operator between chewing cycles. Fig. 7 shows a photograph of the built chewing device where the linkage is inverted with mandible teeth up and the maxilla teeth down for convenience of collecting chewed food particles. 4.2. Motion planning While the linkage can trace a desired chewing trajectory, the velocity along the trajectory still needs to be profiled. With respect to a chewing trajectory (Fig. 8), the molar teeth moves at constant velocity during the occlusion phase, and then speeds up from occlusal velocity to a maximum velocity and back down to occlusal velocity in a specified time. The occlusion starting and ending positions can be found by a horizontal line of 0.5 mm down from the maximum intercuspal position [13]. The linkage constructed was simulated for a lateral chewing trajectory in SolidWorks (Fig. 8). Each point on the trajectory corresponds to the crank shaft rotating 4.5 and the occlusal phase of 36 turn of crank shaft is found. As the time to complete this phase is specified as 0.12 s (Table 1), the occlusal velocity of the crank is 300/s. The start angle and final angle of crank are found 18 and 342 (Fig. 8a). Considering a 1:42 gear reduction between the motor and the crank, the occlusal velocity, start angle and final angle of the motor shaft are
Motor & control unit Crank Ground link
Coupler Link 6
Follower
Link 5 Handle for the adjustable sagittal plane
Handle for the adjustable ground
Quick teeth attachment mechanism Mandible molar
Shock absorber Food retention mechanism Maxilla molar Maxilla molar repositioning table
Handle for the adjustable maxilla
Fig. 7. The constructed chewing device.
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Fig. 8. Definition of the occlusal phase.
12,600/s, 756 and 14,364, respectively. The time taken to open and close the mouth is specified of 0.65 s (Table 1). Based on these values, a cubic trajectory of the motor shaft is found as [16] hðtÞ ¼ 756 þ 12; 600t þ 38; 471t2 39; 457t3 _ ¼ 12; 600 þ 76; 942t 118; 371t2 hðtÞ
ð1Þ
€ hðtÞ ¼ 76; 942 236; 742t
ð3Þ
ð2Þ
The above planned trajectory is for the lateral chewing. As the chewing device is intended for performing a variety of trajectories between the lateral and vertical chewing, the trajectory other than the lateral chewing will be different. An actual planned trajectory is decided by occlusal angle, occlusal time and opening/closing time (Fig. 8b), which can be set up in the motion control GUI (see Section 6). 4.3. Motor selection After the materials of the parts are specified for the linkage and a constant force of 150 N is applied vertically at the coupler point ‘P’, the linkage can be simulated in SolidWorks to find the driving torque required
Moment - Y (newton-mm)
2603
1578
552
-473
-1498 0.00 0.06 0.12 0.18 0.24 0.30 0.36 0.42 0.48 0.54 0.60 Time (sec)
Fig. 9. The torque required at the crank shaft.
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Table 3 Comparison of required and achievable specifications at the crank Parameter
Required
Estimated capability
Speed (rpm) Torque (N m) Acceleration (/s2)
100 2.6 190
190 3.82 414
at crank shaft. Fig. 9 shows a crank torque versus time plot when the crank runs at 300/s which is the occlusal speed of the crank. The maximum torque the crank requires to run the chewing device is 2.6 N m. Consequently, the output of the geared motor must be able to produce a minimum torque of 2.6 N m at 300/s (or 78 rpm) to achieve the desired chewing force of 150 N. In addition, the required acceleration is estimated at 190/s2 [12]. A brushless DC motor finally chosen could deliver 6.0 N m of torque continuously and 7.5 N m of torque for short periods. With the gear ratio of 1.57, the torque, speed and acceleration at the crank can be 3.82 N m, 190 rpm and 414/s2, respectively, which meets the required performance of the crank (Table 3). 5. Analysis of the linkage chewing device 5.1. Trajectory and force evaluation A simple way to compare the trajectories that the device can produce and the desired chewing trajectories is to use a pen to trace the trajectories achieved and overlay them. The pen used to trace the trajectories was modified so that the spring was used to push the nib out rather than retracting it. The pen was securely attached to the slider of the six-bar linkage and the card was setup in a vertical fashion so that the nib was
Fig. 10. The overlay of the achieved and desired trajectories (solid line = actual, dotted line = desired): (a) later chewing; (b) vertical chewing.
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in contact with the card. It was found from numerous measurements that the trajectories produced by the chewing device are close to the desired ones during the occlusion but slightly different in the opening/closing phases, as illustrated in Fig. 10. This minor difference is due to the play in the joints of the linkage, and insignificant to the entire chewing as it occurs only in the opening/closing free motion. The force testing was performed by the use of a load cell. This idea involves having the teeth attaching point (link 5) pressing down on the load cell to measure the force applied. The chewing device was set to run continuously and the force that the linkage can apply was measured. The results show that the chewing device could comfortably apply the desired 150 N chewing force and would stall at approximately 260 N. 5.2. Stress and deformation analysis The six-bar linkage can be simulated in COSMOS/Works to test if the device can withstand the forces that will be applied. When a force of 150 N was applied at the teeth attaching point, the stress analysis was performed at the occlusal position. Results show that there is no excessively large stress on the device, with the largest stress being concentrated where the linear bush of the link 5 of the four-bar linkage is (Fig. 11). This is due to the fact that the linear bush makes a relatively sharp edge in the structure. This stress concentration was expected when the structure was designed, and hence needs not to be avoided as the link 5 is strong enough to withstand that level of stress. The deformation of the device was also analysed to examine the buckling that occurs when the 150 N load was applied at the teeth attaching point. The results show that the deformation is 0.004 mm at the place where the linear bush meets the shaft that it slides on (Fig. 12). This can be considered negligible as this amount of buckling in the shaft will not cause the linear bush to jam.
Fig. 11. The stress analysis of the linkage.
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Fig. 12. Deformation analysis of the linkage.
6. Control system and software Because the chewing cycle time and occlusal time vary between people and foods being chewed, motion control of the motor is required. This control was implemented in National Instruments ‘Labview’ programming language to allow flexibility in subsequent prototypes. As the device was to be controlled from a Labview program it made sense to choose a control card that could easily be interfaced with Labview. The communication between the control card and the computer based software was done via a RS-232 serial interface. For the chewing device to function in a way that the human operation would be satisfied with, it is important to include all the functions that would be necessary for simple operation. These functions are as follows, which can be seen in GUI in Fig. 13: • Set to lower position – this function sets the chewing device to the occlusal position so that the teeth can be aligned when setting up the device. • Set to top position – this function sets the chewing device to the position where the teeth are maximum distance apart so that a food sample can be placed in it. This can be thought of as the mouth being open. • Start chewing – this will be used to make the device chew by making the device follow a velocity profile that matches that of a human chewing velocity profile. The number of chews will also be able to be set. • Single cycle – this function will be used as a quick select ‘one chew’ button and will only perform one chewing cycle. • Low speed manual control – the user will be able to use this control to make the chewing device move at a slow speed to check the occlusion once the teeth have first been set up. • Master stop – this will be used as a safety feature that allows the user to stop it at any time during any function. It should be cautious that this stop stops only the execution of those motion programs by setting the velocity of the motor to zero. To enhance the safety, an emergency button is still in order.
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Fig. 13. GUI implementing the operational functions.
Fig. 14. GUI for specifying the occlusion.
The operator may wish the chewing device to chew foods differently. To this end, the device has to allow different velocity profiles (Fig. 14). This can be implemented by changing the parameters for the velocity profiles in the controller. These control parameters are: • Occlusal time – the time the occlusal phase is to take. • Opening/closing time – the time it takes to return to the start of the occlusal phase. • Occlusal angle – this specifies the point where the occlusion begins and ends. 7. A chewing experiment The chewing device designed is to reproduce the trajectory of the molar teeth during human chewing cycles. It employs anatomically correct teeth geometries with accurate occlusion. The trajectory of the jaw can be adjusted to give a range of vertical and lateral movements so that different foods can be processed appropriately. The speed of the jaw can also be adjusted to simulate the motions observed during human chewing.
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Fraction passing through 1.4mm seive
90% 80% 70% 60% 50% 40%
Chewing device
2g sample 4g sample
30%
Chewing device
20% 10% 0% 0
2
4
6
8
10
12
14
Subject number
Fig. 15. Comparison of particle size between human subjects and the chewing device.
Validation of the device was performed by comparing the resulting particle size of the bolus produced by the chewing device with the particle size of a bolus produced by a human subject. The device was tested on a cereal bar by taking 1 g slices and placing them onto the teeth. The machine was made to undergo two cycles after which artificial saliva was added in the proportion measured during human chewing trials. The food particles were rearranged on the teeth and the device was made to carry out another 5 cycles. The particles were again rearranged on the teeth before chewing for another 5 cycles, repeating this pattern until the total number of chewing cycles was that observed in human chewing. The bolus was then collected and washed through 1.4 mm and 0.25 mm sieves and dried. The fraction of solid particles passing through the 1.4 mm sieve was then compared with the results collected from human subjects as a partial validation of the device. The results are seen in Fig. 15, where those in the shaded box is the particle size using the chewing device developed and the rest is that of human chewing on 2 g and 4 g food sample. It can be found that although there is some variability between the fractions passing through the 1.4 mm sieve in the device chewed samples, it is of a similar magnitude to that observed in the human subjects. While further validation is necessary it is believed that the device has enough flexibility to be developed into a routine laboratory apparatus for the purposes of pre-processing foods in a systematic and reproducible manner for subsequent nutritional analysis and for evaluation of the dynamics of food texture changes during chewing. 8. Conclusion The linkage chewing device for use in food evaluation was developed and the mechanism design, construction, motion control and simulation and experimental validation were described. The design specifications were derived from published in vivo measurements of human chewing. While the four-bar linkage was for chewing trajectory, the six-bar linkage was to keep the molar teeth moving in a set orientation. A variety of chewing trajectories were achieved by varying the ground link length. The motion of the actuator was planned to implement various chewing motions required for different foods. The operation of the device was made easy via GUIs programmed in Labview. While initial experiments show the promising results by the device, more validations of chewing are required before it becomes a routine laboratory apparatus for the purposes of pre-processing foods.
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Acknowledgements The work in this paper was supported by the Baking Industry Research Trust, New Zealand and by the NZ Foundation for Research, Science and Technology, through Innovative Foods contract C02X0401 (Lifestyle Foods for Energy Balance – The Carbohydrate Story). It is acknowledged that the validation data were provided by Kylie Forster and Christine Lawrence of Institute of Food, Nutrition and Human Health, Massey University, New Zealand. References [1] P.W. Lucas, The structure of the mammalian mouth, in: Dental Functional Morphology: How Teeth Work, Cambridge University Press, United Kingdom, 2004, pp. 13–54. [2] P.W. Lucas, How the mouth operates, in: Dental Functional Morphology: How Teeth Work, Cambridge University Press, United Kingdom, 2004, pp. 55–86. [3] F. Mongini, G. Tempia-Valenti, G. Benvegnu, Computer-based assessment of habitual mastication, Journal of Prosthetic Dentistry 55 (1986) 638–649. [4] K. Anderson, G.S. Throckmorton, P.H. Buschang, H. Hayasaki, The effects of bolus hardness on the masticatory kinematics, Journal of Oral Rehabilitation 29 (2002) 689–696. [5] P.W. Lucas, Tooth shape, in: Dental Functional Morphology: How Teeth Work, Cambridge University Press, United Kingdom, 2004, pp. 87–132. [6] M.A. Peyron, C. Lassauzay, A. Woda, Effects of increased hardness on jaw movement and muscle activity during chewing of viscoelastic model foods, Experimental Brain Research 142 (2002) 41–51. [7] K. Foster, A. Woda, M.-A. Peyron, Effect of texture of plastic and elastic model foods on the parameters of mastication, Journal of Neurophysiology 95 (2006) 3469–3479. [8] H. Takanobu, T. Yajima, et al., Quantification of masticatory efficiency with a mastication robot, in: Proceedings of the IEEE Internal Conference on Robotics and Automation 1998, pp. 1635–1640. [9] W.L. Xu, J. Bronlund, J. Kieser, A robotic model of human masticatory system for reproducing chewing behaviours, IEEE Robotics and Automation Magazine 12 (2) (2005) 90–98. [10] J. Torrance, J.-S. Pap, W.L. Xu, J. Bronlund, K.D. Foster, Motion control of a chewing robot of 6 RSS parallel mechanism, in: Proceedings of International Conference on Autonomous Robotics and Agents, Palmerston North, New Zealand, 12–14 December 2006, pp. 593–598. [11] J.-S. Pap, W.L. Xu, J. Bronlund, Design of a biologically inspired chewing robot, IEEE Transactions on Industrial Electronics, in press. [12] D. Lewis, A robotic chewing device for food evaluation, Master of Engineering Thesis, Massey University, New Zealand, 2006. [13] T. Ogawa, M. Ogawa, K. Koyano, Different responses of masticatory movements after alteration of occlusal guidance related to individual movement pattern, Journal of Oral Rehabilitation 28 (2001) 830–841. [14] D.J. Anderson, Measurement of stress in mastication, Journal of Dental Research 41 (1956) 175–189. [15] T. Thompson, How to use and interpret the coupler curve and centrode atlas, 1999. Available from: