Mechanism, design and motion control of a linkage chewing device

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on one side of the mouth. The mandible then closes and breaks up these food particles and then the particlesfall off the teeth back on to the tongue for repositioning during the next cycle [2]. The opening of the mouth ofthe chewing cycle is approximately vertical [3]. The speed of the mandible in the opening phase initially startsslowly and increases as the mouth opens. When the mouth starts to close, the mandible moves laterally out-ward 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 theteeth come together at a 0� angle and a line where the teeth come together at a 30� angle. The trajectories usedto chew different food particles differ depending on both the shape and the texture of the food particles, thusgenerating a different chewing action for different foods. If a vertical chewing motion is used, the teeth usetheir cusps to fracture the food particles. Where as if a more lateral chewing motion is used, the teeth use theirsharp 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 deter-mine chewing movements in food sciences [4,6,7]. Measurements were made continuously over the masticatoryprocess and included some of the following: frequency, length of chewing, tracking of jaw movement, forcedistribution, application of compression and shear forces on the food and particle size and structure of thebolus 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, suchdevices usually use a simple straight motion (mostly food compression) and are not able to simulate the entiresuite of complex functions and movements involved during mastication. Since the early 1990s there have beenattempts in developing masticatory robots for food texture assessment [8–11]. While robotic chewing devicesthat possess multiple degrees of freedom (DOF) of motion are able to reproduce chewing behaviour in three-dimensional space, a single DOF linkage device for chewing is pursued in this study. A linkage device is muchsimpler in structure and motion control and more reliable in operation. The presence of a straight line trajec-tory in the sagittal plane presents the opportunity to reproduce the chewing motion in 2D using a simplelinkage.

In this paper, the chewing linkage is specified to meet basic human chewing behaviours in terms of kine-matic 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, thelinkage is made with an adjustable ground link. The motion of the actuator is planned according to differentvelocity requirement in occlusal phase and opening/closing phase of the chewing, and the GUI (graphical userinterface) in Labview facilitates the various chewing operations of the device. The validation of the device isperformed 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 ver-tical and lateral displacements and opening (exit) and closing (entry) angles, as illustrated in Fig. 1, as well asthe time to complete them [2]. The trajectory of the first molar is simply a vertically compressed version of theincisor trajectories, while the entry and exit angles to and from occlusion are not greatly different [12]. Theincisor trajectory can be measured but vary between lateral chewing (grinding) and vertical chewing (crunch-ing), depending on the type of food being chewed. Due to the fact that chewing is performed on the molarteeth, the chewing device must follow the trajectories of the molar teeth. As no actual data is available, thetrajectories of the molar teeth during chewing can be estimated by simulation from the trajectories of the inci-sor [12,13], as given in Table 1.

To evaluate different foods the chewing device to be developed should be able to achieve any trajectorybetween 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 appliedon the teeth vary with the type of food being chewed. The force applied to a single tooth is also different to thatof total force between all the contacting teeth during chewing. On foods such as biscuits, carrots and cooked

Please cite this article in press as: W.L. Xu et al., Mechanism, design and motion control of a linkage ..., Mech. Mach.Theory (2007), doi:10.1016/j.mechmachtheory.2007.03.004

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Fig. 1. A tooth trajectory and its defining parameters.

Table 1Values of the trajectory parameters for lateral and vertical chewing [12,13]

Lateral chewing Vertical chewing

Closing angle (�) 46.6 72.5Opening angle (�) 113.1 78Total angle (�) 66.5 5.5Vertical opening (mm) 14.6 15.1Lateral displacement in opening (mm) 1.1 0.4Lateral displacement in closing (mm) 4.0 3.1Cycle time (s) 0.77 0.7Occlusal time (s) 0.12 0.16Opening/closing time (s) 0.65 0.54

W.L. Xu et al. / Mechanism and Machine Theory xxx (2007) xxx–xxx 3



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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 cantrace a 2D trajectory. The kinematic parameters for the linkage include crank link ‘a’, coupler link ‘b’, followerlink ‘c’ and ground link ‘d’, as well as angle of ‘c’ and distance ‘BP’ for the coupler point ‘P’. A four-bar link-

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Fig. 2. Kinematic parameters for a four-bar linkage [15].


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age in its standard form can only perform one set trajectory, and in the case where a range of trajectories arerequired to be reproduced, the ground link can be made adjustable manually.

The Cedarville engineering atlas [15] is used to find a number of suitable trajectories that have entry andexit angles that closely match a lateral chewing cycle as specified in the above section. When a trajectory isfound that matches the desired occlusal angles of a lateral chewing motion it is marked down as a possiblesolution. As vertical chewing motions are also required, this can be achieved by further changing the groundlink length. Fig. 3 shows the final choice of the lateral chewing trajectory where the link parameters are shownat the top with varying ‘BP’ length.

After the occlusal angles are examined, the final design chosen is 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 linklengths, 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 crankchosen is 10 mm long when its pivotal and joint bearings are taken into account.

The chewing trajectories by the linkages are compared with those from real measurements of human chew-ing in Table 2. It can be found that in terms of the occlusal angles, the linkage can achieve a close match withthe lateral chewing trajectory while still having reasonable trajectories for the vertical chewing; however, thelinkage has larger vertical opening and lateral displacements. This should be acceptable as these aspects of the

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Fig. 3. Candidate trajectories of the four-bar linkage.

Table 2Comparison between the trajectories by linkages and humans

Lateral chewing Vertical chewing

Human Linkage Human Linkage

Closing angle (�) 46.6 45 72.5 99Opening angle (�) 113.1 112 78 105Total angle (�) 66.5 67 5.5 6Vertical opening (mm) 14.6 23 15.1 34Lateral displacement in opening (mm) 1.1 3 0.4 3Lateral displacement in closing (mm) 4.0 9 3.1 0


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chewing trajectory do not impact on the food breakdown process as long as they are sufficient to clear the foodbetween chewing cycles. The motor can be sped up during this part of the cycle to ensure representative mas-ticatory behaviour is simulated.

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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, respec-tively. It can be seen that the occlusal position shifts, the vertical opening displacement increases and the lat-eral displacement decreases as the length of the ground link gets smaller. This confirms that the linkage is ableto reproduce various chewing trajectories. The chewing device to be constructed can adjust the occlusal posi-tion 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 couldcommence. The basic designs of the crank, coupler and follower are straightforward only with the joint pointsof the links matching the lengths determined. The ground link needs to have a 12 mm adjustment that effec-tively changes the link length between 38 mm and 50 mm. Fig. 5 shows the final four-bar linkage constructedwhere the adjustable ground link is 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 can-not keep the mandible or teeth in same proper orientation over the entire trajectory. A simple way to resolvethis is to add another two links (links 5 and 6 in Fig. 6) to the four-bar linkage, thus making it a six-bar link-age. The two links are connected by a sliding joint between them, and link 5 is attached onto the coupler by arevolute 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 trajectoriesin the sagittal plane of an angle ranging between 0� and 30� to the horizontal plane, the base of the six-barlinkage can be tilted manually.

To have balanced dynamics to reduce the forces and impact, the chewing device was constructed symmet-rically by placing two identical four-bar linkages on each side of the device (Fig. 6). The cranks of the twolinkages were mounted on a single shaft driven by a single motor via a spur-gear train.

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4-bar linkages

Link 5

Link 6

Sliding joint

Revolute joint

Frame tilted for a saggital plane

Mandible teeth attaching point

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 attach-ment mechanism, a molar teeth repositioning table, a shock absorber that prevents excessive impact force anda simple food retention mechanism that collects chewed food particles. Food repositioning may be performedby the operator between chewing cycles. Fig. 7 shows a photograph of the built chewing device where the link-age is inverted with mandible teeth up and the maxilla teeth down for convenience of collecting chewed foodparticles.

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While the linkage can trace a desired chewing trajectory, the velocity along the trajectory still needs to beprofiled. With respect to a chewing trajectory (Fig. 8), the molar teeth moves at constant velocity during theocclusion phase, and then speeds up from occlusal velocity to a maximum velocity and back down to occlusalvelocity in a specified time.

The occlusion starting and ending positions can be found by a horizontal line of 0.5 mm down from themaximum intercuspal position [13]. The linkage constructed was simulated for a lateral chewing trajectoryin SolidWorks (Fig. 8). Each point on the trajectory corresponds to the crank shaft rotating 4.5� and theocclusal 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 reductionbetween the motor and the crank, the occlusal velocity, start angle and final angle of the motor shaft are

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Food retention mechanism

Mandible molar

Maxilla molar

Link 5

Link 6

Coupler

Follower

Ground link

Crank

Motor & control unit

Handle for the adjustable ground

Quick teeth attachmentmechanism

Handle for the adjustable sagittal plane

Shock absorber

Handle for the adjustable maxilla

Maxilla molar repositioningtable

Fig. 7. The constructed chewing device.


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Fig. 8. Definition of the occlusal phase.




D12,600�/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]

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TEhðtÞ ¼ 756þ 12; 600t þ 38; 471t2 � 39; 457t3 ð1Þ

_hðtÞ ¼ 12; 600þ 76; 942t � 118; 371t2 ð2Þ€hðtÞ ¼ 76; 942� 236; 742t ð3Þ

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variety of trajectories between the lateral and vertical chewing, the trajectory other than the lateral chewingwill be different. An actual planned trajectory is decided by occlusal angle, occlusal time and opening/closingtime (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 ver-tically at the coupler point ‘P’, the linkage can be simulated in SolidWorks to find the driving torque required

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0.00 0.06 0.12 0.18 0.24 0.30 0.36 0.42 0.48 0.54 0.60Time (sec)

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Fig. 9. The torque required at the crank shaft.

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Table 3Comparison of required and achievable specifications at the crank

Parameter Required Estimated capability

Speed (rpm) 100 190Torque (N m) 2.6 3.82Acceleration (�/s2) 190 414




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Fat crank shaft. Fig. 9 shows a crank torque versus time plot when the crank runs at 300�/s which is the occlusalspeed of the crank. The maximum torque the crank requires to run the chewing device is 2.6 N m. Conse-quently, 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 estimatedat 190�/s2 [12].

A brushless DC motor finally chosen could deliver 6.0 N m of torque continuously and 7.5 N m of torquefor 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 isto use a pen to trace the trajectories achieved and overlay them. The pen used to trace the trajectories wasmodified so that the spring was used to push the nib out rather than retracting it. The pen was securelyattached to the slider of the six-bar linkage and the card was setup in a vertical fashion so that the nib was

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Fig. 10. The overlay of the achieved trajectory 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 thechewing device are close to the desired ones during the occlusion but slightly different in the opening/closingphases, as illustrated in Fig. 10. This minor difference is due to the play in the joints of the linkage, and insig-nificant 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 con-tinuously and the force that the linkage can apply was measured. The results show that the chewing devicecould 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 thatwill be applied. When a force of 150 N was applied at the teeth attaching point, the stress analysis was per-formed at the occlusal position. Results show that there is no excessively large stress on the device, withthe 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 concen-tration was expected when the structure was designed, and hence needs not to be avoided as the link 5 is strongenough to withstand that level of stress.

The deformation of the device was also analysed to examine the buckling that occurs when the 150 N loadwas applied at the teeth attaching point. The results show that the deformation is 0.004 mm at the place wherethe linear bush meets the shaft that it slides on (Fig. 12). This can be considered negligible as this amount ofbuckling in the shaft will not cause the linear bush to jam.

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Fig. 11. The stress analysis of the linkage.


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Fig. 12. Deformation analysis of the linkage.




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Because the chewing cycle time and occlusal time vary between people and foods being chewed, motioncontrol of the motor is required. This control was implemented in National Instruments ‘Labview’ program-ming language to allow flexibility in subsequent prototypes. As the device was to be controlled from a Labviewprogram it made sense to choose a control card that could easily be interfaced with Labview. The communi-cation 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 impor-tant 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 bealigned when setting up the device.

• Set to top position – this function sets the chewing device to the position where the teeth are maximum dis-tance 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 thatmatches 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 chew-ing cycle.

• Low speed manual control – the user will be able to use this control to make the chewing device move at aslow 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 func-tion. It should be cautious that this stop stops only the execution of those motion programs by setting thevelocity 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.




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OThe operator may wish the chewing device to chew foods differently. To this end, the device has to allowdifferent velocity profiles (Fig. 14). This can be implemented by changing the parameters for the velocity pro-files 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.
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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 beadjusted to give a range of vertical and lateral movements so that different foods can be processed appropri-ately. The speed of the jaw can also be adjusted to simulate the motions observed during human chewing.


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Mechanism, design and motion control of a linkage chewing device

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