Mechanism, design and motion control of a linkage chewing device for food evaluation.doc

available online at sciencedirectmechanism and machine theory 43 (2008) 376-389mechanismandmachine t/locate/mechmtmechanism, design and motion control of a linkage chewing device for food evaluationw.l. xu a,*, d. lewis a, j.e. bronlund a, m.p. morgenstern ba institute of technology and engineering, college of sciences, massey university, new zealand b new zealand institute for crop and food research ltd., new zealandreceived 30 january 2007; received in revised form 12 march 2007; accepted 16 march 2007 available online 27 april 2007abstracta 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 four-bar 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 control1. introductionthe 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 molarscorresponding author. tel.: +64 9 414 0800; fax: +64 9 443 9774. e-mail address: w.l.xumassey.ac.nz (w.l. xu).0094-114x/s - see front matter 2007 elsevier ltd. all rights reserved. doi:10.1016/j.mechmachtheory.2007.03.004w.l. xu et al. / mechanism and machine theory 43 (2008) 376389377on 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 three-dimensional 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 deviceeach 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 cooked378w.l. xu et al. / mechanism and machine theory 43 (2008) 376389lateral opening displacementlateral clnsui.e displacementfig. 1. a tooth trajectory and its defining parameters.table 1values of the trajectory parameters for lateral and vertical chewing 12,13closing 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 chewing46.6113.166.50.770.120.65vertical chewing72.5 785.5 4meats 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 devicea 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-bargroundfig. 2. kinematic parameters for a four-bar linkage 15.w.l. xu et al. / mechanism and machine theory 43 (2008) 376389379linkage 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 i) = 3.8-5 to achieve horizontal and vertical chewing motions, coupler (link b) = 3.5, coupler (distance bp) = 3, coupler (angle y) = 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 offig. 3. candidate trajectories of the four-bar linkage.table 2comparison between the trajectories by linkages and humanslateralchewingverticalchewinghumanlinkagehumanlinkageclosing angle ()46.64572.599opening angle ()113.111278105total angle ()66.5675.56vertical opening (mm)14.62315.134lateral displacement inopening (mm)1.130.43lateral displacement inclosing (mm)4.093.10380w.l. xu et al. / mechanism and machine theory 43 (2008) 376389the 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.w.l. xu et al. / mechanism and machine theory 43 (2008) 376389381fig. 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 device4.1. the six-bar linkageas 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.fig. 6. design of a six-bar crank-slider linkage.mandible teeth attaching point382w.l. xu et al. / mechanism and machine theory 43 (2008) 376389while 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 planningwhile 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 aremotor & contro unitcrank ground linkfollowercoupler link 6 link 5handle for theadjustable sagittal planequick teeth attachment mechanismmandible molarfood retention mechanismmaxilla molarmaxilla molarrepositioningtableshock absorberhandle for the adjustable groundhandle for the adjustable maxillafig. 7. the constructed chewing device.w.l. xu et al. / mechanism and machine theory 43 (2008) 376389383fig. 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 166(f) = 756 + 12,600; + 38,4712 39,457;3(1)6(f) = 12,600 + 76,942; 118,371;2(2)6(f) = 76,942 236,742;(3)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 t