Four-bar System Research Articles

Four-bar Geometry is Shared among Ecologically DivergentFish Species.

Understanding the factors that influence morphological evolution is a major goal in biology. One such factor is the ability to acquire and process prey. Prey hardness and evasiveness are important properties that can impact evolution of the jaws. Similar diets and biomechanical systems have repeatedly evolved among fish lineages, providing an opportunity to test for shared patterns of evolution across distantly related organisms. Four-bar linkages are structures often used by animals to transmit force and motion during feeding and that provide an excellent system to understand the impact of diet on morphological and biomechanical evolution. Here, we tested how diet influences the evolutionary dynamics of the oral four-bar linkage system in wrasses (Family: Labridae) and cichlids (Family: Cichlidae). We found that shifts in prey hardness/evasiveness are associated with limited modifications in four-bar geometry across these two distantly related fish lineages. Wrasse and cichlid four-bar systems largely exhibit many-to-one mapping in response to dietary shifts. Across two iconic adaptive radiations of fish, an optimal four-bar geometry has largely been co-opted for different dietary functions during their extensive ecological diversification. Given the exceptional jaw diversity of both lineages, many-to-one mapping of morphology to mechanical properties may be a core feature of fish adaptive radiation.

FOUR-BAR MECHANISM FOR A PORTAL CRANE: A BRIEF OVERVIEW

The present article aims to increase knowledge of a four-bar mechanism. A four-bar system is a planar mechanism. There are many types of simple mechanisms, such as: Chebyshev, Chebyshev lamda, Hoecken, Roberts, Watt’s, Grasshopper, horse-head, pantograph and Peaucelier. More complex mechanisms are: Stewart platform or Jansen’s linkage. The determination of the degrees of freedom (DOF) for a system is done using the Chebychev-Gruebler-Kutzbach relationship. Due to this fact, the DOF for the four-bar system has the value one. Moreover, we analyze the following angles: θ, α, β and φ3in the mechanism. Finally, using Matlab software the drawing and the dynamic simulation of a four-bar mechanism is carried out. Besides, the dynamic simulation is represented after 3s, 6s and 12s.

Automation of a seed on tray seeder machine

The machine aims to fully automate the process to sow seeds. Generally, these types of activities are semi-automatic, however, the proposed solution aims to improve the efficiency of the process and the reduction of human intervention. It mainly has a mechanical part whose technique is based on a four-bar system, as for the electronic and control part it is commanded by an Arduino card. The mechanical design was carried out using CAD software, and based on the results obtained by various flexural and deformation analysis software, it was possible to select the materials and the motor to be used. The process works from operational requirements such as: transmitting the linear movement of the components, placing and aligning the transport mechanism, transmitting enough power to drill and place the seeds and finally controlling the air flow. As a result, this automated method represents 25% more efficiency and a 50% reduction in personnel compared to the manual method. In the same way, a filling of 87% of cavities for seeds was obtained, this being its highest efficiency with a pressure in the range of 0.2 to 0.3 MPa in the pressure ejector.

Common evolutionary trends underlie the four-bar linkage systems of sunfish and mantis shrimp.

Comparative biomechanics offers an opportunity to explore the evolution of disparate biological systems that share common underlying mechanics. Four-bar linkage modeling has been applied to various biological systems such as fish jaws and crustacean appendages to explore the relationship between biomechanics and evolutionary diversification. Mechanical sensitivity states that the functional output of a mechanical system will show differential sensitivity to changes in specific morphological components. We document similar patterns of mechanical sensitivity in two disparate four-bar systems from different phyla: the opercular four-bar system in centrarchid fishes and the raptorial appendage of stomatopods. We built dynamic linkage models of 19 centrarchid and 36 stomatopod species and used phylogenetic generalized least squares regression (PGLS) to compare evolutionary shifts in linkage morphology and mechanical outputs derived from the models. In both systems, the kinematics of the four-bar mechanism show significant evolutionary correlation with the output link, while travel distance of the output arm is correlated with the coupler link. This common evolutionary pattern seen in both fish and crustacean taxa is a potential consequence of the mechanical principles underlying four-bar systems. Our results illustrate the potential influence of physical principles on morphological evolution across biological systems with different structures, behaviors, and ecologies.

Using linkage models to explore skull kinematic diversity and functional convergence in arthrodire placoderms

Biomechanical models offer a powerful set of tools for quantifying the diversity of function across fossil taxa. A computer-based four-bar linkage model previously developed to describe the potential feeding kinematics of Dunkleosteus terrelli is applied here to several other arthrodire placoderm taxa from different lineages. Arthrodire placoderms are a group of basal gnathostomes showing one of the earliest diversifications of jaw structures. The linkage model allows biomechanical variation to be compared across taxa, identify trends in skull morphology among arthrodires that potentially influence function and explore the role of linkage systems in the early evolution of jaw structures. The linkage model calculates various kinematic metrics including gape angle, effective mechanical advantage, and kinematic transmission coefficients. Results indicate that the arthrodire feeding system may be more diverse and complex than previously thought. A range of potential kinematic profiles among arthrodire taxa illustrate a diversity of feeding function comparable with modern teleost fishes. Previous estimates of bite force in Dunkleosteus are revised based on new morphological data. High levels of kinematic transmission among arthrodires suggest the potential for rapid gape expansion and possible suction feeding. Morphological comparisons indicate that there were several morphological solutions for obtaining these fast kinematics, which allowed different taxa to achieve similar kinematic profiles while varying other aspects of the feeding apparatus. Mapping of key morphological components of the linkage system on a general placoderm phylogeny illustrates the potential importance of four-bar systems to the early evolution of jaw structures.

Computational Analysis of Multibody Dynamic Systems Using Nonlinear Recursive Formulation

. In this paper the computer implementation of the nonlinear recursive formulation in multibody dynamics systems is described. The organization of the computer algorithm which is used to automatically construct and numerically solve the system of loosely coupled dynamic equations expressed in terms of the absolute and joint coordinates is discussed. The inertia projection schemes used in most existing recursive formulations for the dynamic analysis of deformable mechanisms lead to dense coefficient matrices in the equations of motion. Consequently, there are strong dynamic couplings between the joint and elastic coordinates. By using the inertia matrix structure of deformable mechanical systems and the fact that the joint reaction forces associated with the elastic coordinates do represent independent variables, a reduced system of equations whose dimension is dependent of the number of elastic degrees of freedom is obtained. This system can be solved for the joint accelerations as well as the joint reaction forces. The multibody flexible four-bar system is used as an example to demonstrate the use of the procedure discussed in this paper.

Advanced mechatronic design using a multi-objective genetic algorithm optimization of a motor-driven four-bar system

In this work we present a genetic algorithm based method to design a mechatronic system. First, we present the sequential approach where we optimize the geometry of the mechanism, for a given path, and then solve the dynamic problem where we take into account the characteristics of the motor along with the inertia of the different links of the mechanism. Several types of objective functions are tested. We show, however, that this sequential method does not yield acceptable results for the dynamic behavior due to the fact that the geometry is assumed fixed when optimizing the dynamics. This led us to formulate a global optimization problem where all the parameters of the mechanism are considered simultaneously. The problem is then presented as a multi-objective optimization one where the geometry and the dynamics are considered simultaneously. The obtained solutions form what is called a “Pareto front” and they are analyzed for several different design conditions. This paper also shows the advantages of a multi-objective optimization approach over the single-objective one.

A test of mouth-opening and hyoid-depression mechanisms during prey capture in a catfish using high-speed cineradiography

Detailed morphological analyses have identified a number of different mechanical pathways by which the morphologically complex cranial system of fishes can achieve mouth opening and hyoid depression. However, many of these proposed mechanisms remain untested. Furthermore, very little is known about the precise timing of activity of each of these mechanisms, and about the magnitude of each mechanism's total contribution to its proposed function. In the present study, all mouth opening and hyoid depression mechanisms described for Clarias gariepinus, an air-breathing catfish, are analysed. High-speed X-ray videos were recorded during prey capture of three catfish implanted with small, radio-opaque markers in the cranial elements potentially involved. A kinematic analysis was performed from which data were used as input in planar four-bar models. This analysis shows that the opercular mouth-opening mechanism initiates mouth opening, but is not able to cause the complete mouth openings as observed on the X-ray videos. The latter is accomplished through the protractor hyoidei muscles, which couple hyoid depression to lower jaw depression in a four-bar system and also reinforce lower jaw depression by shortening during the final stage of mouth opening. Although the angulo-ceratohyal ligament was previously hypothesised to play a part in mouth opening, our results show that it probably does not, but rather functions as a hyoid-elevator during mouth closure. Finally, hyoid depression is exclusively achieved by the four-bar mechanism involving neurocranial elevation and pectoral girdle retraction, generally without any reinforcement by shortening of the sternohyoideus muscle. In contrast to the results from a recent analysis on sunfish, the catfish's sternohyoideus gradually elongates during hyoid depression.

The Derivation of Knee Joint Types from the Geometry of the Cruciate Ligament Four-bar System

The system of the anterior (a) and posterior (p) cruciate ligaments and their distances between attachments to femur (f) and tibia (t) as found in the knee joint of tetrapods is considered as a planar crossed four-bar linkage. The shape of thefemoralarticulating surfaces (condyles) can be calculated starting from a flat or curvedtibialarticulating surface and known bar-lengths (Menschik, 1974Z. orthop.112, 481–493; Huson, 1974Orthopäde3, 119–126).Regression analysis of the dimensions of the cruciate ligament four-bar system of 11 species of mammal and one species of bird revealed a general ratio of (a):(t):(p):(f)=(7.1):(7.9):(10.0):(6.1). These data differ from the results obtained by Badoux (1984)Acta Anat.119, 60–64) who examined only dog and horse. Our data of the dog agree with those of Badoux, i.e. (a):(t):(p):(f)≈(10):(8):(10):(4).Based on these ratios between bar-lengths, two types of knee joint shapes were distinguished. The shape of the dog's joint (“type A”) has a very large femoral condyle compared with the tibial articulating surface. Maximum knee angulation is 170–180°. Sliding between the articulating surfaces of this joint is distributed approximately uniformly over the whole angulation range. The general shape obtained from the regression analysis (“type R”) has a relatively small femoral condyle and an angulation range of about 174°. Uniformly distributed sliding occurs within this range over an angle less than 90°.Theoretically derived, limiting requirements concerning maximum angulation range (Δγmax≤180°), stabilization (e.g. avoidance of a perpendicular position of the cruciate ligaments to the articulating surfaces; Δγ78.5≥90°) and uniformly distributed sliding (Δγs≥30°) lead to at least two differentpossibleknee joint shapes. These shapes closely correspond to the tworealknee joint shapes found from the statistical analysis mentioned above. This was verified by studying quantitative characteristics obtained from the derivation of knee joint shapes from the bar lengths and vice versa. The bird (Ardea) possessed a knee joint shape, very different from the shapes described above (i.e. f>t, typeD1).

Ontogeny of the osteocranium in the African catfish, Clarias gariepinus Burchell (1822) (Siluriformes: Clariidae): Ossification sequence as a response to functional demands.

The ontogeny of the bony skull of the African catfish, Clarias gariepinus, is studied from initial ossification until a complete skull is formed. The ossification sequence in C. gariepinus seems to be related to the functional demands that arise in a developing larva. Early ossification of the opercular bone coincides with the initiation of opercular skin movements. Early ossifications involve several dentulous bones, formed shortly before the transition phase from endogenous to exogenous feeding. The enlarging branchiostegal membrane becomes supported by the gradual adding of branchiostegal rays. Parasphenoid ossification may be related to protection of the brain during prey transport, whereas the several hyoid bones, including the parurohyal, are formed in relation to the increasing loads exerted onto the tendons of the sternohyoideus and consequently onto the hyoid bar. Overall skull reinforcement occurs almost simultaneously, with a whole set of perichondral bones arising especially at places of high mechanical load. The suspensorium becomes protected against dislocation in an anteroposterior direction through a ligamentous connection, which even becomes partially ossified, forming the sesamoid entopterygoid. Later, the cranial lateral-line system becomes enclosed by a set of gutters, which close, frequently becoming plate-like later in ontogeny. The brain also becomes covered dorsally. Additional dentition (prevomeral tooth plates) formation seems to coincide with formation of the opercular four-bar system, as well as with the time the digestive system becomes completely functional. Eventually, unossified regions between the bones become closed off, fortifying and completely covering the skull. J. Morphol. 235:183-237, 1998. © 1998 Wiley-Liss, Inc.

A novel classification of planar four-bar linkages and its application to the mechanical analysis of animal systems.

A novel classification of planar four-bar linkages is presented based on the systematical variation of one, two or three bar lengths and studying the transmission properties (input-output curves) of the linkages. This classification is better suited to the study of biological systems than the classical Grashof-classification used in engineering as it considers the change of structural elements, in evolution for example, instead of evaluating the possibilities for the rotation of a particular bar. The mechanical features of a wide range of planar linkages in vertebrates, described by various authors, have been included in this classification. Examples are: skull-levation and jaw-protrusion mechanisms in fishes, reptiles and birds, the coral crushing apparatus of parrotfishes, and catapult-mechanisms in feeding pipefishes. Four-bar replacement mechanisms, e.g., crank-slider mechanisms in feeding systems of fishes and cam-mechanisms in mammalian limb-joints, and more complex linkages than four-bar ones, e.g., six-bar linkages and interconnected four-bar linkages in fish feeding mechanisms are also discussed. In this way, an overview is obtained of the applicability of planar linkage theory in animal mechanics to mechanical functioning and the effect of possible variations of bar lengths and working ranges in evolution. Four-bar system analysis often provides a rigorous method of simplifying the study of complex biological mechanisms. The acceptable width-range of necessary and undesired hysteresis ('play') in biological linkages is also discussed.

The Angles of Femoral and Tibial Axes with Respect to the Cruciate Ligament Four-bar System in the Knee Joint

The system of the anterior ( a) and posterior ( p) cruciate ligaments and their distances between points of attachment to the femur ( f) and tibia ( t), respectively, as found in the knee joint of tetrapods is considered as a crossed planar four-bar linkage. The maximum lower leg rotation range follows from the lengths of the bars of the cruciate ligament system. The extreme flexion and extension positions of the leg can be derived when this range is combined with the angles between the femoral and tibial long axes and the cruciate ligament system. The "retroposition" of the femoral and tibial articulating surfaces is determined by the dimensions of the cruciate ligament four-bar system and the bending range of the leg. The above theory is applied to data from the knee joints of ten species of mammals and a bird.