However, if the force exerted by the teeth on the food exceeds the puncture force, the system gains additional mobility as the mandible can now elevate to drive the teeth through the food. the four-bar linkage). However, once combined (n=2), the four-bar linkage effectively eliminates two of the DoF of the five-bar linkage, resulting in a total mobility of two DoF for one side of the skull (Fig. A well-documented example of a CKC containing a ligamentous link is the four-bar opercular linkage (Fig. The examples presented so far have considered CKCs composed entirely of rigid elements for which the mobility is constant; that is, Eqn1 holds under all conditions as long as the system remains a CKC. I discuss the implications of this classification, including that mobility itself may be dynamically manipulated to simplify motor control. Firstly, the mobility of this transient CKC indicates the number of DoF the organism has for manipulating the food item (while maintaining a biting grasp) to best align the trajectory of the teeth with the fracture plane of the food. Mobility has direct implications for motor control: greater DoF give an organism a greater number of ways in which to move but also a greater number of DoF that must be controlled (Turvey et al., 1982; Newell and McDonald, 1994; Todorov and Jordan, 2002; Berthouze and Lungarella, 2004; Hong and Newell, 2006). This is because a rigid element will faithfully transmit forces and torques in any direction (compare this with the conditional mobility of CKCs containing compliant elements, discussed below). A consideration of such different examples of CKCs from the perspective of mobility broadens our traditional conception of what constitutes a CKC and expands the potential functions of CKCs from transmitting force and motion to include their dynamic and substantial effect on mobility. The four-bar opercular linkage of largemouth bass (A) includes a link composed of ligamentous and bony elements (purple). I hope that in demonstrating the ways in which mobility can vary structurally and dynamically in musculoskeletal systems, this Commentary encourages the study of mobility both as a potential explanation for different motor control strategies and as a useful concept for comparing otherwise seemingly disparate musculoskeletal systems. Standing on a single foot and assuming the hip, knee and ankle joints have three, one and two rotational DoF, respectively (e.g. 1, top right), like the human lower limbs, it remains unresolved whether two-leg standing is more stable because it expands the base of support or because the legs form a CKC. In addition, because this linkage is composed entirely of rigid skeletal elements, the mobility of the transient CKC remains constant regardless of the distribution of forces. I apply this mobility-based classification to five biomechanical systems: the human lower limbs, the operculumlower jaw mechanism of fishes, the upper beak rotation mechanism of birds, antagonistic muscles at the human ankle joint and the human jaw processing a food item. As long as the food contacts the teeth, the joint between the food and teeth can be represented as a 3D sliding joint with five DoF, permitting the food item full rotational DoF and two translational DoF along the tooth surface (Fig. Search for other works by this author on: National Science Foundation These experiments presuppose a means of clearly quantifying the mobility of a musculoskeletal system, a topic also in need of further investigation. This closed chain decreases mobility at the jaw joint to two DoF, permitting primarily yaw and protrusion (C).

However, a difference is that the taut length of a muscle is neurally controlled. The human CT scan was downloaded from the Visible Human Project at the University of Iowa (mri.radiology.uiowa.edu/visible_human_datasets.html). How can mobility be considered in combination with range of motion?

5A; Gallo et al., 2006; Iriarte-Daz et al., 2017; Menegaz et al., 2015): two rotational DoF (depressionelevation and yaw) and one translational DoF (protractionretraction). Department of Ecology and Evolutionary Biology. For transient CKCs with constant mobility (Fig. using specially designed footwear) would enable each factor to be evaluated independently. In forming (and maintaining) this transient CKC, the mandible has lost a DoF. Because these skeletal elements remain permanently articulated, the number of loops, n, does not change across behaviors. Food puncture adds at least one additional DoF, increasing the mobility to at least eight DoF (D) and restoring three rotational DoF to the jaw joint, including mandibular elevation (E). It is this role of CKCs in reducing mobility that has been underappreciated and relatively unexplored across a range of musculoskeletal systems. The four- and five-bar linkages connect to form a multiloop linkage with two DoF (D) that couples rostral rotation of the quadrates with upper beak elevation (E) and permits quadrate adductionabduction independent of upper rotation (F). Closed chains of skeletal elements in the skulls of birds explain how jaw muscles drive upper beak rotation (Van Gennip and Berkhoudt, 1992; Hoese and Westneat, 1996; Dawson et al., 2011; Gussekloo and Bout, 2005; Olsen and Westneat, 2016). Elsewhere, mobility can also be used to refer to the full range of motion of a system. Here, I propose a CKC classification to explain the different ways in which mobility of musculoskeletal systems can change dynamically during behavior. I use permanent and transient to refer to a constant versus variable number of loops, respectively, and constant and conditional to refer to constituent joint mobilities that are constant versus variable, respectively. 4G). Each DoF in a musculoskeletal system represents a dimension or axis along which the organism can move but also a dimension along which the neural system must control motion, unless that dimension is redundant or irrelevant for a particular task (Todorov and Jordan, 2002). And how should the mobility of a ligament under tension but still capable of strain be represented? one of which will be held in a Global South country. For example, do muscular hydrostats have finite mobility? Tigriopus californicus copepods with the most powerful mitochondria are the brightest red, providing an honest and direct link between the attractiveness of a creature and their metabolic prowess. This common framework allows dynamic changes in mobility to be compared across systems. However, during food processing, if a food item is grasped between the upper and lower teeth, it closes a loop between the upper and lower mandible (Fig. And for some 3D four-bar linkages with hinge joints at particular orientations (Chen and You, 2005), the equation only works if the linkage is treated as a special type of planar (2D) linkage (d=3). Lond. Generally used interchangeably with linkage; however, mechanism sensu stricto may refer to a linkage in which one link is stationary. If the equation presented in the previous section is applied to the human lower limbs, they can be categorized as a transient CKC with constant mobility (Fig. Thus, I also discuss implications of this classification for motor control. Without a food item, the mandible is a single-link three-DoF open chain (A). A second example can be found in the skull of birds (Fig. Here, the total DoF of a joint or linkage; full mobility for a particular body means three rotational and three translational DoF. After all, maintaining isometry under a changing force regime is a sufficiently complex control problem in itself that it may not simplify the larger control problem.

1, top left), such as the kinetic cranial mechanism of birds, does mobility evolve under selection for motor control? Add a one- or two-hand grip on a nearby piece of furniture and you become especially tumble-proof. For example, the existence of transient CKCs with conditional mobility suggests that different motor control strategies may be employed to dynamically change mobility. 1). And while additional contacts do expand the base of support, this may not account entirely for the increased stability. In this Commentary, I have shown how a simple equation (Eqn1) can be used to quantify mobility in various biomechanical systems. 3F). Two or more links connected by joints that do not loop back on themselves; also known as a open-chain linkage. The bird cranial linkage demonstrates the mobility-reducing effect not only of closed chains but also of a multiloop linkage (n>1). By planting the second foot and closing the open chain, the mobility is reduced by six (n=1 and d=6), giving the lower limbs and pelvis six DoF when standing on two feet (Fig. An experimental setup in which the base of support can be modified independently of the number of ground contacts (e.g. CKCs can have either a permanent or a transient number of loops and have constituent joint mobilities that are either constant or conditional. The CKC classification in Fig. owls; Olsen and Westneat, 2016) have two widely spaced processes that limit quadrate rotation to a single axis and reduce the linkage mobility to one DoF. In addition, previous work has focused mostly on structurally permanent CKCs; thus, the commonalities between permanent and transient CKCs have not been fully appreciated. The number of different ways in which a mechanical system can change conformation, or the number of parameters needed to fully specify the conformation of a system. For such linkages, mobility must be calculated from the kinematic constraint equations or using a virtual loop approach (Zhang and Mu, 2010). Clockwise from top left: the cranial kinetic mechanism of mallards, the human lower limbs, the human upper jaw and mandible with a food item, and the four-bar opercular mechanism of largemouth bass (top) and antagonistic muscles that act at the human ankle (bottom). Given the centrality of mobility to motor control (Saltzman, 1979; Turvey et al., 1982; Newell and McDonald, 1994; Zatsiorsky, 1998; Todorov and Jordan, 2002; Hong and Newell, 2006), one would expect mobility to be a relevant control parameter. Adding contacts does not change the body's mass, lower the center of gravity, shift the projection of the center of gravity or increase friction all factors typically associated with increasing stability (Tanaka et al., 1996; Holbein and Chaffin, 1997; Hoffman et al., 1998; Whiting and Rugg, 2006; Hof, 2007).

This could be tested by perturbing systems while also varying the compliance and mobility of the chain-closing element; for example, a feeding system processing foods with different material properties (e.g. Applying Eqn1, the resulting CKC has a total of seven DoF, five for food motion and two for jaw joint motion (Fig. 5B). Take, for example, the tibialis anterior and soleus, an antagonistic muscle pair that is involved in rotating the foot about the ankle (Fig. Why does increasing the number of contacts with a fixed frame increase an organism's stability? Given that, in general, systems that have fewer degrees of freedom are easier to control, what implications might such dynamic changes in mobility have for motor control? As the quadrates suspend the lower beak (Fig. 5B) and forms a transient CKC (the reader can verify this with the aid of a soft food item, such as a grape). Here, mechanism is used to refer to a biological system with a particular function (e.g. In the following sections, I discuss the application of the mobility formula to each of the four classes of CKCs that I propose. Barrett and Callaghan, 2017), including the ability to strain in tension, for the purpose of calculating mobility I represent them here as two links joined by a one-DoF sliding (prismatic) joint and two spherical joints at either end (purple in Fig. There are linkages for which the ChebychevGrblerKutzbach equation does not return the correct mobility, such as some multiloop linkages with parallel, in-series hinge and linear sliding joints (Gogu, 2005). 2C. Considering each of the four categories of CKC discussed here provides a means of answering this question. However, the equation works for all examples here and, to my knowledge, there is no linkage representing a musculoskeletal system reported to violate the mobility equation. All rights reserved. 2A).

Sci. 4E). 2022 The Company of Biologists. If the ligament is taut and in tension, the mobility decreases to four DoF (D) and opercular elevation can drive lower jaw depression (E). Lastly, for transient CKCs with conditional mobility (Fig. R. Soc. decreases the likelihood of falling). Parallel to this four-bar linkage, the neurocranium, quadrate, pterygoid, palatine and upper beak form a five-bar linkage (Fig. However, relative to an equivalent OKC, CKCs also reduce mobility, defined as the total degrees of freedom (DoF; see Glossary) or the total number of independently variable ways in which a system can move. For example, a joint may allow motion along a particular DoF, but if the allowed motion is too small to be biologically relevant, that DoF is hardly significant. An antagonistic muscle pair at the human ankle (F) can be modeled as a multiloop linkage. 4H). The concept of freezing DoF is used throughout the motor coordination literature (e.g. a single muscle controlling a two-DoF joint; Fig. Secondly, treating the food item as a link in a CKC provides one approach to including toothfood interactions in the study of feeding systems (Brainerd and Camp, 2019). Analogous to the previous examples of intrinsic compliant tissues (e.g. In this Commentary, I propose a classification of how the mobility of biological CKCs can (or cannot) change during behaviors (Fig. 3D). The author gratefully acknowledges support from the National Science Foundation (grant DBI-1612230). A mechanical system consisting of two or more links connected by joints, as an open or closed kinematic chain. This permits the quadrate to rotate forward and backward with upper beak rotation (Fig. The human mandible with a food item has a mobility that changes with food contact and manipulation. 3E) and adductabduct independently of upper beak rotation (Fig. For example, ligaments cannot resist compression, resist tension only when they are taut, and can be twisted about their long axis. And a CKC in mantis shrimps shows how energy stored in compression of an exoskeletal segment can drive extremely rapid extension of an appendage (Patek et al., 2007; McHenry et al., 2012). Aaron M. Olsen; A mobility-based classification of closed kinematic chains in biomechanics and implications for motor control. 2B). If a food item is simply held between the teeth without puncture (B), the toothfood joint acts as a 3D sliding joint with five DoF (inset), and the system becomes a seven-DoF closed chain (orange arrows). Transforming an OKC into a CKC (e.g. However, when the sliding joint reaches its maximum excursion and is under tension, its mobility becomes 0 and the link represents a taut ligament. Both the opercular mechanism in fishes and the human ankle joint have dynamic mobilities that depend on the mobilities of the constituent joints. For simple coupling (i.e. As long as the food is simply held and not punctured, the mandible can protrude or retrude and yaw but not depress or elevate substantially. In their Review, Ateah Alfakih, Penelope Watt and Nicola Nadeau discuss the energetic cost of colour change and highlight how this can be avoided or lessened in animals that change colour rapidly or slowly. The problems of degrees of freedom and context-coordinations variability, Skull mechanics in the pigeon, Columba livia, a three-dimensional kinematic model, A test of mouth-opening and hyoid-depression mechanisms during prey capture in a catfish using high-speed cineradiography, Closed loop problems in biomechanics. The CKC formed when both feet contact the ground is structurally transient because n changes depending on whether one or both feet are in contact with the ground: standing on a single foot forms an OKC, in which case n=0, whereas standing on both feet forms a single-loop CKC (n=1). 3A), where the bones of the palate (jugal, palatine, pterygoid and quadrate) form four- and five-bar parallel linkages (see Glossary) that elevate and depress the upper beak (Bock, 1964; Van Gennip and Berkhoudt, 1992; Hoese and Westneat, 1996; Dawson et al., 2011; Olsen and Westneat, 2016). In this way, the distinction between a structurally transient versus permanent CKC (Fig. Eng. Arnold et al., 2010), the lower limbs and pelvis have a total of 12 DoF (Eqn1; Fig. Two or more links connected by joints to form a continuous loop; also known as a closed-chain linkage. Also, for all remaining figures, numbered orange arrows indicate one possible set of parameters (DoF) for specifying the system conformation, and equations correspond to Eqn1 (where M is the total mobility). The mallard CT scan was downloaded from digimorph.org, with thanks to the University of Texas High-Resolution X-ray CT Facility, Dave Dufeau and National Science Foundation grant IIS-9874781 to D. Dufeau. These levels form a descriptive hierarchy: for a single configuration there are multiple potential geometries and for a single geometry there are multiple potential conformations. Thus, in the case of a CKC containing a ligamentous link, the CKC is permanently closed but the value of fi in Eqn1 changes; the magnitude of this change is conditional on the direction of forces transmitted through the ligament, the conformation of the system and the material properties of the ligament. Rather, these contacts may increase stability in part by transforming the limbs from open kinematic chains (OKCs; see Glossary) into a transient closed kinematic chain (CKC; see Glossary). This Commentary extends mobility to systems with non-rigid elements, but the general usefulness of applying linkages with rigid links to systems with compliant elements warrants further exploration. Published by The Company of Biologists Ltd, Linkage mobility can be calculated from an equation known as the ChebychevGrblerKutzbach criterion (, A model of the lower limb for analysis of human movement, Motor skill acquisition under environmental perturbations: on the necessity of alternate freezing and freeing of degrees of freedom, Unsteady locomotion: integrating muscle function with whole body dynamics and neuromuscular control, Functional morphology of vertebrate feeding systems: new insights from XROMM and fluoromicrometry, XROMM analysis of rib kinematics during lung ventilation in the green iguana, Iguana iguana, Rib kinematics during lung ventilation in the American alligator (Alligator mississippiensis): an XROMM analysis, Reevaluating musculoskeletal linkages in suction-feeding fishes with X-ray reconstruction of moving morphology (XROMM), Swimming muscles power suction feeding in largemouth bass, Rib motions don't completely hinge on joint design: costal joint anatomy and ventilatory kinematics in a teiid lizard, Salvator merianae, Mobile assemblies based on the Bennett linkage.