I Lafoz

M A Mozas

O Charrier

C Fernández De La Hoz

IMA Systems Development and Configuration: From UML to Binary. A Proposal of UML Profile to be used with the ARINC 653 Standard

Keywords: IMA systems, partitioning, ARINC 653, UML profile, XML schema, qualified tools, SW architectural design, VxWorks

The ARINC 653 standard is used more and more often for Safety-Critical Systems in Aerospace. The experience from the design and implementation of this kind of systems introduces new considerations to take into account compare to classical software development workflow, mainly related to the objective of multiple applications running on the same system. The return of experience that is presented in this paper includes a proposed UML extension (via profile) that resolves the lack of UML modelling formalism for the ARINC 653 artefacts, the XML schema updates to fit the objective of application independency, a validated way of automatically generating code relating to all the ARINC 653 elements, an optimal framework for defining tests and required stubs, and the use of qualified tools to verify and generate the binary version of the system configuration tables.

Introduction.

The advantages of IMA architectures have been widely discussed and demonstrated in recent years (multiple applications sharing and reusing the same computing resources, software isolated from the underlying bus and hardware architecture, maximize reuse, reduction of the cost of changes in terms of re-test, etc.) [START_REF] Parkinson | Safety-Critical Software Development for Integrated Modular Avionics[END_REF]. Despite a number of IMA architectures and standards have been emerged, the ARINC Specification 653 has achieved the widest adoption in the avionics community [START_REF] Fernández De La Hoz | ARINC Specification 653. Avionics Application Software Standard Interface[END_REF]. The current paper presents the specific characteristics of the design of ARINC 653 systems in section 2, and proposes and describes in detail a UML extension to deal with this design in chapter 3. Chapter 4 is focused on the description of the use of XML schema for defining the configuration of this kind of system. Once the design and configuration phases are covered, chapters 5 and 6 present an automatic generation of the configuration tables and a qualified validation process of them. Furthermore, automatic generation related to ARINC 653 artefacts is also described in terms of code and, in chapter 7, in terms of partition tests and stubs. Chapter 8 shows the achieved experience with the technology described.

ARINC 653 Systems Design Specificities.

The classical software design and development workflows don't usually consider the partitioning requirements of IMA architectures. Moreover, the design of a complete partitions architecture becomes a challenge for the System Architect. The EADS-CASA experience in the design and development of complete IMA systems is here presented in terms of a set of criterions to guide the partitions selection and design. A partition based design must take into account both the available resources, such as budget (time and staff), CPU and memory, and some system requirements, such as DAL criticality level, flexibility and fault tolerance. The goal of the selection/design of the partitions procedure is to reach the best balance between the use of resources and the accomplishment of requirement by focusing on the impact of using partitioning with respect to the next Quality Factors:  Certification Effort. A higher DAL a higher development and overall verification cost. Nevertheless, the isolation between software with different DAL assignments allows the application of different processes according to the needs of each software partition.  Safety. The isolation between partitions prevents failure propagation.  Reusability. The reusability reinforces the well-defined software component functionality, suitable for software reuse, and reduces undesirable execution coupling of software verified in equivalent contexts.  Scalability. The isolation between software reduces the needs of regression testing in case of software changes and allows the introduction or removal of software without changing execution conditions. Some others possible quality factors could be considered for deciding the partitioning as Security, IO Partitions, Development Tool-Chain or Languages, etc., but they are out of the scope of this analysis. An iterative procedure is shown in Figure 1, in order to drive the trade-off between the impact on the considered parameters and the requirements and available resources and find the most beneficial solution. The detailed description of this iterative decision flow is out of the scope of this paper, nevertheless a brief view on it has been shown in order to justify some of the concepts presented.

Once the partitioning architecture is defined a new UML profile is proposed in order to deal with the lack of modelling formalism of the ARINC 653 elements: partitions, processes, inter-partitions communications, etc. Furthermore, the new UML extension [START_REF] Omg | UML 1.4 Specification[END_REF] allows integrating in the model the design of the partitions and the rest of the UML design in the first stages of the architectural design. Thus, a complete coherence checks of the whole architecture at the design level, which reduces the possible undetected design errors. The cost of a re-design of the partitioning architecture, in terms of modification of interfaces (APEX ports) and distribution of functionality, could be, in many cases, quite huge or just unacceptable. So, as soon as the partitioning design is jointly checked with the application software architecture, the reduction in the risk of a bad design is mitigated.

UML Extension for supporting ARINC 653.

UML/ARINC-653 profile has been created based on "XML Schema Element Relationship" (fig 5.2-1 in [START_REF] Fernández De La Hoz | ARINC Specification 653. Avionics Application Software Standard Interface[END_REF]), shown in Figure 2, and on "Service Requirements", (chapter 3.0 in [START_REF] Fernández De La Hoz | ARINC Specification 653. Avionics Application Software Standard Interface[END_REF]). This extension has been built for UML 1.4 [START_REF] Omg | UML 1.4 Specification[END_REF]. The main difference in doing it for UML 2.1 [START_REF] Omg | UML 2.1 Specification[END_REF] would be that stereotypes for ARINC-653 communication resources would apply to UML Ports instead of to Classes. The semantics of most of stereotypes and tags are the same as stated in [START_REF] Fernández De La Hoz | ARINC Specification 653. Avionics Application Software Standard Interface[END_REF]. Some new information has been added it order to support the actual OS implementation specificities (depending on the OS supplier), and to relate ARINC-653 entities with logical software entities.

UML Extension Stereotypes Description.

The following tables list the most relevant stereotypes and the related information defined for the profile. From the logical design point of view, there is complete independence about the actual mechanism used to distribute, to run and to communicate the software components. Even the code derived from logical design is independent of the component plane supposed, on the one hand, that the interfaces act like wrappers of the concrete implementation of the communication mechanism, which depends on the component design and, on the other hand, that active logical entities are not aware about where the execution thread comes from.

In the other side, it is important to take into account the nature of communication mechanisms supported by ARINC-653 resources (asynchronous, blockingtimed-out, unidirectional…) when designing the logical solution, particularly the interfaces definition, to guarantee the feasibility of getting advantage of flexibility in the mapping with the component plane.

Moreover, the policy for realization and usage of interfaces in the logical plane (polling, call-back registration…) must be defined before logical detailed design and implementation, because it can condition detailed design decisions and because it will became a requirement for the interface wrapper realization.

From other point of view, the fact of having a formalintegrated model for the solution, allows verifying the integral coherence of the whole design, by taking into account both the logical architecture (coming from the application domain), and the ARINC-653 services configuration and usage. Even due to the formality on the description, much correctness verification can be done automatically.

Besides, the integrated model allows making time analysis, by considering the performance constrains at logical plane (time and memory) in front of the ARINC-653 services configuration and behaviour (partition scheduling configuration, communication performance and memory configuration). Performance and Time constrains specification could be defined by using [START_REF] Omg | UML Profile for Schedulability, Performance and Time[END_REF] or [START_REF] Omg | UML Profile for Modelling and Analysis of Real-time and Embedded Systems (MARTE)[END_REF].

ARINC 653 XML Configuration Schemas.

As described in the ARINC 653 Specification Part 1 [START_REF] Fernández De La Hoz | ARINC Specification 653. Avionics Application Software Standard Interface[END_REF], an ARINC 653 system is configured using "Static Data Areas accessed by the OS". This XML Schema definition is the return of experience of Wind River and its customers, which includes hosting Flight Management, Data Management or Mission Computer applications on the same system in both civil and military aircrafts. This Schema has been proposed as a start point for the ARINC 653 XML Definition Subcommittee, led by Wind River, and counting for ARINC 653 Part 1 Supplement 3. This XML Schema definition has been used as reference for the UML profile definition.

Automatic Code Generation of ARINC 653

Artefacts.

One important advantage of formal models is to get the possibility of generating automatically some code, which is typically routine, tedious, and often error prone. In our scenario, it is not only one advantage, but also a requirement for making feasible the feature of trying out easily (in an efficient way) different architecture designs. At least, we consider beneficial the automatic generation of code for ARINC-653 configuration tables, interfaces implementation (wrapper and body), partitions procedures and processes procedures.

Anyway, the activity of code generation should be flexible enough to support different possible scenarios:  With respect to the source code, some aspects can differ from a project to other. o Coding language. o Safety level, and associated implementation constrains. o Policy for usage/realization of interface wrappers, etc.

 With respect to the ARINC-653 configuration tables, there can be specificities and even standard deviations, depending on the OS manufacturer.

So, the activity of code generation must take into account the architecture information and the pattern applicable for the output.

Application of the Proposed Extension to the Partition Testing.

One main advantage of using ARINC-653 (IMA) is the increase of testability at partition level, because of the clearly defined interfaces and the well defined and controlled partition execution environment (time and memory).

Once reached this point, it is a temptation to trying to take advantage from the ability of code generation described in chapter 5 (mainly relating with interfaces and configuration tables), as well as of the formalism required for defining the external partition interfaces (interface wrapper and realization/usage policy). So, a generic test framework solution, could hook with partition code, just by complementing the partition under test; that is, by realizing the interfaces required by the partition, using the interfaces realized by the partition, and respecting the budget of time and memory used by the partition.

As long as the required partition behaviour has been defined by means of formal UML behaviour diagrams, the test case could be described by using instances of Sequence diagrams extracted from State chart diagrams and Sequence diagrams (for checking requirements about sequencing and time constrains) with concrete data values (for checking requirements about algorithms and data transformation).

Return of Experience.

The technology described along this paper has been defined, implemented and successfully used in the framework of the Advanced Air Refuelling Boom System Project developed by the Military Transport Aircraft Division of EADS-CASA.

The UML profile has been applied in an actual ARINC 653 system created, tested and validated using Wind River's VxWorks 653 OS. It implements a separation in two layers at the Software Design Level, which allows multiple capabilities :

 Evaluation of different implementations keeping the Logical solution stable.  Verification of the coherence of the whole design and application time analysis.  Easy creation of test stubs for code running inside an ARINC 653 partition.

The return of experience shows easy modelling of an ARINC 653 approach with optimal results and important reduction of the coding time and the proportion of coding errors.

Configuration and development processes are also key factors for successful certification  Time and integration are where the challenges are, not the applications, the OS or the hardware Special emphasize should be put on these two areas from the start of a program. Both areas need to be carefully designed.

The right balance needs to be found between built-in configuration and data driven configuration for all parts of a system  Data driven configuration allows changes to be bring in with minimal impact, even during the certification cycle Use a unified and qualified process to manage all data driven configuration data

Conclusion

The presented ARINC 653 UML profile optimally extends standard UML for supporting partitioning design and allows connect it with a classical software component based design. The use of this new profile provides some clear advantages, as flexibility, feasibility, verifiability, reusability, etc., widely described along the paper. Besides, automatic code generation of both ARINC 653 elements and configuration tables is also provided, which increase the reliability and the reduction of effort and errors cost. Related to the configuration tables of an ARINC 653 the followed XML schemas policy has been described and the main advantages of its use have been also highlighted. Taking into account the application of all these concepts to Safety-Critical Systems, the certification point of view has been also considered. Special interest has been put in the qualified validation process of the mentioned ARINC 653 configuration tables, which allows directly translate them to binary. Finally, a feasible and reliable testing framework has been also proposed mainly focused to the partition testing.

Acknowledgement

Special thanks to the Military Transport Aircraft Division of EADS-CASA for the support during the development of this paper and for providing the frame of a concrete project environment, in which this technology has been developed.



  Testability. The clearly defined and controlled interface of a partition, besides the standard execution environment definition, makes the testing process and tools easier and more accurate.  Design Cost. The higher design cost must be considered in terms of data coupling, synchronization, coherence and complexity of interfaces between partitions. Moreover, are there a maximum affordable/reasonable number of partitions/ports from the design point of view?  Performance. Increasing the number of partitions produces a loss of performance due to the next issues: o Switching Partition Time. The context switching between partitions always implies a loss of time. This time directly depends on the operating system features. o Worst-Case Time Assignment. The time or minor frame assigned to a partition must support the worstcase execution time. o Worst-Case Memory Assignment. The memory assigned to a partition must support the worst-case execution resources usage. o Inter-Partition Communication. The spent of time of the standard mechanism for communicating partitions based on APEX ports is higher than other classical or intrapartition communication mechanisms.

Figure 1 :

 1 Figure 1: Iterative Decision Flow to Balance the Partitioning Design.

Figure 2 :

 2 Figure 2: UML Representation of XML Schema Elemnt Relationship.

Figure 3 :

 3 Figure 3: Example. Multi-Partition Solution.

Figure 4 :

 4 Figure 4: Example Alternative Intra-Partition/Multi-Process solution.

Figure 5 :Figure 6 :

 56 Figure 5: Code Generation Dependencies.

Table 1 :

 1 Module Stereotype Properties.

	Stereotype	Base Class		Tags
	Module	Class		ModuleName
				ModuleVersion
				TargetType*
	Tag	Type		Multiplicity
	ModuleName	NameType		[0..1]
	ModuleVersion	NameType		[0..1]
	TargetType	Enumeration	of:	[1]
		OsManufacturer
	Stereotype	Base Class	Tags
	Partition	Class	PartitionIdentifier
			PartitionName
			Criticality
			SystemPartition
			EntryPoint
	Tag	Type	Multiplicity
	Partition Identifier	Integer	[1]
	PartitionName	NameType	[0..1]
	Criticality	Enumeration of:	[1]
		LEVEL_A,
		LEVEL_B,
		LEVEL_C,
		LEVEL_D,
		LEVEL_E
	SystemPartition	Boolean	[1]
	Entry Point	NameType	[1]

*Target Type represents the specificities (and deviation from the standard) introduced by OS manufacturers.

Table 2 :

 2 Partition Stereotype Properties.

	Stereotype	Base Class	Tags
	Pseudo Partition	Class	Name
			PhysicalAddress
			Procedure
	Tag	Type	Multiplicity
	Name	NameType	[0..1]
	PhysicalAddress	Integer	[0..1]
	Procedure	NameType	[0..1]

Table 3 :

 3 Pseudo Partition Stereotype Properties.

	Stereotype	Base Class	Tags
	EntryPointClass*	Dependency

Table 4 :

 4 Entry Point Class Stereotype Properties. Logical class that defines the EntryPoint method for the Process.

	<<EntryPointClass>>	dependency	relates	a
	<<Process>> with the Stereotype Base Class		Tags
	Process	Class			Name
					StackSize
					BasePriority
					Period
					TimeCapacity
					DeadLine
					EntryPoint
					Preamble*
	Tag	Type			Multiplicity
	Name	NameType		[1]
	StackSize	Integer			[0..1]
	BasePriority	Integer			[1]
	Period	Float			[1]
	TimeCapacity	Float			[0..1]
	DeadLine	Enumeration	of:	[0..1]
		Soft, Hard
	EntryPoint	String			[1]
	Preamble	String			[0..1]

Table 5 :

 5 Process Stereotype Properties.

	Stereotype	Base Class		Tags
	QueuingPort	Class		PortName
				MaxMessageSizeDire
				ction
				MaxNbMessages
	Tag	Type		Multiplicity
	PortName	NameType		[1]
	MaxMessageSize	Integer		[1]
	Direction	Enum.	of:	[1]
		Source
		Destination
	MaxNbMessages	Integer		[1]

Preamble represents a method called before EntryPoint for specific partition initialization.

Following stereotypes are focusing on the Inter-Partition Communications modelling.

Table 6 :

 6 Queuing Port Stereotype Properties.

	Stereotype	Base Class	Tags
	Memory	Class	RegionName
	Requirements		Type
			SizeBytes
			PhysicalAddress
			Access
	Tag	Type	Multiplicity
	RegionName	NameType	[0..1]
	Type	String	[1]
	SizeBytes	Integer	[1]
	PhysicalAddress	Integer	[1]
	Access	String	[1]

Table 17 :

 17 Memory Requirements Stereotype Properties.

	PartitionPeriodStart	Boolean	[1]

Table 21 :

 21 Window Schedule Stereotype Properties.

	3.2 Modelling pattern for UML/ARINC 653.
	Based on this UML extension for ARINC-653, we
	propose a SW Design in two planes: a conventional
	design to deal with the logical architecture of the
	solution, based on elements from the application
	domain, and a component design based on ARINC-
	653 elements. Both planes are connected in specific
	points, which are interface realizations and
	Process/EntryPoint. This approach allows trying out
	and evaluating different implementation solutions
	while keeping stable the logical architecture.

Stereotype

Base


The nature of the "liquid sunlight"

Amelia Carolina Sparavigna

The nature of the "liquid sunlight" Amelia Carolina Sparavigna 1 1 -Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy ORCID 0000-0003-4502-8974 ABSTRACT Today, the term "liquid sunlight" refers to a green fuel obtained by means of a process inspired by the natural photosynthesis. The method to have this fuel is based on the combination of compatible inorganic and biological components to transform light, water, and carbon dioxide to methane. A similar term, "sunlight-toliquid" or "sun-to-liquid", exists for a recently proposed synthesis of a gas, which is further processed to obtain kerosene. Here we will show that in the past the term "liquid sunlight" was used for the petroleum. Actually, the meaning of the term, today and in the past, is the same: conversion of the sunlight energy into a fuel.

What is the "liquid sunlight"? This is a term that we find in [START_REF] Bourzac | News Feature: Liquid sunlight[END_REF], referring to a green fuel obtained by a device designed in Berkeley, at the Joint Center for Artificial Photosynthesis. Inside the device, "arrays of nanowire electrodes and bacterial colonies are using the light to turn water and carbon dioxide into methane, the main component in natural gas". The process wants to imitate what the plants are doing during the photosynthesis. So the liquid sunlight is referring to the fuel that we can obtain starting from the fundamental process of splitting water into oxygen and hydrogen, in an artificial photosynthesis which is producing hydrocarbons [START_REF] Bourzac | News Feature: Liquid sunlight[END_REF].

The article [START_REF] Bourzac | News Feature: Liquid sunlight[END_REF] is proposing a discussion on the evolution of researches in this area since the 1970s. "The inspiration came in 1972, when Akira Fujishima at Kanagawa University and Kenichi Honda at the University of Tokyo showed that two electrodes -one titanium dioxide and the other platinum -would catalyze the splitting of water when illuminated with visible light" ( [START_REF] Bourzac | News Feature: Liquid sunlight[END_REF] is referring to article [START_REF] Fujishima | Electrochemical photolysis of water at a semiconductor electrode[END_REF]). This research inspired scientists to work on artificial photosynthesis. Among then, we find those of the National Renewable Energy Laboratory in Boulder, Colorado.

After many years and studies to find the best catalyser and electrodes, a new approach is given by the recruitment of bacteria "to help do the job". A team at the University of California, Berkeley, has made a solar fuel system with the use of "living catalysts" too [START_REF] Nichols | Hybrid bioinorganic approach to solar-to-chemical conversion[END_REF]. The system is based on nanowire electrodes. The nanowires have carpeted surfaces to absorb more light and hold more catalyst. In the cell, one of the electrodes is seeded with bacteria. Also in Harvard, researches are working on the use of microbes [START_REF] Torella | Efficient solar-to-fuels production from a hybrid microbial-water-splitting catalyst system[END_REF].

After the report given in [START_REF] Bourzac | News Feature: Liquid sunlight[END_REF], many articles had been published on this subject and on the fuels produced by bacteria in general. However, the aim of this discussion is not the report of the literature, but the use of the term "liquid sunlight". The term is clear, it is the liquid fuel that we can obtain from sunlight [START_REF]Liquid Sunlight[END_REF], as explained by Peidong Yang, who is proposing the system developed at Berkeley [START_REF] Nichols | Hybrid bioinorganic approach to solar-to-chemical conversion[END_REF] also for deep space missions [START_REF] Yang | [END_REF], in order to have an effective manner to produce fuel and oxygen for the crew.

As previously told, the "liquid sunlight" is a fuel obtained by means of a strategy inspired by the natural photosynthesis. The researchers combined compatible inorganic and biological components, to transform "light, water, and carbon dioxide to the value-added product methane." In [START_REF] Nichols | Hybrid bioinorganic approach to solar-to-chemical conversion[END_REF], it is described a solar-to-chemical conversion platform which is interfacing photoactive inorganic materials that produce hydrogen from water and sunlight with microorganisms that consume hydrogen to drive the transformation of carbon dioxide to methane with high efficiency.

In fact, the term "liquid sunlight" is impressive. It is evoking the possibility to have a sort of liquid phase of the light, that is, a liquid fuel which is the condensate of sunlight energy. We can find a term of this kind also in the "SUNlight-to-LIQUID", which is the title of a project of European Horizon 2020, for the development of an integrated solar-thermochemical synthesis of liquid hydrocarbon fuels [START_REF]SUNlight-to-LIQUID: Integrated solar-thermochemical synthesis of liquid hydrocarbon fuels[END_REF]. We find this term rendered as Sun-to-Liquid, fuels from concentrated sunlight [8]. As told in [8], the project is devoted to produce renewable transportation fuels from water and carbon dioxide with concentrated sunlight. In [9], it is claimed that the project, which is funded by the EU and Switzerland, "has now successfully demonstrated the first synthesis of solar kerosene."

The sun-to-liquid fuels is produced in a solar thermochemical reactor. The solar reactor, developed by ETH Zurich, is obtaining a synthesis gas which is a mixture of hydrogen and carbon monoxide, from water and carbon dioxide via a thermochemical redox cycle. Then, this gas is processed to kerosene by an on-site gas-to-liquid system by HyGear. Therefore, the sun-to-liquid is the kerosene, a well-known combustible hydrocarbon liquid derived from petroleum. So the European project aims to obtain a product which is the same of that which is coming from the fossil fuel resources.

Kerosene is known for centuries. In the 10th century, the Persian scholar Muhammad Al-Razi (Muhammad ibn Zakarīya Rāzi) described in his Book of Secrets the distillation of petroleum, to have oil for lamps [START_REF] Bilkadi | The Oil Weapons, Saudi Aramco World[END_REF]. In the West, it was the Canadian physician and geologist Abraham Gesner who carried out in 1846 the first public demonstration of this illuminating liquid. Gesner later called it "kerosene", a word he invented and used as a marketing tool [START_REF] Mcniven | The Yankee Road: Tracing the Journey of the New England Tribe that Created Modern America[END_REF]. Kerosene was an inexpensive liquid and substituted the whale oil in lamps for lighting systems.

Soon petroleum became the liquid by means of which it was possible to obtain light and heat. It was returning the sunlight from which it had origin. So, in a book of 1898, Alexander Winchell defines it the "liquid sunlight" [START_REF] Winchell | Walks and talks in the geological field[END_REF]. He also defined the natural gas as the "gaseous sunlight". The "solidified sunlight" was the coal and the coal-beds. Here the beginning of what he is telling on petroleum and natural gas in [START_REF] Winchell | Walks and talks in the geological field[END_REF]. "XXIV. Liquid Sunlight. Petroleum. The history of the search for native oil is romantic. Known for ages, it remained a mere curiosity till 1859. Even in America, where popular intelligence is supposed to utilize every possible advantage, petroleum rose only to the importance of a quack remedy for aches and other evils. But suddenly it assumed the sceptre of king. Men pursued it with the sound and fury of dogs on the track of their prey. They lost their power of reasoning on the subject. They could not be convinced that mineral oil is a geological product, fixed in its relations to the earth and to the strata as unchangeably and as intelligibly as iron or salt. They would not listen to the counsel of science. Every man was confident in his self-wisdom, and never inquired on what grounds he believed and acted as he did. There was oil -millions of barrels of it; and many investors were fortunate if not wise; and many, though wise, were not fortunate. It was a new situation." [START_REF] Winchell | Walks and talks in the geological field[END_REF].

Alexander Winchell is mentioning a date, 1859. He is referring to the oil discovery at Oil Creek Pennsylvania and to th following oil rush.

In [START_REF] Winchell | Walks and talks in the geological field[END_REF] the "gaseous sunlight is introduced in the following manner.

"Illuminating and Heating Gas is one of the products of the earth. ... its origin is undoubtedly similar to that of oil, and that oil is chiefly the product of the distillation of shales charged with vegetable matter -probably ancient sea-weeds. As sunlight is the active agent in vegetable growth, a stem or a leaf is simply a body of transformed sunlight. When imbedded in the rocks it is strictly and literally fossil sunlight. In petroleum, ancient sunlight is preserved in liquid form; in natural gas it is gaseous." Soon after the Winchell's book was published, the petroleum became "that liquid sunlight which is revolutionizing the economic life of mankind", as told in a book of 1925 [START_REF]The World's Work. A History of Our Time[END_REF]. In [START_REF] Martin | Heat and fire[END_REF], coal, oil, and gas are defined the "gifts from the sun." "When we burn coal, we are setting fire to the remains of an ancient forest, and setting free energy from the sun that was held inside the coal for thousands of years. Can you now tell why coal is called "black sunlight"? And why oil is called "liquid sunlight"?" [START_REF] Martin | Heat and fire[END_REF].

The "black sunlight" is illustrated in [START_REF]Black Sunlight" circa (1920) Bray Studios[END_REF]. As in the case of the "liquid sunlight", it is the sunlight solidified in coal. "The sun's emanations of light and heat became transformed into stem and frond and tissue. The coal is ancient sunlight that has been locked up like a treasure and buried in the earth for ages. … Here, in this flame [the flame from coal], the old sunlight is regenerated; this is the very sunlight which became latent in vegetable cells so long ago. It is locked-up sunlight set free after a long imprisonment." [START_REF] Winchell | Walks and talks in the geological field[END_REF] In [START_REF]New Book of Knowledge[END_REF], we find the other terms used for petroleum: "Black gold", "crude," and "Texas tea". Today, the term "black gold" is more familiar than the term "liquid sunlight". The reason is that we have not been using oil for a long time in the lamps for illumination and the use in heating systems is limited in western countries. Then, the "sunlight" is no more linked to oil. So, in the past, the "liquid sunlight" was the petroleum, the liquid in which the energy of the sun was condensed and that was recovered for many uses. Today, it is the liquid fuel that we can obtain from sunlight in renewable or green processes. Again, it is the energy of the sun which is condensed in a material that we can use for fuel.


Joanne Becker
email: joanne.becker@univ-amu.fr

Mermoz Emmanuel

Linares Jean-Marc

Joint loading estimation method for horse forelimb high jerk locomotion: jumping

Keywords: joint loading, jumping, kinematics, modelling, OpenSim

Maximal local loads in animal joints are necessary to design bio-inspired mechanical joints. Many studies presented methods to determine joint reaction forces in humans and animals. However, many of these methods are invasive, and no work has been published yet about the joint reaction forces in the horse forelimb during jumping. Non-invasive methods to measure the kinematics and ground reaction force of a horse forelimb were used in this work. A musculoskeletal model of horse forelimb was built with mechanical methods for the estimation of joint reaction forces. The entire forelimb was reconstructed by scanning real bones geometry with a 3D optical scanner and modeling all the muscles on a Computer Assisted Design (CAD) software. The model dynamics were simulated with OpenSim in order to estimate the joint loading. This study allows knowing an order of magnitude of the loads at the joints at jumping in order to determine latter the maximal joint contact loading values that will be a key at designing bio-inspired joints for mechanical assemblies.

Introduction

The imitation of highly performing articulations could lead to a crucial change in the design of current mechanical systems. Even if animal joints areusually simplified as hinge or spherical joints [START_REF] Lerner | Modulating tibiofemoral contact force in the sheep hind limb via treadmill walking: predictions from an opensim musculoskeletal model[END_REF] , their articulations present complex contact surfaces that should take part in locomotion performances.Unguligrade animals show interesting locomotion characteristics because their vertebral column is stable and their locomotor limbs move principally in sagittal plane. Horses in particular are real athletes, presenting high sportive performances and large loads in their joints [START_REF] Harrison | Relationship between muscle forces, joint loading and utilization of elastic strain energy in equine locomotion[END_REF] . The horse was chosen as the experimental subject of this study because it is easily accessible and very easy to train.

In order to mimick these articulations, it is necessary to know the local pressures through these joints. In Picault et al. (2018) [START_REF] Picault | Smart pressure distribution estimation in biological joints for mechanical bio-inspired design[END_REF] , the authors gave a method to determine the contact areas and local pressure values with finite elements. These local pressures cannot be computed without the determination of joint loadings of an animal articulation. The aim of our work is therefore to determine the equivalent joint loadings of horse forelimb articulations for a high jerk in order to compute latter the local pressures to design bio-inspired joints.

Several works in medical sciences have investigated the estimation of joint reaction forces in humans. On the one hand, this enables to assess the characteristics of reactions in joints (force, direction…), and on the other hand, to understand injuries, fatigue fractures… In human, many athletes and aged people present hip injuries [START_REF] Paluska | An overview of hip injuries in running[END_REF][START_REF] Boyd | Common hip injuries in sport[END_REF] , and knee injuries [START_REF] Patil | Tibial forces measured in vivo after total knee arthroplasty[END_REF][START_REF] Walter | Decreased knee adduction moment does not guarantee decreased medial contact force during gait[END_REF] . The joint reaction forces information would enable to better design knee or hip prostheses in order to improve their lifetime and to reduce the pains. In humans, these estimations can be assessed by in vivo measurements using the prostheses as measuring devices [5] , but this method is invasive and costly. In the recent years, researchers have developed modelling techniques for a better understanding of movement dynamics and estimation of internal joint reaction forces. One of these methodologies is the finite element modelling which was widely used to better understand joint behavior in human [START_REF] Li | A validated three-dimensional computational model of a human knee joint[END_REF][START_REF] Donahue | A finite element model of the human knee joint for the study of tibio-femoral contact[END_REF][START_REF] Pena | A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint[END_REF] . Another developed method is the musculoskeletal modelling which first has been applied on human lower limb modelling [START_REF] Delp | OpenSim: opensource software to create and analyze dynamic simulations of movement[END_REF][START_REF] Ward | A model of the lower limb for analysis of human movement[END_REF][START_REF] Hamner | Muscle contributions to propulsion and support during running[END_REF][START_REF] Reinbolt | Simulation of human movement: applications using OpenSim[END_REF] but more recently also on animals like horse [START_REF] Harrison | Relationship between muscle forces, joint loading and utilization of elastic strain energy in equine locomotion[END_REF][START_REF] Panagiotopoulou | A preliminary case study of the effect of shoe-wearing on the biomechanics of a horse's foot[END_REF] , sheeps [START_REF] Lerner | Modulating tibiofemoral contact force in the sheep hind limb via treadmill walking: predictions from an opensim musculoskeletal model[END_REF] and ostriches [START_REF] Hutchinson | Musculoskeletal modelling of an ostrich (Struthio camelus) pelvic limb: influence of limb orientation on muscular capacity during locomotion[END_REF] .

The work presented in this paper aims at building a musculoskeletal model of the entire forelimb of the horse to compute the joint reactions forces at jumping. For this purpose, this work first presents noninvasive measurements to collect markers trajectories and ground reaction forces values. Then the methods for the modelling of the complete horse forelimb and for the computation of the joint reaction forces are presented. The joint loadings were first computed at trotting to compare with literature and then at high jerk locomotion by jumping a fence of 1m high.

Materials and methods

Animal used for in vivo experiments

For the experiments, a French Saddle sport horse weighing 560 kg and judged free of obvious lameness was ridden by a professional rider. The total weight of the horse, his rider and the equipment was about 650 kg.

Gait instrumentation

In these experiments, the video and force plate data were simultaneously recorded for the horse and his rider for both trotting and jumping a small fence of 1m high. Seven non-distracting principal markers were attached to the animal's skin: top of scapula, shoulder, elbow, wrist joint, metacarpophalangeal (MCP) joint, phalangeal (P1-P2) joint, extremity of the hoof (Fig. 1). Four secondary markers were placed on the long segments to determine the position and orientation of each segment during gait. No secondary markers were placed on the phalanxes. Too many markers on such short segments could lead to some confusions when following their trajectories. A 60Hz 1440p board camera was following the horse, at a distance (𝑑), in order to build a travelling system and to simplify mathematical processing like distortion (Fig. 2). From the resulting videos, the markers trajectories were followed with a video analyzer called Kinovea (Fig. 1).

A 300mm*300mm force plate with a measuring frequency of 10000 Hz was buried under 100mm of sand for the horse to land naturally on it. For the jumping experiment, the fence was placed at the right distance for the horse to land on it. The kinematics and ground reaction forces data were synchronized by analyzing the time of the video when the foot hit the ground and match it with the time of the force recording when the signal grows. The speed of the horse was recorded during the measurements with a speedometer.

Gait analysis and compensation

These noninvasive instrumentations led to the need of method developments for processing the resulting trajectories. The first level of correction needed is a compensation of the differences of speed between the horse and the camera. To correct these differences, a reference point was chosen under the saddle. As it was located on the horse's trunk, the horizontal speed of this point was supposed to represent the horizontal speed of the horse, so it should be horizontally motionless on the camera image if the horse and the camera had the same speed. Its abscise coordinates were therefore subtracted to the abscise coordinates of all other markers (Eq. ( 1)).

In Eq. (1), 𝑍 𝑐𝑜𝑟𝑟_𝑟𝑒𝑓 (𝑡) is the new abscise of the marker after correction, 𝑍(𝑡) is the initial abscise of the marker, and 𝑍 𝑟𝑒𝑓 (𝑡) is the abscise of the point under the saddle.

After correcting the speed differences between the horse and the camera, the effect of the mean speed of the horse,v was introduced in the horizontal coordinates using Eq. ( 2). This enabled to obtain trajectories with the horse moving horizontally instead of running on the spot.

𝑍 𝑠𝑝𝑎𝑡𝑖𝑎𝑙 (𝑡) = 𝑍 𝑐𝑜𝑟𝑟_𝑟𝑒𝑓 (𝑡) + v × 𝑡 (2)
In Eq. ( 2), 𝑍 𝑐𝑜𝑟𝑟_𝑟𝑒𝑓 (𝑡) is the abscise coordinate calculated in the previous correction, v is the speed of the horse and 𝑡 is the time running. 𝑍 𝑠𝑝𝑎𝑡𝑖𝑎𝑙 (𝑡) is the resulting abscise from adding the speed of the horse to get horizontal movement of the horse in the space.

These resulting trajectories showed that the foot stance phase during the ground contact was not on a same horizontal line for all strides. This error was corrected by imposing 𝑍 𝑃 7 (𝑡) = 0 at each stance phase. After these corrections, another measurement error was observed: the distances between markers were not constant across time. These errors were due to the varying distance between the horse and the camera on the one hand and to skin artifact on the other hand. The skin artifact represents the difference of trajectory between the marker on the skin of the horse and the real movement of the bone under the soft tissues. The correction used, here, was derived from the method proposed by Cheze et al. [START_REF] Cheze | A solidification procedure to facilitate kinematic analyses based on video system data[END_REF] : a length constraint value was defined on each segment between the markers and this value had to repeat itself across time. The reference length constraint value was defined at the time𝑡 𝑟𝑒𝑓 for which the distances between markers were the closer to the lengths measured directly on the horse. This method is called a solidification procedure and mathematically, the Eq. ( 3), Eq. ( 4) and Eq. ( 5) need to be respected at all time.

||𝑷 𝒊 𝑷 𝒊+𝟏 (𝑡)|| = ||𝑷 𝒊 𝑷 𝒊+𝟏 (𝑡 𝑟𝑒𝑓 )|| (3) ||𝑷 𝒊 𝑺 𝒋 (𝑡)|| = ||𝑷 𝒊 𝑺 𝒋 (𝑡 𝑟𝑒𝑓 )|| (4) ||𝑺 𝒋 𝑷 𝒊+𝟏 (𝑡)|| = ||𝑺 𝒋 𝑷 𝒊+𝟏 (𝑡 𝑟𝑒𝑓 )|| (5)
In Eq. ( 3), Eq. ( 4) and Eq. ( 5), 𝑃𝑖 represents the principal marker at the joint 𝑖 (𝑖 = 1 to7), and 𝑆 𝑗 represents the secondary marker between 𝑃 𝑖 and 𝑃 𝑖+1 (𝑗 = 1 𝑡𝑜 4).This final correction was applied for each segment and enabled to correct both problems of varying distance between horse and camera and skin artifact. The complete procedure of correction used for our gait experiments is summarized in Fig. 3.

Geometry of bones

In literature, authors often used CT tomography [START_REF] Lerner | Modulating tibiofemoral contact force in the sheep hind limb via treadmill walking: predictions from an opensim musculoskeletal model[END_REF] , or MRI on cadavers [START_REF] Harrison | Relationship between muscle forces, joint loading and utilization of elastic strain energy in equine locomotion[END_REF] to obtain the bones geometry. In this study, an industrial optical 3D digitizer called GOM ATOS 3 was used to scan the geometry of the forelimb bones of a horse skeleton. The numerical data of bone geometry were uploaded on CATIA V5 software in order to fit to the dimensions of the horse used for kinematics experiments. The distances between the principal markers are supposed to correspond to the bones lengths. This allows to deduce a value of scale factor (f=1.2).On CATIA V5 software, the surfaces were filled and assigned with a homogenous material with the same mean density as bone (bones=1800 kg.m -3 ).

Kinematic modelling

Our forelimb skeleton model consisted of six segments: the scapula, the humerus, the radius and ulna combined, the carpal bones combined with the metacarpal bone and the sesamoid bones, the proximal phalanx (P1), and finally the distal phalanx and middle phalanx (P2-P3) combined. These choices of combinations led to a model with five joints: shoulder, elbow, wrist, metacarpophalangeal (MCP) joint, interphalangeal joint (P2-P1). These joints were modeled with a ball in socket joint at the shoulder and revolute joints at the other articulations [START_REF] Zajac | Muscle and tendon Properties models scaling and application to biomechanics and motor[END_REF] . As the kinematics is known in 2D, the ball in socket would be simplified as a revolute joint leading to a five degree-of-freedom model. To determine the joints axes of rotation, the surfaces of each articulation were best fitted with simple surfaces with CATIA V5 software (Fig. 4). For the shoulder, the center of the sphere was therefore chosen as the center of the joint and the axis of rotation, 𝑧 𝑠ℎ𝑜𝑢𝑙𝑑𝑒𝑟 was chosen normal to the plane of movement. For the hinge joints like the elbow joint, contact surfaces were best fitted with cylinders, defining the cylinder center as the frame center and the cylinder axis as rotation axis. It is supposed in that work that the both specimens of horse studies have no specific abnormal characteristic that would generate significant difference in the axis orientation of the articulation.

Musculoskeletal modelling

Muscles, tendons and ligaments were manually designed in CATIA V5 software using geometry and insertion information from the 3D Horse Anatomy of Biosphera software. The resulting surfaces of the muscles were filled in order to assign them a material with muscles density (muscles=1070 kg.m -3 ). The muscles were then scaled and attached on the skeleton enabling to deduce the coordinates of the insertion points and the inertial properties of each segment (Fig. 5).

NMS Builder was used to build an OpenSim Model [START_REF] Delp | OpenSim: opensource software to create and analyze dynamic simulations of movement[END_REF] actuated by the 23 muscle-tendons and 5 ligamentous passive elastic structures defined before. Large muscles were represented with several strides to improve their efficiency due to the variation of angle between fibers and moment arms. The force-length curves of each tendon and ligament were modeled by fitting with the experimental data found in the literature [START_REF] Swanstrom | Determination of passive mechanical properties of the superficial and deep digital flexor muscle-ligament-tendon complexes in the forelimbs of horses[END_REF][START_REF] Swanstrom | Musculoskeletal modeling and dynamic simulation of the thoroughbred equine forelimb during stance phase of the gallop[END_REF][START_REF] Swanstrom | Passive and active mechanical properties of the superficial and deep digital flexor muscles in the forelimbs of anesthetized Thoroughbred horses[END_REF] . The fiber length and pennation angles of most muscles were based on the literature [START_REF] Brown | Force-and moment-generating capacities of muscles in the distal forelimb of the horse[END_REF][START_REF] Watson | Muscle architecture of biceps brachii, triceps brachii and supraspinatus in the horse[END_REF][START_REF] Payne R C | The role of the extrinsic thoracic limb muscles in equine locomotion[END_REF] . For the muscles that were not studied in previous papers, the properties were chosen in a coherent manner according to the size, the location and the role of the muscle. The physiological crosssectional area (PCSA) of each muscle was determined from its 3D modelling on CATIA V5 and the maximum isometric force of each muscle was recalculated from its value of PCSA using a maximum isometric stress of 35 N/cm 2 (Eq. ( 6)).

F iso max = PCSA * 𝜎 𝑖𝑠𝑜 𝑚𝑎𝑥 (6) The tendons slack lengths were measured from the CAD-modeling of muscles. Wrapping surfaces (spheres or cylinders) were located at strategic locations to constraint the soft structures to get around bones and not to pass through them. The final musculoskeletal is represented in Fig. 5.

Dynamic computations

The angular variations at joints during locomotion were computed using the inverse kinematics module of OpenSim software. This tool enables to best fit the angular variations of joints with the coordinates of each markers. Then, the inverse dynamics tool of OpenSim software was used to deduce the moments at joints taking into account the ground reaction force, the mechanical inertias and the masses of the musculoskeletal model. The forces in the muscles of the model and their activations were computed using the Static Optimization tool of OpenSim and the joint reactions were then computed.

Adjustments of the musculoskeletal model according first dynamic computations

Generally, the forces generated by muscles parameters are not high enough to reach the given kinematics and moments reserves would be added by OpenSim to satisfy the fundamental equations of the Dynamics. These reserves would affect joint reactions loads calculations and should be as small as possible. In this work, some strategies were used to reduce reserves values. First, large muscles were modelled with at least three strides. The joint presenting the highest reserves was then identified and blocked to better manage the complexity of kinematics. Then, the active muscles at each articulation were identified and compared to the activations recomputed by OpenSim. The activation is directly linked to the tendon slack length: if the length value is too small or too big, the muscle might not activate at all. The tendon lengths were optimized on these muscles and their impact on the joint reserve was investigated. Then, the maximal isometric forces of muscles were increased for the muscles affecting the joint until the reserves were maximally reduced. Fig. 6 summarizes the different methods for adjustment of the musculoskeletal model.

Results

Kinematics results

The horse trotted at a mean speed of 4±0.1 m.s -1 and at jumping, the speed of the body was about 5 m.s - 1 . The trajectories were corrected according to Fig. 3and the solidification procedure resulting trajectories are shown in Fig. 7. The inverse kinematics tool of OpenSim enabled to determine the angular variations at each joint, which are represented in Fig. 8. At rest, the shoulder angle is opened of 125 deg, and at trotting it varies from -3.8% to +15.6% around this value. The elbow is initially opened of 150 deg, and it closes up to -37.7% and opens up to +6.5%. The initial position of the wrist is 175 deg and across trotting it goes from -39.1% to +8.6% of this value. At rest, the MCP joint is opened with 154 deg, and at trotting it closes only to -1% but opens up to +54.9%. Finally, the P2-P1 angle has an initial opening of 172 deg, and closes up to -0.8% but opens up to +28.2%.

At jumping, the angular variations are globally wider. At the shoulder joint, the angle varies from -13% to +7.6%, at elbow joint it varies from -53% to +6.4% and at wrist joint it goes from -57.6% to +9.3%. The MCP joint closes up to -12.7% and opens up to +48.3% and finally, the P2-P1 angle varies around its rest position from 0.87% to 28.8%.

Ground reaction forces results

The measured ground reaction forces in the three directions at trotting and jumping are given in Fig. 9. The maximal vertical forces at trotting and jumping on the sand are respectively: 9.19 N/kg and 11.69 N/kg. It can be observed that the contact force at jumping is about 27% higher and also that the contact time is shorter.

3.3Results of dynamic simulations: reserves reductions

With the initial degree-of-freedom and muscles configurations, joints showed high reserves at trotting, especially for shoulder and MCP joints (Fig. 10.a). The MCP rotation was blocked at its initial position (154 deg) because it presented the higher reserve. Before validating the reserves reduction with the rotation blocking method, the kinematics were analyzed to verify that the blockage of this rotation did not affect the kinematics of other joints. Very few differences were observed, the worst being at the MCP marker with 0.037 m, for a horse of 1.70 m high, representing therefore only 2.2% of its height. After modifying the kinematics, the muscles that should be active at each joint were identified and their parameters were changed in order to reduce the reserves. The resulted reserves values for trot are given in Fig. 10.b and Table 1 and the muscular parameters changes are summarized in Table 2. The reserves were reduced to almost zero, meaning that the final model dynamic resolution can handle the imposed ground reaction forces and movement without any artificial torque addition.

Concerning the reserves at jumping, they were much higher and the trotting muscular parameters were not sufficiently high to reduce the reserves at jumping (Fig. 10.d). The parameters were therefore modified (Table 3) and the values of reserves in the jumping study were reduced at least from 66% (Fig 10 .e and Table 1). When running the trotting simulation with jumping muscular parameters, the resulting reserves were still very low (Fig. 10.c), which validated the use of these muscular parameters for trotting simulation too. Fig. 11 compares the computation of joint reactions forces at trotting with trotting and jumping muscular parameters. These values are very similar, especially for shoulder, MCP and P2-P1 joints.

Results of dynamic simulations: joint loadings

The norms of the joint reaction forces computed by OpenSim for the trot simulation are given in Table 4 and Fig. 12.a. The highest maximal contact force is at the wrist joint with 50.4 N/kg, followed by the elbow joint at 39.2 N/kg and the MCP joint at 34.9 N/kg. The joint reaction force at the shoulder is the lowest with 21.7 N/kg, close to the P2-P1 joint reaching 28.2 N/kg. At jumping (Fig. 10.b), the values of joint reaction forces were higher with 47.5 N/kg at the shoulder, 74.2 N/kg at the elbow, 78.5 N/kg at the wrist, 58.9 N/kg at the MCP and 58.6 N/kg at the P2-P1 joint. The results of Table 4 indicate that the vertical joint loading increased a lot from trotting to jumping with at least 45.2% of increase for the P2-P1 joint and more for the others, whereas the ground reaction force increased of only 27% from 9.19 N/kg to 11.69 N/kg. The horizontal component of the joint reactions did not show a similar evolution across joints between trotting and jumping. These differences of increase percentages for the vertical component and of evolution for the horizontal component are linked to the high differences of kinematics, speeds, and angular evolutions of joints between trotting and jumping. The norms and directions of the computed forces are represented in (Fig. 13) for both trotting and jumping.

Discussion

The computed results for trotting are compared to literature in order to check our model. Our measurements of joint angles are very close to previous studies [START_REF] Dutto | Joint work and power for both the forelimb and hindlimb during trotting in the horse[END_REF] and this enables to validate the correction methods applied to the kinematics data. Peak shoulder and elbow joints angles measured for trotting were 144.5 deg and 159.7 deg respectively, which are very similar to the values reported by Dutto et al. [START_REF] Dutto | Joint work and power for both the forelimb and hindlimb during trotting in the horse[END_REF] (138 ±5 deg and 150±10 deg). For the wrist and MCP joints, the measured values are 190.9 deg and 238.5 deg respectively and those are also very close to the values given by Dutto et al. [START_REF] Dutto | Joint work and power for both the forelimb and hindlimb during trotting in the horse[END_REF] (186 ±9 deg and 231±4 deg) and also by Harrison et al. [START_REF] Harrison | Relationship between muscle forces, joint loading and utilization of elastic strain energy in equine locomotion[END_REF] (182 ±2 deg and 241±4 deg). Finally, for the phalangeal joint, the measured value was 220.5 deg, which shows high similarity with Dutto et al. [START_REF] Dutto | Joint work and power for both the forelimb and hindlimb during trotting in the horse[END_REF] who reported a value of 220±3 deg. At jumping, the joint angular variations intervals were larger than at trotting, due to wider movements to reach the jumping kinematics. These intervals are approximatively the same for shoulder and P2-P1 joints. For the elbow, the wrist and the MCP joints, the articulations close and open more at jumping than at trotting.

The joint loading values at trot are quite different from the values found by Harrison et al. [START_REF] Harrison | Relationship between muscle forces, joint loading and utilization of elastic strain energy in equine locomotion[END_REF] for the comparable values at MCP (40.6 N/kg for Harrison et al. [START_REF] Harrison | Relationship between muscle forces, joint loading and utilization of elastic strain energy in equine locomotion[END_REF] , 34.9 N/kg for us) and wrist (28 N/kg for Harrison et al. [START_REF] Harrison | Relationship between muscle forces, joint loading and utilization of elastic strain energy in equine locomotion[END_REF] , 50.4 N/kg for us) joints (Fig 12 .a). This can be explained by a higher speed (4 m.s -1 for us against 1.4 m.s -1 for Harrison), because the increase of speed causes higher ground reaction force to keep the position against gravity [START_REF] Dutto | Ground reaction forces in horses trotting up an incline and on the level over a range of speeds[END_REF] and this leads to higher moments at MCP and wrist [START_REF] Dutto | Joint work and power for both the forelimb and hindlimb during trotting in the horse[END_REF] causing higher joint loadings. This can also be explained by the difference of ground material: sand in our study instead of rubber matting or turf track for Harrison et al. [START_REF] Harrison | Relationship between muscle forces, joint loading and utilization of elastic strain energy in equine locomotion[END_REF] . The modeling simplifications and the reduction of reserves also play a major role on the joint reactions.

Another interesting aspect is the significant link between angular opening and joint loading. For the elbow and the wrist joints which presented the largest angular openings with 84.3 deg for elbow and 86.1 deg for wrist at trot, it was observed that they also presented the highest joint loadings of the limb with 39.2 N/kg for elbow and 50.4 N/kg for wrist at trot. This was also observable at jumping. This study presented some limitations in terms of measurements and modelling methods. Our kinematics measurement methods were fast and simple to settle and non-invasive at all but it needed important corrections after all. To validate the measurement method, it could be interesting to compare the resulting trajectories with trajectories from Vicon or other techniques measurements. The kinematics errors lead to large nonphysical forces. In OpenSim a Residual Reduction Algorithm function enables to minimize the effects of modeling and marker data processing errors using a numerical optimization independent from error sources brought to the fore in the experiments. In this paper, the compensation methods were based on observed physical sources like differences of speeds or skin artifact. The application of the proposed compensation methods to the kinematic measurements reduced the best fit residues of OpenSim kinematics module without markers weighting, from 0.0168 to 0.0088 representing 48% of reduction. To test the effectiveness of this method, it has been compared to the results given by OpenSim's inverse kinematics module where the markers were weighted according to their relevance. This module computes a best fit residue of 0.0093. The proposed method was considered efficient and retained for kinematic compensation for this specific kinematic measurement.

Conclusion

The overall goal of this study was to describe a method to determine the joint contact loading in the horse forelimb at high jerk dynamics like jumping. To our knowledge, this study is the first to estimate joint reaction forces in the forelimb of a horse at jumping. Non-invasive methods were used for the measurements of kinematics and ground reaction forces and this enabled to keep the horse in its usual environment and to optimize the repeatability of the results. The kinematics needed compensations because of the simplicity of our measurements. A musculoskeletal model was built with mechanical methods: the bones were scanned with the GOM ATOS 3 to retrieve their geometry on CATIA V5, a CAD software. The determination of the centers and directions of joints with CATIA V5 ensures reliability and accuracy. The 3D modelling of muscles enabled to avoid dissecting a horse cadaver. This modelling enabled to deduce the accurate positions of the insertion points and the inertial parameters of segments. This methodology can be easily reused for other experimental campaigns on other horse specimens. The dynamics calculations were first run at trotting to validate the model and then at jumping. As part of bio-inspiration, these results will contribute to design the bio-inspired joints.

Fig. 1 Right forelimb equipped with the markers followed by Kinovea software. The green markers are the principal markers and the blue ones are the secondary markers. The secondary markers were placed between the principal markers but unaligned with them. Fig. 2 Top view of the running experiment. The horse moved along a virtual line, followed by the camera at a distance d. It passes over a force plate buried in the sand. At jump, a fence was placed before the force plate. The distance was readjusted after several passages. 2) and the jumping parameters (Table 3).

Table 4.

Comparison of values at trotting and jumping for the net joint moment and the joint reaction forces. The increase between trot and jumping is given in %.

List of figures

Fig. 1 Right forelimb equipped with the markers followed by Kinovea software. Fig. 11 Comparison of the vertical joint loading results for the trotting parameters (table 3) and the jumping parameters (table 4).

Fig. 3

 3 Fig. 3 Procedure of correction of the trajectories. 𝑃 𝑖 represents the principal marker at the joint 𝑖, and 𝑆 𝑖 represents the secondary marker between 𝑃 𝑖 and 𝑃 𝑖+1

Fig. 4

 4 Fig. 4 Methodology to find the joint local frames. Examples of the shoulder and the elbow.

Fig. 5

 5 Fig. 5 Reconstruction of the entire forelimb on CATIA V5 and construction of the OpenSim model from the Biosphera Software (without the wrapping surfaces).

Fig. 6

 6 Fig. 6 Solutions for adjusting the model.

Fig. 7

 7 Fig.7 Trajectories of the markers before and after applying the solidification procedure.

Fig. 9

 9 Fig.9 Ground reaction forces measured at trot (a) and at jumping a fence of 1m high (b). The black dashed line represents the limit between swing and stance phases.

Fig. 10

 10 Fig. 10 Reserves at trot: (a) Before adjustments. (b) After adjustments. (c) After applying the jumping model adjustments. Reserves at jump. (d) Before adjustments with the final configuration of trot. (e)After adjustments. The black dashed line represents the limit between swing and stance phases.

Fig. 11

 11 Fig.11Comparison of the vertical joint loading results for the trotting parameters (Table2) and the jumping parameters (Table3). (a) Shoulder vertical reaction force. (b) Elbow vertical reaction force. (c) Wrist vertical reaction force. (d) MCP vertical reaction force. (e) P2-P1 vertical reaction force.

  Fig.11Comparison of the vertical joint loading results for the trotting parameters (Table2) and the jumping parameters (Table3). (a) Shoulder vertical reaction force. (b) Elbow vertical reaction force. (c) Wrist vertical reaction force. (d) MCP vertical reaction force. (e) P2-P1 vertical reaction force.

Fig. 12

 12 Fig. 12 Results of joint loading for trotting (a) and jumping (b). For trotting, the results are compared to Harrison (2010) values. The black dashed line represents the passage from swing to stance phase.

Fig. 13

 13 Fig. 13 Representation of the maximal joint reaction forces in the right forelimb of a horse (a) at trotting and (b) at jumping a 1m fence.

Fig. 2

 2 Fig. 2 Top view of the running experiment.

Fig. 3

 3 Fig. 3 Procedure of correction of the trajectories.

Fig. 4

 4 Fig. 4 Methodology to find the joint local frames. Examples of the shoulder and the elbow.

Fig. 5

 5 Fig. 5 Reconstruction of the entire forelimb on CATIA V5 and construction of the OpenSim model from the Biosphera Software (without the wrapping surfaces).

Fig. 6

 6 Fig.6 Solutions for adjusting the model.

Fig. 7

 7 Fig.7 Trajectories of the markers before and after applying the solidification procedure.

Fig. 8

 8 Fig. 8 Joints angular variations across time.

Fig. 9

 9 Fig. 9 Ground reaction forces measured at trot.

Fig. 10

 10 Fig. 10 Reserves at trotting and jumping.

Fig. 12

 12 Fig.12 Results of joint loading for trotting and jumping.

Fig. 13

 13 Fig.13 Representation of the joint reaction forces in the right forelimb of a horse at trotting and at jumping a 1m fence.

Acknowledgement

We thank Arroyave Tobon Santiago, Thouveny Thomas and Perrotey Arthur for their precious help on this work. We also thank Avisse Tristan and Demassieux Jacques for the help on the experiments. We thank the GIR Laboratory of Airbus Helicopters members Erik Faravel and Hamiache Romain for their help on ground reaction forces measurements. Airbus Helicopters/Aix-Marseille Université Scientific Chair on Bio-Inspired Mechanical Design funded this work. * The reference data can be found online at: https://simtk.org/docman/?group_id=1728

Maximal reserves values at trot and jumping for the initial and final models. The decrease of reserves between the initial and the final models are given in %.