# MULTIBODY SIMULATION OF THE HUMAN BODY MOTION IN SPORTS

### Abstract

This paper presents a complete methodology for the study and analysis of the human body motion. The final objective is to simulate in a computer the behaviour of the human body when performing a physical activity, so as to obtain from the simulation some biomechanical results like velocities, accelerations, internal and external forces.. . that cannot be measured directly and that are of interest in order to study or improve the activity. In a general way it can be said that the methodology consists of recording the actual motion, and then feeding this motion into a mechanical model of the human body, so as to make it move like the original human body. The method is implemented as a software tool, that has been applied mainly to sport activities, although it is of general purpose and can be applied to other fields of biomechanics. The methodology begins with the capture of the actual motion of the human body during the activity to be simulated. This capture is carried out by using a number of fixed video cameras, covering the entire exercise area. Normally two cameras are used, but very complex exercises can require three. Once the cameras are positioned, they are calibrated using . an appropriate three dimensional structure of known size. The recording process is done at a standard rate of 25 images per second, with all the cameras synchronized so as to obtain the frames at the same time value. The recorded video motions are then digitized using a manual process. In this process every frame is presented on the computer screen where the user has to identify with a mouse a set of key points of the human body, that will be used later to define the motion. Automatic digitization methods are not normally used in sports, because of the difficulty of putting optical sensitive marks in the athlete's body during competitions. After this digitization process, the 3D coordinates of the points are obtained by the well known direct linear transformation technique, resulting in the trajectories of the key points of the body. The digitization process is very error prone for several reasons: operator picking errors, small image size, pixel size ... making the trajectories unsuitable for use as Input to a multi body solver. The digitized trajectories are conditioned in a two step process. First, a filtering technique is applied to every trajectory, so as to smooth it by eliminating high frequency components originated by the motion capture operations. Usually a Butterworth of third order is used, with a two pass technique. The second step of data conditioning is carried out during the construction of the mechanical model, as described later. In the presented methodology the human body is considered as a multi body system, and a mechanical model is created for it by using the natural coordinates concept where the position and orientation of the joints and elements of the mechanism are defined by the artesian coordinates of a set of points and unit vectors located at the joints. This approach has proven to be very efficient for multi body analysis. Using this formalism, different models have been created, depending on the particular application. Most of these models correspond to the whole human body, but it also possible to create models for parts of it, like one arm or two leg. The general purpose character of the presented method allows to deal with all these types of models in the same way. A typical model of the whole body has 23 points, 18 vectors and 33 parts, with 28 revolute joints and 3 universal joints This gives 34 degrees of freedom, plus the 6 ones corresponding to the rigid body motion. The mechanical model of the human body requires the definition of the size of the different parts that compose it and the orientation of the joints with respect to the parts where they are located. Using natural coordinates this is done by specifying the coordinates of the points and the components of the vectors with respect to the local reference frames of the different parts This information is not known in advance, and the solution used in the presented method consists in obtaining it from the trajectories of the key points recorded form the real motion. Really two problems exist: first, some points of the mechanical model do not exist among the key points whose trajectory has been recorded, and particularly none of the vectors exist. Second, the distances between the recorded points change during motion because of the recording errors; the experience shows that in some cases this variation can reach up to 10%. To solve both problems the idea is to define the position of a point or unit vector of the model as a function of the positions of other points or vectors whose position is known. This process is applied recursively until arriving at a point whose position has been recorded. The definition process requires the use of complex algebraic expressions and for this purpose a symbolic manipulator js used. It has a C-Iike syntax, and allowsâ€˘ operations with mixed scalar and vectorial entities including dot and vector products, logical and relational operations, loop statements, mathematical functions... The manipulator also allows to solve the second problem on the error of the recorded data : it includes specific functions to evaluate the average value of a magnitude over a period of time. By using all these functionalities it is possible to uniquely define the coordinates of all the points and vectors of the mechanical model in their local reference frames : in this way the size of the mechanism is completely defined in a symbolic way, starting only from the recorded trajectories. All the symbolic expressions are defined in a model file, that is compiled by the software system. The last step in the simulation of the mechanical model of the human body consists in its dynamic simulation. As the motion of the mechanism is completely defined, an inverse dynamics analysis is carried out giving as results all the forces and torques involved in the motion : joint reactions, contact forces with the ground ... Other interesting magnitudes Iike energies, angular momentum ... are obtained as well The definition of the inputs to the mechanism is done' by specifying the values of the angles at the model joints in function of time. These angular values are not recorded in the motion capture, so their value is calculated as a function of the position of the points and vectors, by using again the symbolic manipulator. The velocities and accelerations necessary for the inverse dynamics are calculated by numerical differentiation of the recorded motion, after a curve fitting with cubic splines, to assure a smooth motion. The inverse dynamics is carried out using a standard method based in the Lagrange multipliers. The software system allows to graphically represent the motion of the human body model obtained by simulation. For this purpose a geometrical model of the human body is used; it is composed by a set of polygons associated to every part of the mechanica.1 model, with appropriate size and graphical properties. It is also possible to include in the animation a representation of the forces and torques, as well as the trajectories of some points. A number of examples have been studied with the proposed methodology, in the sports domain : football head and foot shots, slam dunk in basket ball, tennis drive, jumps and races. An experimental validation of the method is also included.
Section

Keynote-Lectures

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