Since its first measurement in 1679, the usefulness of the location of whole body centre of mass (COM) data has progressed from having largely theoretical value into being an instrument with several diagnostic and applied scientific uses. This thesis describes first the biomechanical and measurement theory foundation of COM research and then details the historical development of methods to measure COM location and the various applied uses of this variable. Original research data presented in this thesis then go on to provide the first direct measurements of COM movement in walking humans. A second study quantifies the accuracy of the most commonly used current technique to quantify COM location (the kinematic segmental method) by determining the limits of agreement between it and a direct measurement method (the reaction-board), in lying and running subjects. In the latter studies a novel reaction-board measurement method is developed making use of life-sized projections of subjects in various stride positions and used to place runners into recumbent static running positions. These data demonstrate that reaction-board and segmental methods report COM locations with a mean difference of 1.6cm and agree to within limits of 6.0cm for the location of COM in recumbent individuals. The final study described in this thesis compares single COM measurements made using two kinematic segmental methods (models) to a direct suspension technique of measuring COM location. The suspension technique used is adapted from the original method of determining COM location upon which kinematic segmental methods derive their origin. The data show that both cadaver-derived kinematic models of COM, and kinematic models derived from live human data, differ from a direct COM suspension method, and that cadaver based estimates display greater accuracy (agreement with the direct suspension method). This study also uniquely provides information on the effect of whole body mass, body fat or body water on the accuracy of segmental models in male subjects.

The center of gravity (CG) in the golf club head is crucial to the launch angle, launch velocity and spin of golf balls after the golf impact. The CG locations in this study refer to the depth of CG, height of CG and distance of CG, which were determined by the change of shell thickness of a golf club head. By means of the finite element method (FEM), the researcher analyzed the impact process for golf balls and golf head clubs. Then he discussed the relationship between club heads and ball behaviors after impact. He also simulated the trajectory by the numerical method on the basis of the impact results of the golf ball. To sum up, a longer carry was generalized by deeper CG, lower CG and higher loft angle for a golfer with a slow club head speed. A shallower CG, higher CG and lower loft on a club head for a golfer with a fast club head speed were also verified in this study. Finally, a series of impacts produced by FEM and numerical method were generalized. Specifically, the method can be used to predict the flying distance of golf ball. It also can help predict the proper CG locations for golf club head designing.

My diploma thesis deals with measuring the center of gravity (CG) the motorcycle. The first part is outlined with legislation and the types of motorcycle division. I mention the theoretical types of measuring the CG the motocycle there too. These methods are applied to the issue of motor vehicles. The chosen one way of measuring the center of gravity which is used for practical measurements of gravity the motocycle. The practical part included the weighing of the different types of motorcycles with a different occupancy. These values are then processed and the resulting CG are calculated for each motorcycle. The values of CG were compared by experiment with the program for the analysis of road accidents and reconnoitred the measured results with this program results. In the last chapter is the evaluation of individual CG motorcycle and the influence of changes in occupancy due to a motorcycle.

This thesis sets out to derive an analytical model for a center of gravity (CG) measuring platform and examines its validity through experimental testing and Finite Element Modeling. The method uses a two-stage platform tilting process to first locate the planar CG coordinates and then find the third CG coordinate normal to the platform. An uncertainty model of the measuring platform was also developed, both CG and uncertainty models were implemented in the form of a MATLAB code. A load cell sizing task was also added to the code to assist the Integration Engineers at Jet Propulsion Laboratory in selecting load cells to design their own version of the CG Platform. The constructed CG Platform for this project used an array of six strain gauges, four C2A-06-062LT-120 Tee Rosettes and two C2A-06-031WW-120 Stacked Rosettes. They were bonded onto the legs of three truss shaped bipods. Results from the Platform Tilting Tests could not be used to validate the CG model as the measured CG and weight values found from the experimental tests contained a considerable amount of error. The errors in the Platform Tilting Tests are believed to stem from the initial errors observed during the bipod rod and strain gauge calibration tests. As an alternative, an FE model of the CG measuring platform was created as another means of validation. The math model of the CG measuring platform was successfully validated by showing that there was less than a 0.01% different between the bipod loads predicted from the MATLAB code and the FE model. Using the FEM generated loads as inputs into the CG code to calculate a CG matched the initial point mass or CG created in the FE model within a 0.01% difference. To validate the CG model even further, another test should be performed using a CG Platform prototype instrumented with load cells to generate new experimental data and compare them with the results from the FE model.

The main goal of this study is the use of polynomial chaos expansion (PCE) to analyze the uncertainty in calculating the lateral and longitudinal center of gravity for a vehicle from static load cell measurements. A secondary goal is to use experimental testing as a source of uncertainty and as a method to confirm the results from the PCE simulation. While PCE has often been used as an alternative to Monte Carlo, PCE models have rarely been based on experimental data. The 8-post test rig at the Virginia Institute for Performance Engineering and Research facility at Virginia International Raceway is the experimental test bed used to implement the PCE model. Experimental tests are conducted to define the true distribution for the load measurement systems' uncertainty. A method that does not require a new uncertainty distribution experiment for multiple tests with different goals is presented. Moved mass tests confirm the uncertainty analysis using portable scales that provide accurate results. The polynomial chaos model used to find the uncertainty in the center of gravity calculation is derived. Karhunen-Loeve expansions, similar to Fourier series, are used to define the uncertainties to allow for the polynomial chaos expansion. PCE models are typically computed via the collocation method or the Galerkin method. The Galerkin method is chosen as the PCE method in order to formulate a more accurate analytical result. The derivation systematically increases from one uncertain load cell to all four uncertain load cells noting the differences and increased complexity as the uncertainty dimensions increase. For each derivation the PCE model is shown and the solution to the simulation is given. Results are presented comparing the polynomial chaos simulation to the Monte Carlo simulation and to the accurate scales. It is shown that the PCE simulations closely match the Monte Carlo simulations. / Master of Science

The thesis deals with the issue of measuring the height of the center of gravity of SUV´s. The first part of thesis is devoted to the issue of center of gravity and the influence of the height of the center of gravity on driving stability. Furthermore, individual methods of measuring the height of the center of gravity in passenger cars are discussed. The analytic part of the thesis is devoted to experimental measurement of the height of the center of gravity of selected SUV´s at different vehicle load, by the method of tilting the vehicle on the axle. The results of the measurements showed that the height of the center of gravity for vehicles with a capacity for five people is in the range from 606 to 697 mm. The lowest value belongs to the vehicle Toyota RAV4 Hybrid, when loaded by the driver. The highest value was found for the vehicle Kia Sportage, when loaded by three passengers. The Landover Defender, which is vehicle, that has a capacity for nine people, was found to have a height of center of gravity ranging from 705 to 874 mm. The lowest value was found when loaded by the driver, the highest value when loaded by nine passengers. Only for the Nissan Qashqai was the growing dependence between the load increase and the height position of the vehicle's center of gravity confirmed. A similar trend was found for the Toyota RAV4 Hybrid, Jeep Compass and Landover Defender. The determined values can be used in the analysis of traffic accidents of SUV’s.

The aim of this thesis is to develop a methodology for obtaining mass properties of a vehicle using specific test rig. Investigated mass properties are the mass, location of center of gravity and the inertia tensor. Accurate measurement of mass properties of vehicles is crucial for vehicle dynamics research. The test rig consists of a frame on which the vehicle is fixed and which is suspended from the ceiling of the laboratory using steel cables. Mass and location of center of gravity are measured using the data from the test rig in equilibrium position and basic static equations. Inertia tensor is measured using the data from dynamical response of the system. For this purpose an identification routine which employs prediction error method is developed using the built&ndash / in functions from the System Identification Toolbox of MATLAB&reg / . The experiment was also simulated using Simmechanics Toolbox of MATLAB&reg / . Identification code is verified using the results of the experiment simulations for various cases.

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As a part of Linköping University’s master program course curriculum, current thesis is performed at Tools and fixtures department (MPCT) of Scania, Oskarshamn. The aim of this master thesis project is to develop a complete construction of the station in CAD which calculates the weight and center of gravity of all the different cabs produced in Scania CV AB. To accomplish this project a generic product development process described in product development textbook by Ulrich and Eppinger (2012), fifth edition and The mechanical design by David G Ullman, fourth edition were extensively used. The whole function from a black box is decomposed into several sub functions and different solutions were identified for these individual functions. By using morphology matrix and proper combinations from these solutions five different concepts were developed and presented to Scania CV AB. The team along with technical design experts in the MPCT department evaluated all the concepts and one concept was chosen for further development. Protecting the weighing scales during loading of cab from forklift onto the station and safety for the cab during tilting are the two main challenges faced during detail design phase. We were able to achieve these operations by incorporating a lifting table into the station design. Thanks to the custom made multi-tasking lift table which is manufactured and supplied by HYMO. With the help of sensors, speed of the lifting table can be controlled with two operating speeds-High & Low. Lifting table moves in its lowest speed whenever it approaches the weighing scales. Incorporation of Jacob safety into the lifting table allows the table to always operate in low speed when the lift link is in action. These sensors ensure high safety for the cab and weighing scales. Apart from this, an emergency stop has been provided to stop the entire operation in case of emergencies. In this proposed design, the center of gravity values will be determined in two stages and the weight readings are recorded in computer during these stages. For determining the longitudinal and transverse distances of CG, weight readings from all the weighing scales is essential once the cab is loaded on the station from the forklift. For determining the vertical distance of CG, two weight readings and measured tilt angle is required. A calculation module will allow the user to enter these values and obtain the result in no time. This developed 3-D CAD model with 2-D drawings are presented to Scania and the obtained results of this work fulfilled the set of requirements set for this master thesis.

The thesis is focused on aircraft flight level control in case when the location of center of gravity changes during flight. The theoretical part of the thesis describes basics of aerodynamics, which are necessary to understand airplane's behavior and its control theory. Basics of state theory and stability of systems, as it is used for design of linear model. This part also mentions mathematical equations of nonlinear model of business jet and discusses conventional and adaptive methods used to design autopilot parameters. Several autopilots were designed in practical part of the thesis. The most important part is the logic used to determine location of center of gravity of the airplane. The models use nonlinear model of an airplane that better represents the real environment and conditions.