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Engineering Mechanics
Published in P.K. Jayasree, K Balan, V Rani, Practical Civil Engineering, 2021
P.K. Jayasree, K Balan, V Rani
The parallel axis theorem is used for finding the rectangular moment of inertia about an axis different from the centroidal axis of the section. The centroidal rectangular moments of inertia, Ix¯andIy¯, are determined using Equations 4.28a and b where y and x are the distances of an elemental area dA from XX and YY axes, respectively.
Mathematics
Published in Keith L. Richards, Design Engineer's Sourcebook, 2017
The parallel axis theorem may be used to refer the moment of inertia of a rigid body about a given axis to an offset parallel axis which is not necessarily the centre of mass of the body. The theorem is also known as the Huygens–Steiner theorem. The theorem has importance when calculating the sectional properties of a complex section.
Kinetics in Angular Motion
Published in Emeric Arus, Biomechanics of Human Motion, 2017
Parallel axis theorem states the relationship between the moment of inertia about an axis through a segment’s CoM and about any other parallel axis. Ia = ICoM + M ⋅ h2, where Ia is the moment of inertia about an axis other than through the joint center, ICoM is the moment of inertia of the body about the parallel axis through its CoM, M is mass of the segment, and h is distance from the joint center to the segment center of mass (distance between the parallel axes). The M ⋅ h2 can be substituted with the m ⋅ r2 or m ⋅ d2, where m is the mass and r or d represents the distance.
Effects of different helmet-mounted devices on pilot’s neck injury under simulated ejection
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2023
Jinglong Liu, Heqing Liu, Weiping Bu, Yawei Wang, Peng Xu, Minglei Wu, Yubo Fan
Four different conditions of helmets with mounted devices were defined respectively. The Visor Up and Visor Down represented the two positions of the Visor on helmet, without Night Vision Goggle (NVG). For Visor Down, the CG of the helmet located much forward and down compared with that of Visor Up, while both of the helmets with visor had the same mass. The NVGBV denoted that the helmet with NVG locating below the Visor, while the VBNVG denoted the helmet with the Visor locating below NVG. It could be seen that when the NVG was added to the helmet, the mass of helmet was increased and the centre of gravity also moved forward extremely. The mass and the moment of inertia were added to the rigid head according to the parallel axis theorem. To compare with the above four cases, the model without a helmet (No Helmet) was also considered as control. Due to the symmetry of helmet in the X–Z plane, the Y-axis coordinate of the CG of the helmet was set to zero.
Methods of strengthening cross-laminated timber manufactured using Irish Sitka Spruce: a preliminary study
Published in Journal of Structural Integrity and Maintenance, 2023
Emily McAllister, Daniel McPolin, Jamie Graham, Grainne O’Neill
The theoretical strength and stiffness of a CLT/GRP composite panel strength can be achieved by homogenizing the composite using the Young’s modulus of the materials in each layer of the panel and transforming it into a single material using modular ratios, as previously used by O’Ceallaigh (2018). From this, the parallel axis theorem can then be used to calculate the moment of inertia for the cross section of the panel. Thus, bending stresses on positions of the panel can simply be calculated for various loads. However, it is important to note that at this point this theoretical modelling is only suitable for the calculation of strength characteristics up to the moment of serviceability failure of the outermost component in the CLT panel. Post elastic behaviour, most notably in the outmost compression zone is not yet considered in the model. This theoretical modelling technique can also be used to calculate the same characteristics when the panel has an existing strengthening layer.
Quadrotor Attitude Dynamics Identification Based on Nonlinear Autoregressive Neural Network with Exogenous Inputs
Published in Applied Artificial Intelligence, 2021
Alexander Avdeev, Khaled Assaleh, Mohammad A. Jaradat
The most common practice is to find a relationship between input commands and angular rates, as done in Bresciani (2008). Thus, the output of a model should be the rate of change of the angles rather than the angles themselves. Dynamics of the fourth degree of freedom (DOF), namely z-axis acceleration, present little interest, because they correspond to a first-order linear system and are decoupled from the other DOFs. Identifying angle rates separately from z acceleration has one more advantage. Quadrotors are inherently unstable, so flying them without any control loops is impossible. However, if the goal is to identify only the angular dynamics, a quadrotor can be placed on a test stand with a spherical joint. Such a joint eliminates three DOFs, namely translational motion in all three axes. Nevertheless, if certain conditions are met, the motion in the remaining three DOFs remains unaffected. Obviously, the first condition is friction is kept as small as possible. The second one is that axis of rotation of the joint must be placed as close to the CG of the quadrotor as possible. Failing to meet this condition results in identifying a completely different system, because the moment of inertia changes in accordance with the parallel axis theorem. The red circle in Figure 3 shows the joint and its connection to the quadrotor.