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Stewart Platform
Published in Rajesh Singh, Anita Gehlot, Intelligent Circuits and Systems, 2021
Degree of freedom refers to the extent to which a mechanical system or a solid inflexible body can move in a three-dimensional space. For example, the rigid train cars connected by the engine in series have only one degree of freedom because the movements of the cars behind the engines are restricted to the shape of the railway tracks.
Theory of Vibrations
Published in Swami Saran, Dynamics of Soils and Their Engineering Applications, 2021
In the preceding sections, vibrations of systems having single degree of freedom have been discussed. In many engineering problems, one may come across the systems which may have more than one degree of freedom. Two degrees freedom cases arise when the foundation of the system is yielding thus adding another degree of freedom or a spring mass system is attached to the main system to reduce its vibrations. In systems when there are a number of masses connected with each other, even if each mass is constrained to have one degree of freedom, the system as a whole has as many degrees of freedom as there are masses. Such an idealisation is done for carrying out dynamic analysis of multistoreyed buildings.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
The position and orientation of a body can be described by their distance from a perpendicular set of fixed axes called a coordinate system. The minimum number of independent or generalized coordinates needed to completely describe the position and orientation of a system of rigid bodies is equal to the number of degrees of freedom for the system. The number of degrees of freedom equals the number of nonindependent coordinates used to describe the position and orientation of each body of the system minus the number of constraints equations governing the system’s motion. Therefore, the maximum number of independent coordinates needed to completely describe the position and orientation of a rigid body in space is six. Three independent equations are required to locate and describe the rigid body in translation with respect to time; the other three independent equations of motion are required to define its orientation and rotation in space with respect to time.
Roll motion mitigation of a barge-type floating wind turbine under random excitation using a tuned liquid column damper
Published in Journal of the Chinese Institute of Engineers, 2023
To simplify the numerical model of the floating wind turbine system, the barge and wind turbine are modeled as a single rigid body. In general, the rigid body has six degrees of freedom. For offshore or ship engineering, they are surge, sway, heave, roll, pitch, and yaw, respectively. The roll or pitch motion is typically the largest amplitude of all the six degrees of freedom of a floating system subjected to waves. When a TLCD is tuned to the roll or pitch natural frequency of the floating system to minimize this specific motion, it has almost no effect on suppressing the other motions. Thus, only roll motion is focused in this study. In addition, the barge with the aid of TLCD must have adequate stability in its unmoored state. Thus, the mooring system is not considered, and its effect on the dynamic behavior of the barge is negligible. The problem becomes two-dimensional, as shown in Figure 1.
A micropolar continuum model of diffusion creep
Published in Philosophical Magazine, 2021
At high temperatures, solid polycrystalline materials can deform by diffusion creep, where defects within the crystalline lattice move by diffusion. At scales much larger than the grain scale the material behaves as if it were a Newtonian viscous fluid, with an effective shear viscosity which depends on the grain size [1–4]. At the microscale individual grains can be considered as rigid bodies, which interact by the plating out or removal of material at grain boundaries, leading to a macroscale strain. Rigid bodies have both translational (velocity) and rotational (angular velocity) degrees of freedom to describe their motion. However, when a material is treated as a Newtonian viscous fluid at the macroscale, the microscale rotational degrees of freedom are lost, as the classical Cauchy continuum is based on point particles with only translational degrees of freedom.
Application of SPH to Single and Multiphase Geophysical, Biophysical and Industrial Fluid Flows
Published in International Journal of Computational Fluid Dynamics, 2021
Paul W. Cleary, Simon M. Harrison, Matt D. Sinnott, Gerald G. Pereira, Mahesh Prakash, Raymond C. Z. Cohen, Murray Rudman, Nick Stokes
Object motion and deformation is easily included in this framework: If an object represents a rigid structure that is able to move, then either kinematic or dynamic equations can be applied for each degree of freedom.For deforming bodies, such as the surfaces of moving athletes (see Sections 4.1 and 4.2), the nodal positions and the normal vectors of the boundary particles are updated at each time-step to reflect the current shape of the object surface (such as for a human model).If a boundary is thin and able to elastically deform in response to the fluid forces applied, such as for an elastic membrane, then dynamics Equations (4) and (7) are solved but with the inclusion of linear visco-elastic forces based on the extension of the distance between boundary particles from the original ‘natural’ length. These membranes can have multiple layers, can be anisotropic and can be modified dynamically with mobile contraction and relaxation patterns (which are required for the intestinal flow in Section 5).If an object is not a membrane, then the forces on the boundary can also be passed to a coupled FEM solver to predict the deformation of the object structure.