The motion of robots and the motion of aerospace vehicles are two examples. Rigid body structures and dynamics can get complicated most rigid body motion is three-dimensional. Rigid motion can be translational, rotational, or both. The Newton-Euler equation is utilized to describe rigid body motion. Newtonian approach - Six scalar quantities are used to describe the motion of the rigid body in space.It also introduces the concepts of virtual displacements, generalized forces, and generalized coordinates. Lagrange’s equation-based approach - Scalar quantities, such as potential energy and kinetic energy, are used.It is necessary to understand the mechanics of rigid bodies when designing systems with translational as well as rotational motion. The concept of no internal degrees of freedom and constant distance between the particles helps in assessing the rigid body dynamics in the Newtonian approach. There are no internal degrees of freedom for the particles in a rigid body. The rigid body particles are not affected by stress, strain, or vibrations. Rigid bodies retain their shape irrespective of the force applied to them. The distance between the particles in a rigid body remains unchanged even under the application of force. The mass particles are held inside the rigid body by massless bonds of length. Rigid Body DynamicsĪ rigid body can be defined as a body consisting of many mass particles. In engineering mechanics, the Newton-Euler equation is used to analyze rigid body dynamics. The two equations mentioned above for rigid body form the Newton-Euler equation. The Euler equation relates moments with the centroidal mass moment of inertia and angular acceleration of the rigid body and is of great importance in rotational rigid body dynamics. When applying Newton's second law to rigid bodies, usually the acceleration of the center of mass is considered for translational motion. According to this law, the net force acting on a body is equal to the product of mass and acceleration. The fundamental law that correlates force and motion is Newton’s second law. The Newton-Euler equation governs the motion of humanoid robotsįorces and motion are related. Newton-Euler equations give the relationship between the motion of the center of gravity of a rigid body with the sum of forces and moments acting on the rigid body. Newton-Euler equations are the fundamental equations used in classical mechanics to describe the combined rotational and translational dynamics of a rigid body.
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