16.07 Dynamics Fall 2004 Lecture d16-2D Rigid Body Kinematics In this lecture, we will start from the general relative motion concepts introduced in lectures Dll and D12 and then apply them to describe the motion of 2D rigid bodies. We will think of a rigid body as a syster of particles in which the distance between any two particles stays constant. The term 2-dimensional implies that particles move in parallel planes. This includes, for instance, a planar body moving within its plane but also a general 3d body rotating about a fixed axis. Motion Description Even though a rigid body is composed of an infinite number of particles, the motion of these particles is constrained to be such that the body remains a rigid body during the motion. In particular, the only degrees of freedom of a 2D rigid body are translation and rotation Parallel axes Consider a 2D rigid body which is rotating about point O, and, simultaneously, point O is moving relative to a fixed reference frame o P TOr In order to determine the motion of a point P in the body, we consider a set of axes r'y, parallel to ry at O T ror+ ao+(ap)oJ. Peraire 16.07 Dynamics Fall 2004 Version 1.2 Lecture D16 - 2D Rigid Body Kinematics In this lecture, we will start from the general relative motion concepts introduced in lectures D11 and D12, and then apply them to describe the motion of 2D rigid bodies. We will think of a rigid body as a system of particles in which the distance between any two particles stays constant. The term 2-dimensional implies that particles move in parallel planes. This includes, for instance, a planar body moving within its plane, but also a general 3D body rotating about a fixed axis. Motion Description Even though a rigid body is composed of an infinite number of particles, the motion of these particles is constrained to be such that the body remains a rigid body during the motion. In particular, the only degrees of freedom of a 2D rigid body are translation and rotation. Parallel Axes Consider a 2D rigid body which is rotating about point O′ , and, simultaneously, point O′ is moving relative to a fixed reference frame O. In order to determine the motion of a point P in the body, we consider a set of axes x ′ y ′ , parallel to xy, with origin at O′ , and write, rP = rO′ + r ′ P (1) vP = vO′ + (vP )O′ (2) aP = aO′ + (aP )O′ . (3) 1