Kinematics 2. Simplification of a plane motion A plane motion of a rigid body can simplified to a motion of a plane figure in the plane itself. As indicated in the figure, when studying a plane motion of a A rigid body, we do not need to consider its geometrical shape and size are not needed and instead, considering the motion of a plane figure is enough to determine the velocity and acceleration of any point in the rigid body
11 2．Simplification of a plane motion A plane motion of a rigid body can simplified to a motion of a plane figure in the plane itself. As indicated in the figure, when studying a plane motion of a rigid body, we do not need to consider its geometrical shape and size are not needed， and instead, considering the motion of a plane figure is enough to determine the velocity and acceleration of any point in the rigid body
远动学 二.平面运动的简化 刚体的平面运动可以 简化为平面图形S在其自 身平面内的运动.即在研 究平面运动时,不需考虑 刚体的形状和尺寸,只需 研究平面图形的运动,确 定平面图形上各点的速度 和加速度. 12
12 二．平面运动的简化 刚体的平面运动可以 简化为平面图形 S在其自 身平面内的运动．即在研 究平面运动时，不需考虑 刚体的形状和尺寸，只需 研究平面图形的运动，确 定平面图形上各点的速度 和加速度．
ananas 89-2 Plane motion can be decomposed into translation and rotation Equations of plane motion 1. Equations of plane motion To determine the position of a plane figure, which represents the plane motion of a rigid body, only the position of a line segment in this figure is needed to be determined The position of a line segment AB can be determined by the B coordinates of point A and the angle between AB and the axis x XA Therefore, the position of the figure s can be determined by these three independent variables IA,VA, p Hence. we have 13
13 §9–2 Plane motion can be decomposed into translation and rotation·Equations of plane motion 1. Equations of plane motion To determine the position of a plane figure, which represents the plane motion of a rigid body, only the position of a line segment in this figure is needed to be determined. The position of a line segment AB can be determined by the coordinates of point A and the angle between AB and the axis x. Therefore, the position of the figure S can be determined by these three independent variables . Hence, we have xA , yA ,
远动学 §9-2平面运动分解为平动和转动 刚体的平面运动方程 平面运动方程 为了确定代表平面运动刚体的平面图形的位置,我们只需确定 平面图形内任意一条线段的位置 任意线段AB的位置可 用A点的坐标和AB与x轴夹 角表示.因此图形S的位 置决定于x4y42q三个 独立的参变量.所以 14
14 §9-2 平面运动分解为平动和转动· 刚体的平面运动方程 一．平面运动方程 为了确定代表平面运动刚体的平面图形的位置，我们只需确定 平面图形内任意一条线段的位置． 任意线段AB的位置可 用A点的坐标和AB与x轴夹 角表示．因此图形S 的位 置决定于 三个 独立的参变量．所以 xA , yA ,
Kinematics x=fi( Equations of plane motion yAf2(r) Pp=f3(t) The xa,Va, can be found from this equation at any instant t, and thus the location of the plane figure S can be determined 2. Plane motion can be decomposed into translation and rotation When point a in the figure S keeps static, the rigid body rotates about a fixed axis When the angle o in the figure S keeps unchanged, the rigid body has translatory motion Therefore, a plane motion can be viewed as the composition of a translation and rotation 15
15 2．Plane motion can be decomposed into translation and rotation When point A in the figure S keeps static，the rigid body rotates about a fixed axis When the angle in the figure S keeps unchanged，the rigid body has translatory motion. Therefore, a plane motion can be viewed as the composition of a translation and rotation． xA , yA , Equations of plane motion ( ) 1 x f t A = ( ) 2 y f t A = ( ) 3 = f t The can be found from this equation at any instant t, and thus the location of the plane figure S can be determined