Kinematics Another example: plane figure S moves from position I to position I L in a interval△t B Select point A as a pole: Translate the figure together with a to the position a'B" and then rotate it around a through an angle Ag to the final position A'B Select point A as a pole: Translate it together with b to the position A"B, and then rotate it around B through an angle A2 to the final position A'B Clearly,AB∥A'B"∥A"B’,△q1=△o2 we have do de lir m1=02 21 41→01t1->04t dt dt >E1=6 2
21 Another example: plane figureＳ moves from position I to position II in a interval t. Select point A as a pole: Translate the figure together with A to the position A'B'', and then rotate it around A through an angle to the final position A'B‘. Select point A as a pole: Translate it together with B to the position A''B', and then rotate it around B through an angle to the final position A'B' Clearly, AB A'B'' A''B' ， we have 1 = 2 1 2 1 2 1 2 1 2 2 0 1 0 lim lim , ; , = = = = → → dt d dt d t t t t
远动学 再例如:平面图形S在△t时间内从位置I运动到位置Il B B 以A为基点:随基点A平动到AB后,绕基点转A1角到AB′ 以B为基点:随基点B平动到A"B后,绕基点转△2角到AB′ 图中看出:AB∥AB"∥A"B,A1=△2于是有 lim lin Im A021=02 ∠t→>0 1→0t dt 182 22
22 再例如: 平面图形Ｓ在ｔ时间内从位置I运动到位置II 以A为基点:随基点A平动到A'B''后, 绕基点转 角到A'B' 以B为基点:随基点B平动到A''B'后, 绕基点转 角到A'B' 图中看出：AB A'B'' A''B' ， 1 = 2 于是有 1 2 1 2 1 2 1 2 2 0 1 0 lim lim , ; , = = = = → → dt d dt d t t t t
Kinematics In conclusion, the translation in a plane motion depends on the selection of the pole, however, the rotation about the selected pole DOES NOT depend on the choice of a pole. (In other words, the instant 8, o of any rotations about any poles are the same The selection of the pole is arbitrary. ( We usually select a point with known motion as the pole
23 In conclusion，the translation in a plane motion depends on the selection of the pole，however, the rotation about the selected pole DOES NOT depend on the choice of a pole．(In other words, the instant , of any rotations about ANY poles are the same）The selection of the pole is arbitrary.(We usually select a point with known motion as the pole. )
远动学 所以,平面运动随基点平动的运动规律与基 点的选择有关,而绕基点转动的规律与基点选取 无关.(即在同一瞬间,图形绕任一基点转动的 E,O都是相同的)基点的选取是任意的。(通常 选取运动情况已知的点作为基点) 24
24 所以，平面运动随基点平动的运动规律与基 点的选择有关，而绕基点转动的规律与基点选取 无关．(即在同一瞬间，图形绕任一基点转动的 ,都是相同的）基点的选取是任意的。(通常 选取运动情况已知的点作为基点)
Kinematics B Crank-rod mechanism Rod AB has plane motion Decomposition of the plane motion B please look at the animation)
25 Crank-rod mechanism Rod AB has plane motion Decomposition of the plane motion （please look at the animation）