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Unformatted text preview: Problems 1 9 PROBLEMS 9.1 Introduction 1. Determine the number of degrees of freedom of the planar elipsograph mechanism in Fig. 9.1. Find the analytical expression of any point P on the link 2. 2. Find the mobility of the planar mechanism represented in Fig. 9.2. 3. Determine the family and the number of degrees of freedom for the mechanism depicted in Fig. 9.3. 4. The roller 2 of the mechanism in Fig. 9.4 undergoes an independent rotation about its axis which does not influence the motion of the link 3. The purpose of the element 2 is to substitute the sliding friction with a rolling friction. From a kinematical point of view the roller 2 is a passive element. Find the number of degrees of freedom of the mechanism. 5. Find the family and the number of degrees of freedom of the mechanism in Fig. 9.5. Problems 2 9.2 Kinematics and force analysis 6. The following data are given for the mechanism shown in Fig. 9.6: AB = CD = 0 . 04 m and AD = BC = 0 . 09 m. Find the trajectory of the point M located on the link BC , for the case a) BM = MC , and b) MC = 2 BM . 7. The planar mechanism depicted in Fig. 9.7 has dimensions AB = . 03 m, BC = 0 . 065 m, CD = 0 . 05 m, BM = 0 . 09 m, and CM = . 12 m. Find the trajectory described by the point M . 8. The mechanism shown in Fig. 9.8 has dimensions AB = 0 . 03 m, BC = . 12 m, CD = 0 . 12 m, ED = 0 . 0 m, CF = 0 . 17 m, R 1 = 0 . 04 m, R 4 = 0 . 08 m, L a = 0 . 025 m, and L b = 0 . 105 m. Find the trajectory of the joint C . 9. I. The length of the links are known for the mechanism shown in Fig. 9.9. The angle of the driver link 1 with the horizontal is = 1 and the angular speed of the driver link 1 is n = n 1 =constant. The input data for ten cases are given in the table in Fig. 9.9. Determine: a)the family f of the mechanism and the number of degrees of freedom of the mechanism; Problems 3 b) the positions of the joints B , C , D , and E ; c) the linear velocities of the joints B , C , D , E , and the angular veloc ities of the links 2, 3, and 4; d) the linear accelerations of the joints B , C , D , E , and the angular accelerations of the links 2, 3, and 4; II. The links 1, 2, and 4 are homogeneous bars made of steel, each with a mass density =7 800 kg m 3 , and each with a constant cross section A s =1 cm 2 . The sliders 3 and 5 have negligible dimensions and can be considered as material points with masses m 3 = m 5 =0.1 kg. Find: e) the forces and moments of inertia for each link; f) the joint forces and the equilibrium moment if an external vertical force of magnitude  F e  =250 N acts on link 5 at the point D . 10. I. The mechanism shown in Fig. 9.10 has links of known length. The angle of the driver link 1 with the horizontal is = 1 and the angular speed of the driver link 1 is n = n 1 =constant. The input data for ten cases are given in the table in Fig. 9.10. Determine: a) the family f of the mechanism and the number of degrees of freedom of the mechanism; b) the positions of the joints B , D , E , F and the trajectory of C ; Problems...
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This note was uploaded on 08/29/2011 for the course MECH 6420 taught by Professor Marghitu during the Summer '11 term at University of Florida.
 Summer '11
 Marghitu

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