Rigid body mechanics 2007 Tronc Commun Université de Technologie de Belfort Montbéliard

Mferney

Description

Examen du Supérieur Université de Technologie de Belfort Montbéliard. Sujet de Rigid body mechanics 2007. Retrouvez le corrigé Rigid body mechanics 2007 sur Bankexam.fr.

Sujets

• 2007

Informations

• Publié par: bankexam
• Publié le: 18 août 2008
• Nombre de lectures: 41
• Langue: Français

Extrait

 

Belfort-Montbeliard - University of Technology : PS 29 - Final exam - Autumn 2007  

  Signature :

  Name :     First name : 

      Mark                     20

Examination duration: 1h50 – Write your answer to the questions on the examination paper. Only the results are required.

None document authorized.  document should be given back.

  Apart from this examination paper, no other   The motionof the following device will be studied. Z 01

B  

A c01  

(S 0 )

 

A  

(S 1 )

G 1  

           G 2    

(S 2 )

X 123

Z 23

  C

(R)

G 2  

(S 3 )  

(S 2 )

G 3

    y 0  z 01   y 1  z 23         x 123  y 23   θ  α        x 0  y 1   z 01  x 123     Geometry and distributed mass modelling.    The system identifies :  - four rigid bodies : (S 0 ), (S 1 ), (S 2 ) and (S 3 ) ; - a motor (Ac 01 ), considered being external to the study, located in parallel with the cylindrical joint (S 0 - S 1 ), drives (S 1 ) relative to (S 0 ) at a known constant velocity 0 ; - a tensile-compressive spring (R) of negligible mass is located between the bodies (S 2 ) and (S 3 ) along a diameter of (S 2 ). 1/6  

M. Ferney, M. Meyer and D. Sauhet  

Belfort-Montbeliard - University of Technology : PS 29 - Final exam - Autumn 2007       six rigid joints. - (S 0 - S 1  cylindrical (S) : 1 - S 2 ) : revolute   (S 2 - S 3 ) : prismatic (S 0 - S 2 ) : S sphere with a geometric plane of 0   (R - S 2  - S sphere (R) : 3 ) : sphere located at the centre of mass G 3 of S 3     The centre of mass of (S 2 ) merged into the centre of the circle and (S 3 ) is assumed to be a punctual body for the kinetic study.   Forces modelling.    The spring is supposed to be a linear elastic spring.  The cylindrical, revolute, prismatic and spheres are supposed to be perfect joints unlike the sphere plane joint. For this joint, the sliding friction is taken into account through the Coulomb’s model.  The system moves in the gravitational field which is defined by the vertical unit vector r z 01   normal of the plane.     Galilean reference frame.       The fixed body (S 0 is supposed to be a Galilean reference frame.) frame     Construct the vectorial geometric model.   Draw the sketch of the joints and write the vectorial models.          S 0     S 1  

       

         

 

 

 

 

 

  

 

S 3  

 

        Define the vectorial model of the bodies  

R 0 R 1 R 2 R 3

= = = =

R 0 R 1 R 2 R 3

  

 

[ A [B,G 1 [B,C,G 2 [ G 3 2/6  

      

S 2  

  

; r x 0 , r y 0 , r z 01 )] ;(x r 123 ,y r 1 ,z r 01 )] ;(x r 123 ,y r 23 ,z r 23 )]   ;( r x 123 ,y r 23 ,z r 23 )] M. Ferney, M. Meyer and D. Sauhet  

Belfort-Montbeliard - University of Technology : PS 29 - Final exam - Autumn 2007   Define the parameters :   - the bases : reminder ;

 

 

- the points :          A  

  r r  r x + B = λ  z 01  = a BC r z 23   123   - the equations of constraint ;      

 

 

G 1

B

r BG 1 = b x   123

 

  

G 2

C

r BG 2 = a x 123   

G 3

r z G 3 C = z 23  

          - the number of the kinematically independent parameters ;      Construct the vectorial models of the forces and the existence conditions of the joints   a. The spring                b. The sphere plane joint (existence condition and Coulomb’s model) - compute the sliding velocity of (S 2 ) with respect to (S 0 ) at the contact point I between the two bodies ;     r G 0,2 (I)=      - express the resultant of the twistor of the interaction forces of (S 0 ) acting on (S 2 )using its property with respect to the sliding velocity;   S r { S 0 →S 2 } =       

 

     

- existence condition of the sphere plane joint ;

3/6  

  

M. Ferney, M. Meyer and D. Sauhet  

 

 

 

Belfort-Montbeliard - University of Techno

Coulomb’ l s aw : - ƒ Rolling without sliding case : o Existence condition           o Equation          ƒ Sliding case : o Existence condition       

o 

 

Equation

logy :

PS 29 - Final exam - Autumn 2007  

        c. The zero components of the interaction forces, according to the assumptions of the perfect joints and the rigid bodies     

           

          d. The gravitational field                e. The twistor applied by the motor (Ac 01 ), not sought in the study.     {Ac 01  ⎯→S 1 } =     Define the unknowns of the motion study      

4/6  

M. Ferney, M. Meyer and D. Sauhet  

Belfort-Montbeliard - University of Technology : PS 29 - Final exam - Autumn 2007   Apply the dynamic theorems   Define the cut :   + unknowns                      S 0  S 1               + unknowns + unknowns         S 2  S 3         Define the unknowns of the motion study      Define the sketch of the characteristics :                     S 0  S 1                         S 2  S 3        

5/6  

M. Ferney, M. Meyer and D. Sauhet  

Belfort-Montbeliard - University of Technology : PS 29 - Final exam - Autumn 2007   Write the scalar consequences of the dynamic theorems,the angular momentum theorem will be computed at point Bas a fixed point with respect to the frame Rwhich can be considered 0 .                         Use the scalar consequences of the dynamic theorems - compute the components of the external forces;                       - compute the components of kinetics;    

 

6/6  

M. Ferney, M. Meyer and D. Sauhet