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

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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.
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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. Z01
B
Ac01
(S0)

A
(S1)
G1
G2
(S2)
X123
Z23
C
(R)
G2
(S3)
(S2)
G3
y0 z01  y1 z23    x123 y23 θ α    x0 y1  z01 x123  Geometry and distributed mass modelling.   The system identifies :  - four rigid bodies : (S0), (S1), (S2) and (S3) ; - a motor (Ac01), considered being external to the study, located in parallel with the cylindrical joint (S0- S1), drives (S1) relative to (S0) at a known constant velocity0; - a tensile-compressive spring (R) of negligible mass is located between the bodies (S2) and (S3) along a diameter of (S2). 1/6
M. Ferney, M. Meyer and D. Sauhet
Belfort-Montbeliard - University of Technology : PS 29 - Final exam - Autumn 2007     six rigid joints. -(S0- S1 cylindrical (S) :1- S2) : revolute  (S2- S3) : prismatic (S0- S2) : S sphere with a geometric plane of0 (R - S2 - S sphere (R) :3) : sphere located at the centre of mass G3of S3  The centre of mass of (S2) merged into the centre of the circle and (S3) 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 vectorrz01 normal of the plane.  Galilean reference frame.    The fixed body (S0is supposed to be a Galilean reference frame.) frame   Construct the vectorial geometric model.  Draw the sketch of the joints and write the vectorial models.      S0  S1

S3

Define the vectorial model of the bodies
R0 R1 R2 R3
= = = =
R0 R1 R2 R3

[A [B,G1 [B,C,G2 [G3 2/6

S2

;rx0,ry0,rz01)] ;(xr123,yr1,zr01)] ;(xr123,yr23,zr23)] ;(rx123,yr23,zr23)] 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 z01 = a BC rz23 123  - the equations of constraint ;

G1
B
r BG1= bx 123

G2
C
r BG2= ax123
G3
r z G3C = z23
- 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 (S2) with respect to (S0) at the contact point I between the two bodies ;   r G0,2(I)=   - express the resultant of the twistor of the interaction forces of (S0) acting on (S2)using its property with respect to the sliding velocity;  Sr{S0S2} =

- existence condition of the sphere plane joint ;
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M. Ferney, M. Meyer and D. Sauhet

Belfort-Montbeliard - University of Techno
Coulomb’ l s aw : - Rolling without sliding case : o Existence condition       o Equation       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 (Ac01), not sought in the study.   {Ac01 ⎯→S1} =   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              S0 S1       + unknowns + unknowns     S2 S3    Define the unknowns of the motion study   Define the sketch of the characteristics :           S0 S1            S2 S3
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;

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M. Ferney, M. Meyer and D. Sauhet