Belfort Montbeliard – University of Technology: PS 29_Mid-term Exam_Fall 2009
1/4 M. Ferney, M. Meyer and D. Sauhet
Name:
First name: k
M
20 a
r
Examination duration: 1h45 – Write your answer to the questions on the examination paper. Only the results are required.
Apart from this examination paper, no other document should be given back.
Answer the following questions on kinematics:
- On mechanics, when modelling a multi-technology system, what is the “ideal core”?
- On mechanics, which reasons justify to change the textual model into the vector model?
- What is the vector model of a rigid body?
- What is the vector model of the helical joint with a reduced pitch λ and an axis ?
- Which unvarying vector elements allow removing the three degrees of freedom of rotation in a joint between two bodies Si and Sj?
- Which quantities allow introducing the time variable in the study of kinematics?
- Which conditions must be checked to ascertain a minimum path between bases?
Signature
) , (A zr
Belfort Montbeliard – University of Technology: PS 29_Mid-term Exam_Fall 2009
2/4 M. Ferney, M. Meyer and D. Sauhet
- What is an equation of constraint?
- When computing the time derivative of vector function, in which situation do we apply the Bour’s relation?
Exercise:
As the part of the kinematics study of a design project the given vector model of the concept described below identifies:
- The vector skeleton:
- The initial parameters:
ψ, φ et z with - The geometric conditions:
- The kinematically independent parameter: ψ z123
z01
y23
y0
A012
C3
B0 z0
θ0
a
0,1
0 0
3 0
r r
=
→ × z C B
→
→ × =
× 2 3 23 0
23 AC y
y r
r
x1
z01
ψ
θ0
1,1*
z123
ϕ 1*, 23
y1 y0
x0 x1
z123 z01
y1 y1*
y1*
y23
x23
x1
z0
z BC r
=
Belfort Montbeliard – University of Technology: PS 29_Mid-term Exam_Fall 2009
3/4 M. Ferney, M. Meyer and D. Sauhet
Questions (questions 3, 4 and 5 are independent):
1. Find the joints sketch, the vector models of the joints and their name.
2. Draw the kinematic sketch
S0 S1
S2 S3
Belfort Montbeliard – University of Technology: PS 29_Mid-term Exam_Fall 2009
4/4 M. Ferney, M. Meyer and D. Sauhet
3. Write, projecting on basis b23, the equations of constraint it may be deduced from the geometric condition
4. Write the equation of constraint if a motor, located in parallel with the joint between the two bodies S0 and S1, drives S1 relative to S0 at a known constant velocity ω0.
5. Find the following kinematics quantities, in terms of the initial parameters.
=
= Ω
) ( V0,3
3 , 0
C r r
=
= Ω
) ( V2,3
3 , 2
C r r
→
→ × =
× 2 3 23 0
23 AC y
yr r
