Equilibrium of Force and Moment Systems – Question, Annotated Marking Scheme and Marked Script
9.
(continued)
A hydraulic manipulator enables the ROV to perform simple servicing tasks on seabed equipment. The jaws of the manipulator are connected to a hydraulic cylinder by a bell-crank lever as shown in Figure Q9( b ).
Marks
Manipulator jaw slide
Right-hand manipulator jaw 60 mm
5 kN
Hydraulic cylinder
Figure Q9( b )
15°
.
F
C
Hinge, H
Figure Q9( c )
45°
150 mm
Figure Q9( c ) shows the bell-crank lever for the right-hand manipulator jaw.
The jaw is designed to exert a maximum horizontal force of 5 kN. The hydraulic cylinder produces a vertical force.
( c ) For the bell-crank lever position shown in Figure Q9( c ):
(i) draw a free body diagram;
(ii) determine the magnitude of the force, F
C
;
(iii) determine the magnitude and direction of the reaction at the hinge, point H.
2
4
3

9. c) i)
150
5 kN
Forces F
C
Lengths
and 5kN
Angles
Reaction magnitude and angle
½
½
½
½
2
Points on script
(1)
(2)
(3)
(4)
45 °
15 °
F
C
60
θ°
R c) ii) For equilibrium
+ iii)
∑
M about H
= 0
(½) (1) (½) (1)
5 × 150 sin 45 ° − F
C
× 60 cos 15 °
530 .
3 − 57 .
96 × F
C
=
=
0
0
Forces (½ each) Distances (½ each)
Trig. Functions (½ each)
Answer (½) Units (½)
F
C
= 9 .
15 kN
∑
R
F
V
×
= sin
0
θ
H
R
− F
C sin θ
H
×
∑
F
H
= 0
5 − R
H
× cos θ
R cos θ
H
×
=
=
=
=
0
0
9 .
15 kN
5 kN
R
R
H
H
=
= 10
5
.
2
4
+ 9 kN
.
15 2 θ
θ
=
= tan
61 .
− 1
3 °
(
9 .
15
5
)
Magnitude including Units
Angle relative to horizontal
If equilibrium of horizontal and vertical forces is stated, without any further successful work then 1 mark for first statement
1
1
½
½
3
1
(8)
(9)
(10)
(5)
(6)
(7)
3
4

7. Correct equation for vertical force equilibrium correct answer based on follow-through error from earlier part of question. 1 mark.
8. Correct equation for horizontal force equilibrium. 1 mark.
1. Lengths not clearly identified. ½ mark not awarded.
2. Forces clearly identified . ½ mark
3. One angle not identified. ½ mark not awarded.
4. Reaction not identified. ½ mark not awarded.
5. Vertical rather than horizontal component of length taken to form moment caused by F
C
. Using Marking
Principle b) iii), 2½ marks out of 3.
6. Incorrect answer from Marking
Instructions, but correct answer based on follow-through error from equilibrium equation. 1 mark.
10. Correct value for direction of reaction vector, based on follow-through error from earlier part of question. ½ mark.
9. Pythagoras used correctly to produce magnitude of reaction.
Final answer lacks units. ½ mark not awarded.