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Lecture Free Body Diagram---------------------------------------------------------------------------------------------------------------------------
The learning goal of this block is the ability to estimate the load on a structure in a posture or
during a movement
Free-Body-Analysis: you should be able to define the body of interest, draw relevant forces
as vectors, and write down and solve an equilibrium equation.
YOU HAVE TO SOLVE A MECHANICAL PROBLEM USING A FBD IN THE EXAM
Forces are important in joints, movement (how much force is needed to throw a ball),
balance, and (over)loading of muscles, and define the mechanical effect of muscles on the
body.
Force can be determined through the Free-Body-Analysis: The force on an entire body is
being looked at and only external forces are taken into consideration.
Initial Steps for a Free Body Analysis (FBA):
1. first, define the body of interest
2. define all forces acting on it
3. write down and solve the movement equation
a. net force determines acceleration (Newton’s law)
b. Net torque determines “rotation”
E.g.: “you are interested in the ground reaction force”.
In this case, the entire human body is the body of
interest → the forces acting on the entire body are: the
Ground reaction force and the gravitational force.
HOWEVER, these two forces are both internal forces
and WILL NOT BE INCLUDED in the movement
equation.
E.g.: “you are interested in the knee force”
In this case, you make a cutting plane on the knee →
there is two possible body of interest, either (1) the lower
leg OR (2) the upper leg with the rest of the body.
Depending on what you know, you pick the best body
of interest.
E.g.: ”you are interested in the hip force”
In this case, you make a cutting plane on the hip → the
bodies of interest are the (1) Left or right leg (pick the
one you want to know) OR (2) the rest of the body with
the remaining leg.
A FULL-DYNAMIC FREE BODY ANALYSIS WILL NOT BE
DISCUSSED DURING THIS BLOCK: which includes all
external forces AND linear and rotational accelerations
--------------------------------------------------------------------------->>>
,During block BBS2052, the FBA will focus on (Quasi-)static: all external forces and NOT
accelerations. In Quasistatic, there could be some acceleration but is too small to be
included.
Follow-up on the steps for an FBA:
1. construct the free body
2. consider all external forces
3. 2 force equilibria
a. ∑Fx = m * ax → the sum of all forces in the x-axis direction (mass * horizontal
acceleration)
b. ∑Fy = m * ay → the sum of all forces in the y-axis direction (mass * vertical
acceleration)
4. Moment equilibrium
a. ∑M = l * α → moment of inertia angular acceleration (you don’t have to
understand this)
5. as we consider only (quasi)static situations, there is no acceleration thus:
a. ∑Fx = 0
b. ∑Fy = 0
c. ∑M = 0
Example: there is a ball on a cone, attached to a rope. Which forces act on the ball?
FBA:
1. define the free body
2. which forces act on this body (from the outer
world on the ball) (direction and size)
Answer FBA:
1. define the free body: BALL
2. which forces act on the free body
a. “cut” the body free from its environment
b. consider only the free body
c. forces can be in the transected structures or contact points = Ground Reaction
Force, the force can be in the gravitational forces in the centre of mass
3. which forces act on this body (from the outer world on the ball)
a. direction
b. size
i. In the picture, the s-vector is the force from the rope
exercising on the ball (the rope does not push but
pools, hence its direction, the g-vector is the
gravitational force and always downwards, and the
d-vector is the force from the cone which is upward
and perpendicular to its surface area
WHEN USING ABBREVIATIONS (TO YOUR OWN LIKING) FOR THE VECTORS,
EXPLAIN WHAT THEY STAND FOR.
4. around which point to determine moment equilibrium?
, FREE BODY DIAGRAM: 10 POINT steps 1/2:
SCHEME
Elbow joint loading during holding a 5
kg weight in the hand: mw= 5 kg, dw=
0.35 m, mla= 4.5 kg, dla= 0.15 m, dm=
0.03 m. d= distance
Step 3:
1. which force do you want to
determine?
2. make a drawing of the relevant
part of the body with enough
anatomical detail to identify the
relevant force and the relevant
Step 4:
joint slit. (NOT OBLIGATORY but
helpful)
3. Cut the “moving” body free: draw
the section plane:
a. through the joint slit
b. “from the skin to skin”
c. not sectioning any bony
tissue.
Step 5:
4. Consider only the free body.
Step 6: Muscle force (in their line of action), Joint reaction force
(in their line of action), the gravitational force (will be neglected),
5. Define the frame of reference (x, y,
and the 5 kg weight forces are depicted.
M; + and -). Everything to the right,
upward, and counterclockwise is
positive
6. Draw the FBD with all relevant
(external) forces
a. Forces acting on the boundary
of the Free body (section
plane or skin)
b. Gravitational forces on the
Free Body Internal forces are
neglected!
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