1) A free body diagram is used to represent all external forces and torques acting on a system. It is an important step in solving kinetics problems. 2) The document provides guidance on constructing free body diagrams including identifying the system, drawing external forces and torques, and specifying the point of application and direction. 3) Lever systems use an effort force to move a load force. There are three classes of levers that vary based on the relative positions of the effort, load, and fulcrum. Mechanical advantage determines the trade off between force and distance of movement.

1. Free Body Diagram
• Is a means of representing all of the external forces
Equilibrium and torques acting on a system
• It is the most important step in solving a problem in
kinetics
Objectives:
Fquads
• Learn how to draw a free body diagram Fcontact
• Define and learn how to solve problems in static System
equilibrium Tflexor
• Define the 3 classes of levers and what each is
best suited for
• Introduce stabilizing and dislocating forces and
how to compute them Wleg+foot
Constructing a Free Body Diagram Identifying the System
1. Identify the system • Depends on the problem being solved
2. Draw a simple picture (diagram) of the system • The forces or torques of interest must act across
3. Identify each of the external forces and torques the boundary of the system (i.e. they must be
(i.e. forces or torques acting across the boundary external forces or torques)
of the system). • The system should behave as a rigid body
4. Identify (or assume) the point of application and (unless you are only interested in the movement
direction of each force and draw into the diagram of the system’s center of mass)
5. Identify (or assume) the axis of rotation and • Typical systems in biomechanics:
direction for each torque and draw into the – the whole body
diagram – a single body segment
6. Add a reference frame to the diagram – a rigid group of body segments
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2. Identifying External Forces/Torques Point of Application & Direction
• Usually known for contact forces
• External forces include: • Weight acts downward from the center of mass
• Resultant joint force is applied at the joint center
– Weight (i.e. force due to gravity)
• Resultant joint torque acts about joint center; can
– Contact forces applied from outside the body assume its direction
– Contact forces applied from within the body • If direction of a force unknown, assume a positive x-
component and a positive y-component
• Two methods of representing contact forces from
• If point of application of a force unknown, include
within the body:
point of application as a variable
– The joint contact force and the force produced
by each anatomical structure across the joint direction Fy location
unknown: F unknown:
(i.e. muscles, ligaments, etc.) x
– A resultant joint force and a resultant joint torque
d F
Example Problem #1 Static Equilibrium
We want to compute the ankle torque during the stance • A system is at rest and will remain at rest
phase of running. Construct an appropriate free • No translation or rotation is occurring or will occur
body diagram. • Conditions for static equilibrium
(from Newton’s 1 st Law):
– Net external force in x direction
Σ Fx = 0 equals zero
– Net external force in y direction
Σ Fy = 0 equals zero
– Net torque produced by all
ΣT=0 external forces and all external
torques equals zero
• Can use any point as the axis of rotation
• Can solve for at most 3 unknown quantities
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3. Example Problem #2 Example Problem #3
A 60 kg gymnast is standing in the position shown. During an isometric (static) knee extension, a
Find the ground reaction force acting on her foot. therapist measures a force of 100 N using a hand
How far forward can she move her center of mass dynamometer in the position shown below
and remain standing? Find the resultant knee joint force and torque.
15 cm Does the dynamometer position affect the measured
force?
KNEE
60°
body center
of mass m = 4.5 kg
80 cm 24 cm
20 cm Fdyn = 100 N
30 cm
10 cm
Levers 1st Class Lever
• Most skeletal muscles act using the principle of • Effort force and load force are applied on
leverage opposite sides of the axis of rotation
• A lever system consists of: • Effort force and load force act in same direction
– An axis of rotation (or fulcrum) • For equilibrium: d⊥load Fload = d⊥effort Feffort
– A resistance force or load
d⊥effort
– An effort force (the applied force that is used to or: Fload = F
move the load) d⊥load effort
• There are 3 classes of lever Fload Feffort
Fload d⊥load d⊥effort
Feffort
axis of rotation axis
Fload Feffort
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4. Mechanical Advantage Mechanical Advantage
d⊥effort • When Mechanical Advantage < 1:
Mechanical Advantage = – Feffort needed is greater than Fload
d⊥load
– Point at which Fload applied moves faster and
• When Mechanical Advantage > 1: greater distance than point at which Feffort applied
– Feffort needed is less than Fload – Good for moving load quickly or through large
– Point at which Fload applied moves slower and range of motion; poor for strength
shorter distance than point at which Feffort applied • A 1st class lever can have a mechanical advantage
– Good for strength, poor for moving load quickly greater than, equal to, or less than 1.
or through large range of motion
Feffort axis Feffort
Fload axis
Fload
2nd Class Lever 3rd Class Lever
• Effort force and load force are applied on same • Effort force and load force are applied on same
side of the axis of rotation side of the axis of rotation
• Effort force applied farther from axis than the load • Effort force applied closer to axis than the load
force (i.e. d⊥effort > d⊥load) force (i.e. d⊥effort < d⊥load)
• Effort and load force act in opposite directions • Effort and load force act in opposite directions
• Good for strength; poor for moving load quickly or • Good for moving load quickly or through large
through large range of motion range of motion; poor for strength
Fload
d⊥load Feffort
Feffort d⊥effort Feffort
d⊥load Fload
axis
Feffort Fload axis
d⊥effort Fload
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5. Stabilization vs. Dislocation Example Problem #4
• Forces do not produce torque only; they also A person is holding their upper limb in the abducted
produce stabilizing or dislocating forces at a joint. position shown. Find the deltoid muscle force and
• Can decompose a force into components parallel the force perpendicular to the joint surface.
to (Fll) and perpendicular to (F⊥) the joint surface Is the deltoid force stabilizing or dislocating?
• F⊥ points towards joint → stabilization What class of lever is this?
• F⊥ points away from joint → dislocation Fdeltoid 30°
Stabilization: Dislocation: F
Fll Shoulder
F⊥ Fll 15 cm
Joint Surface
30 cm
F F⊥
W = 35 N
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