The document discusses dynamic force analysis, which incorporates inertia forces into the examination of mechanisms, specifically using D'Alembert's principle to equate dynamic systems to static ones. It also explains the slider-crank mechanism, detailing its function in converting motion types and illustrating inertia forces and couples in connection with this mechanism. The analysis highlights the kinematic conditions that determine the degrees of freedom within the system.

1. DYNAMIC FORCE ANALYSIS
• When the inertia forces are considered in the analysis of
the mechanism, the analysis is known as dynamic force
analysis.
• Now applying D’Alembert principle one may reduce a
dynamic system into an equivalent static system and use
the techniques used in static force analysis to study the
system.
• Garcia and Bayo (1994), Wang and Wang (1998), Shi and
Mc Phee (2000) were interested in the analytical and
• experimental study of the dynamic response of these
mechanisms

2. slider crank mechanism
Slider-crank mechanism, arrangement of mechanical parts designed
to convert straight-line motion to rotary motion, as in a reciprocating
piston engine, or to convert rotary motion to straight-line motion, as
in a reciprocating piston pump.

3. The Slider-crank mechanism is used to transform rotational
motion into translational motion by means of a rotating driving
beam, a connection rod and a sliding body. In the present
example, a flexible body is used for the connection rod. The
sliding mass is not allowed to rotate and three revolute joints are
used to connect the bodies. While each body has six degrees of
freedom in space, the kinematical conditions lead to one degree
of freedom for the whole system.

4. Inertia force and couple
Figure 1: Illustration of inertia force (i) a translating body (ii) a
compound pendulum, (iii) inertia force
and couple on compound pendulum.
Consider a body of mass moving with acceleration as shown in figure
1(i). According to D’Alembert Principle, the body can be brought to
equilibrium position by applying a force equal to maiFma=and in a
direction opposite to the direction of acceleration. Figure 1 (ii) shows a
compound pendulum of mass m, moment of inertia gIabout center of
mass G while rotating at its center of mass has a linear acceleration of
and angular acceleration of aα. Figure 1(iii) shows the inertia force and
couple acting on the pendulum.

5. Equivalent off-set Inertia force
Figure 2: (i) Illustration of equivalent off-set inertia force
Figure 2(i) shows a body with inertia force iF and inertia couple cI. The
couple can be replaced by two parallel forces (equal in magnitude and
opposite in direction) acting at G and H respectively as shown in Figure
2(ii). If we consider their magnitude of these forces same as that of
inertia force, then the equal and opposite forces at point G will cancel
each other and the resulting force will be a force at H which is in the
same direction as inertia force. If h is the minimum
distance between the force at G and H.

6. Dynamic analysis of Slider Crank
Mechanism

10. Thank You