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D.E.S.H. – Department of Engineering, Sciences and Humanities
FY (AY-20-22-1) – RME – Robot Mechanics and Electronics
Notes 2.3 – Basics of Mechanics of Robots
MOMENT OF A FORCE & MOMENT OF INERTIA
A) Moment of a Force is the Turning effect produced by the force on the body.
It is the measure of its tendency to cause a body to rotate about a specific point or axis. (also known as Torque) always opposes the motion. This opposition is called as Friction Force. A moment is due to a force not having an equal and opposite force directly along it's line of action. Thus ….
Torque = Force x Distance ()
The moment of the force is zero when either …..
- the force is zero OR 2)when the perpendicular distance is zero
Fig .2.3.1 gives real life pictorial presentation of Moment of Force
Fig. 2.3.1 Pictorial presentation of Moment of Force
B) Couple:- Fig. 2.3.2 gives real life pictorial presentation of Couple
Fig .2.3.2 Pictorial presentation of Couple
A couple is formed by two forces that are …..
- equal in magnitude, 2. Opposite in direction and3. parallel in action
D.E.S.H. – Department of Engineering, Sciences and Humanities
FY (AY-20-22-1) – RME – Robot Mechanics and Electronics
Notes 2.3 – Basics of Mechanics of Robots
The effect of a couple on the body is to produce Rotation.
C) Moment of Arm of Couple - The perpendicular distance between the two lines of action of forcesforming the couple is called the “Moment Arm” of the couple. The magnitude of couple is defined as the product of the magnitude of the force and the moment arm. The sense of the couple could be CW (–ve) or CCW (+ve). Couple is measured in “N-m”.
For equivalence …. Couples should have:- 1. Same magnitude 2.Same sense
D) MOMENT OF INERTIA OF A BODY
1) Mass Moment of Inertia – It is the opposition offered by a body to the rotation because its own mass.
The amount of Torque needed to cause any given angular rotation is proportional to the MASS of the body, thus called as the Mass moment of inertia of the body.
D.E.S.H. – Department of Engineering, Sciences and Humanities
FY (AY-20-22-1) – RME – Robot Mechanics and Electronics
Notes 2.3 – Basics of Mechanics of Robots
List of important Formulae for Area Moment of Inertia :-
Fig 2.3.4 for Area Moment of Inertia of Different Systems and their formulae
D.E.S.H. – Department of Engineering, Sciences and Humanities
FY (AY-20-22-1) – RME – Robot Mechanics and Electronics
Notes 2.3 – Basics of Mechanics of Robots
E) Parallel Axis Theorem - Statement:-The moment of inertia of a plane area with respect to any reference axis in its plane is equal to the sum of moment of Inertia with respect to a parallel centroidal axis and product of total area and the square of the distance between the two axes.
I AB = IG + Ah^2
Parallel axis theorem is used to find M. I. about a n axis which is not passing through C.G. of the section. Fig 2.3.5 Parallel Axis theorem explained
Fig 2.3.5 Parallel Axis theorem
F) Perpendicular Axis Theorem Statement:-The moment of inertia of an area with respect to an axis perpendicular to the x-y plane (z-axis) and passing through origin will be equal to the sum of moment of inertia of the same area about x-x and y-y axis.
Izz= Ixx + I yy
G) Verignon’sTheorem:-. Fig 2.3.6 explains Verignon’s Theorem
Fig 2.3.7 Verignon’s Theorem
