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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 2.1 – Basics of Mechanics of Robots
BASIC CONCEPTS –
A) Mechanics is the study of behavior of matter under the action of applied Forces. It is a science that deals with study of Physical phenomenon.
B) Engineering mechanics is the branch of science in which it deals with the laws and principles of mechanics, and their application with the engineering problems
C) Engineering mechanics helps an Engineer in …..1) planning 2) designing 3) construction of various types of structures and machines. e.g. Robots.
D) Figure 1.1 depicts Facets of Engineering Mechanics : A Glance
Figure 1.1 Facets of Engineering Mechanics
E) Statics And Dynamics
Statics – Study of behavior of rigid bodies under the action of applied forces when they are at Rest Dynamics – Study of behavior of rigid bodies under the action of applied forces when they are in Motion
- Kinetics – Study of the Motion of the bodies due to the application of forces.
- Kinematics – Study of motion of the bodies without considering the forces.
F) Importance of Statics and Dynamics in Robotics
- A Robot is a rigid body. A Robot is acted by forces at rest and in motion.
- A Robot needs to have …..1) Coordination 2) Synchronization 3) Stability 4) Balance within its structural parts at rest and in motion as well.
- Hence, while studying Robotics, a sound knowledge of Statics and Dynamics is necessary.
G) Particle – Body – Rigidity – Deformation
- A particle occupies a point in space with negligible dimensions and has no size and shape.
- A body is composed of infinite number of particles.
- A body has definite size and shape.
D.E.S.H. – Department of Engineering, Sciences and Humanities
FY (AY-20-22-1) – RME – Robot Mechanics and Electronics
Notes 2.1 – Basics of Mechanics of Robots
- A body is always limited in all directions.
- In a Rigid body the distance between its particles does not change under the action of the forces.
- Rigid body is an idealized concept as there is no body in the Universe which is 100% Rigid.
- Every body always suffers from deformation. However, if it is extremely small, can be neglected and will not change its overall dimensions
Rigid Body vs Deformable body :- Figure 1.2 distinguishes Rigid Body vs Deformable body
Figure 1.2 Rigid Body vs. Deformable Body
H) Force :- (with slight elastic deformation), a slight stretching of the bolt, and compression of the parts to be held together.
- Force is the capacity to do work.
- Force produces motion in the body.
- Force is a vector quantity, SI unit is Newton
- Force causes …. 1 ) Translation 2) Rotation or 3) both.
I) Characteristics of Force:- Figure 1.3 depicts Characteristics of Force
J) Force System:- A “Force System” consists of multiple forces acting on a body at a point.
K) Types of Force system are …..
Co-planar and Non-Coplanar Force system
Concurrent and Non-Concurrent Force system
Parallel and Non-Parallel Force system
Collinear and Non-Collinear Force system
D.E.S.H. – Department of Engineering, Sciences and Humanities
FY (AY-20-22-1) – RME – Robot Mechanics and Electronics
Notes 2.1 – Basics of Mechanics of Robots
M) Principle of Transmissibility of Force: - “ If a force acts at a point on a rigid body , then it is assumed to act at any point on the line of action of force within the body.”
Figure 1.5 Principle of Transmissibility of Force
N) Resolution of Force:- Force is a vector quantity. So, it can be assumed to be composed of two fictitious components. Along….. 1) X axis 2) Y axis as shown in Figure 1.
Figure 1.5 Force Components
Resultant Force:- It is vector sum of all forces. (algebraic sum). Figure 1.6 depicts Resultant Force
Figure 1.6 Resultant Force
D.E.S.H. – Department of Engineering, Sciences and Humanities
FY (AY-20-22-1) – RME – Robot Mechanics and Electronics
Notes 2.1 – Basics of Mechanics of Robots
O) Law of Parallelogram of Forces:- Law of Parallelogram of Forces
Figure 1.7 Law of Parallelogram of Forces
P) Law of Parallelogram of Forces (Derivation)
Figure 1.8 Law of Parallelogram of Forces derivation
Q) Equilibrium:-
- A rigid body is said to be in equilibrium, when the resultant of the force system on it is zero.
- The resultant of the force system can be a Force or a Moment.
- If the resultant is zero, it implies that the resultant force ( ∑ F) and resultant moment ( ∑ M) both are zero.
- If the resultant force ∑ F = 0, there is No Translation.
- If the resultant moment ∑ M = 0, there is No Rotation.
- Thus the body is said to be in a ……. Complete Static Equilibrium
D.E.S.H. – Department of Engineering, Sciences and Humanities
FY (AY-20-22-1) – RME – Robot Mechanics and Electronics
Notes 2.1 – Basics of Mechanics of Robots
Features of F. B.D
- It is a sketch of a body of interest only
- All the surrounding bodies are removed.
- All of the forces acting on the body are considered and shown.
- All of the forces acted by the body on other bodies are NOT considered.
Steps to draw F.B.D:- A sphere of weight W is resting on a rigid wall and is held by a string. See Figure 1.11 for the FBD of the sphere.
Figure 1.11 Actual structure and FBD of the sphere
U) Lami's Theorem:-
Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non- collinear forces, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding forces
Lami's theorem is also known as Law of sines
Let there are a few forces acting on a body and the body is in a static equilibrium. Assume P, Q and R are the 3 forces keeping the body in equilibrium and a, b and c are the respective angles, then according to Lami’s Theorem…. Figure 1.12 depicts schematic diagram and equation for Lami’s theorem
Figure 1.12 Schematic diagram and equation for Lami’s theorem
D.E.S.H. – Department of Engineering, Sciences and Humanities
FY (AY-20-22-1) – RME – Robot Mechanics and Electronics
Notes 2.1 – Basics of Mechanics of Robots
V) NUMERICALS AND SOLUTION :-
