1.

Homogeneous Transformation Equation:

In robotics, the homogeneous transformation equation is used to represent both
rotation and translation of a robot or object in a single matrix form. It combines
rotation matrix 𝑅and position vector 𝑃as:
𝑅 𝑃
𝑇=[ ]
0 1

It helps in converting coordinates of a point from one frame to another, useful in

robot motion and kinematics analysis.
2. Rotation Matrix:
A rotation matrix is a square matrix used to describe the rotation of a coordinate
frame or vector in space without changing its position.
For example, in 3D:
𝑟11 𝑟12 𝑟13
𝑅 = [𝑟21 𝑟22 𝑟23 ]
𝑟31 𝑟32 𝑟33

It is an orthogonal matrix where 𝑅𝑇 𝑅 = 𝐼and det⁡(𝑅) = 1.

3. Properties of Rotation Matrix:
1. It is an orthogonal matrix, i.e., 𝑅𝑇 𝑅 = 𝐼.
2. The determinant of a rotation matrix is +1.
3. The inverse of a rotation matrix is equal to its transpose, i.e., 𝑅−1 = 𝑅𝑇 .
4. It preserves the lengths and angles of vectors after rotation.
4. Difference between Proximity and Range Sensor:

Proximity Sensor Range Sensor

Detects presence of an object within a Measures the distance between the

certain distance. sensor and the object.
Proximity Sensor Range Sensor

Gives a binary output (object present Gives a continuous output (exact

or not). distance value).

Example: Infrared, capacitive sensor. Example: Ultrasonic, LIDAR sensor.

5. Given point 𝑃 = (4,6,2)𝑇

Translation:
• In x-direction = +7 units
• In z-direction = −4 units

Translation Matrix:
1 0 0 7
0 1 0 0
𝑇=[ ]
0 0 1 −4
0 0 0 1

New Point:
4 11
6 6
𝑃′ = 𝑇 × [ ] = [ ]
2 −2
1 1

Answer:
Translation matrix as above, and the new point is P′ = (11, 6, −2).
1. Trajectory Planning:
Trajectory planning means deciding the path and movement of a robot from one
point to another smoothly and safely, within a given time and limits of speed and
acceleration.
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Response 2
Trajectory Planning:
Trajectory planning means deciding the path and movement of a robot from a
starting point to an ending point smoothly and safely within a given time.
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2. Joint Space Technique:
In the joint space technique, the robot’s motion is planned by controlling each
joint angle separately from its start position to end position.
It focuses on joint movements, not on the actual path of the end-effector in
space.
3. Cartesian Space Technique:
In the Cartesian space technique, the robot’s motion is planned based on the
end-effector’s position and orientation in the workspace (X, Y, Z).
It ensures the tool or hand moves along a desired path in 3D space, rather than
controlling individual joint angles.
4. Different Motion Paths in Trajectory Planning:
1. Linear Path: The robot moves in a straight line from start to end point.
2. Circular Path: The robot moves along a circular or arc-shaped path.
3. Point-to-Point (PTP) Motion: The robot moves directly from one point to
another without following a specific path.
4. Spline or Curve Path: The robot moves along a smooth curved trajectory
using polynomial or spline functi
5. Intermediate Constraints in Point-to-Point (P-to-P) Motion:
1. Velocity Constraints: Limits on the speed of each joint or the end-effector.
2. Acceleration Constraints: Limits on how quickly the robot can accelerate or
decelerate.
 3. Jerk Constraints: Limits on the rate of change of acceleration for smooth
motion.
4. Obstacle Avoidance: Ensuring the path does not collide with objects.
6. Robot Programming & Languages:
1. VAL (Variable Assembly Language) – used in Unimation robots.
2. RAPID – used in ABB robots.
3. KRL (KUKA Robot Language) – used in KUKA robots.
4. V+ – used in Adept robots.
5. Python/C/C++ – general-purpose languages for robot programming.
6. URScript – used in Universal Robots.
7. LISP & PROLOG – used in AI-based robotics.
7. Robot Teach Pendant Method:
The teach pendant method is a way of programming a robot by manually moving
the robot to desired positions using a handheld control device (teach pendant)
and recording those positions.
It is simple, intuitive, and widely used for point-to-point programming.
8. Robot Textual Method:
The textual method programs a robot by writing instructions in a programming
language (like RAPID, KRL, or VAL) instead of manually guiding it.
It allows precise control over robot motion, loops, and logic for complex tasks.
9. Robot Languages:
1. VAL (Variable Assembly Language) – for Unimation robots.
2. RAPID – for ABB robots.
3. KRL (KUKA Robot Language) – for KUKA robots.
4. V+ – for Adept robots.
5. URScript – for Universal Robots.
 6. Python, C, C++ – general-purpose languages used in robotics.
10. Types of Interpolation Path Functions:
1. Linear Interpolation: Moves the robot in a straight line between points.
2. Circular Interpolation: Moves the robot along a circular or arc path.
3. Spline or Polynomial Interpolation: Moves the robot along a smooth
curved path using polynomials or splines.
1. Advantages of Industrial Robotics (Easy Way):
1. Work Faster: Robots can work continuously without getting tired.
2. Do Jobs Accurately: They make fewer mistakes than humans.
3. Save Money: Less need for human workers for repetitive tasks.
4. Safer Work: Robots can handle dangerous jobs instead of humans.
5. Flexible: Can be reprogrammed to do different tasks.
2. Robot Material Handling Applications:
Robots are used to move, lift, and transport materials in industries. Applications
include:
1. Loading and Unloading: Moving parts or products on/off machines or
conveyors.
2. Picking and Placing: Transferring items from one location to another.
3. Assembly Line Feeding: Supplying parts to machines or assembly lines.
4. Packaging: Arranging and packing products for shipment.
These applications increase speed, reduce human effort, and improve safety.
3. Interpolation Motions in Robotics:
Interpolation motion refers to the robot’s movement along a defined path
between two points in a smooth and controlled way. The main types are:
 1. Linear Interpolation (L): Moves in a straight line between points.
2. Circular Interpolation (C): Moves along a circular or arc path.
3. Spline or Polynomial Interpolation: Moves along a smooth curved path
using polynomials or splines for precise motion.
4. Robot Assembly Operation:
Robot assembly operations involve joining parts together to make a final product.
Robots perform tasks like fitting, inserting, fastening, or welding with high
precision and speed.
Example:
• In the automobile industry, robots assemble car parts such as installing
engines, doors, or windshields.
• In electronics, robots place and solder components on circuit boards.
This improves accuracy, productivity, and reduces human labor.
5. Non-Industrial Applications of Robots:
Robots are used outside industries to assist humans in daily life, healthcare, and
research. Examples include:
1. Medical Robots: Assist in surgery, rehabilitation, and patient care.
2. Service Robots: Help in hotels, restaurants, and cleaning tasks.
3. Exploration Robots: Used in space missions, underwater, or hazardous
environments.
4. Educational Robots: Teach programming and STEM concepts in schools and
labs.
They improve efficiency, safety, and convenience in non-industrial areas.
6. Robot Inspection Application in Manufacturing:
Robots are used to check products for quality and defects in factories. They can
measure, scan, or test parts quickly and accurately.
Example:
• Inspecting car parts for scratches or wrong dimensions.
• Checking electronic components on circuit boards.
This helps ensure high quality, reduce errors, and save time.
7. Feature Applications of Industrial Robots:
1. Material Handling: Moving, loading, and unloading materials.
2. Welding: Spot and arc welding in automobile and metal industries.
3. Painting & Coating: Spraying paint or coatings uniformly.
4. Assembly: Joining parts to make products.
5. Machine Tending: Operating machines like CNC or presses.
6. Inspection & Quality Control: Checking products for defects.
These applications increase productivity, accuracy, and safety.
8. resent Applications of Industrial Robots:
1. Automobile Manufacturing: Welding, painting, and assembling cars.
2. Electronics Industry: Assembling and testing circuit boards.
3. Food Industry: Packaging, sorting, and palletizing products.
4. Pharmaceuticals: Handling medicines, packaging, and inspection.
5. Metal & Machinery: Cutting, grinding, and material handling.
These applications improve speed, accuracy, and reduce human labor.
9. Robot Factors in Industries (Easy Way):
1. Payload: How much weight the robot can carry.
2. Reach: How far the robot can stretch.
3. Speed: How fast it can move.
 4. Accuracy: How correctly it does the job.
5. Repeatability: Can it do the same task the same way every time.
6. Flexibility: Can it do different jobs.
7. Environment: Can it work in heat, dust, or tough conditions.
10. Robot Processing Application (Easy Way):
Robots are used to work on materials like cutting, grinding, drilling, or shaping
them.
Example:
• In metal factories, robots cut or polish metal parts.
• In food factories, robots cut or sort food items.
They make work faster, accurate, and easier for humans.