TOPIC 1:
DESIGN OF A CARTESIAN ROBOT
WHAT IS A CARTESIAN ROBOT:
Cartesian system is one that moves in three, orthogonal axes — X, Y, and Z — according to the Cartesian coordinates.
What makes a Cartesian robot a robot is that the axes perform coordinated motion, through a common motion
controller.
The axes of a Cartesian robot are made from some form of linear actuator. Cartesian robots can be constructed from
any type of linear actuator with any variety of drive mechanisms — belt, ball or lead screw, pneumatic actuator, or
linear motor. (Note that rack and pinion drives are also possible.
Applications:
Pick and place
3D printer for making objects
Labelling
Measuring
Components of Cartesian Robots:
1. Motors: Motors are essential components responsible for the movement of Cartesian robots. Electric
motors, such as stepper motors or servo motors, are commonly used.
2. Actuators: Actuators are mechanisms responsible for converting electrical signals into physical motion. In
the context of Cartesian robots, actuators play a crucial role in moving the robot along its linear axes.
Pneumatic and hydraulic actuators might be introduced for larger-scale robots.
3. Controllers: Controllers act as the brain of the Cartesian robot. These are devices or systems that process the
input signals (commands) and convert them into outputs that drive the motors or actuators. Microcontrollers
or programmable logic controllers (PLCs) are commonly used as controllers in robotics.
4. End-Effectors: Discuss the concept of end-effectors, which are tools or devices attached to the robot's arm
for performing specific tasks. In the case of Cartesian robots, end-effectors might include grippers, welding
tools, or sensors. Emphasize the importance of selecting the right end-effector based on the robot's intended
application.
5. Frames and Structures: The frame or structure of the Cartesian robot provides the support and rigidity
necessary for precise movements. Explain the importance of a sturdy frame to prevent vibrations and
inaccuracies in the robot's motion.
6. Linear Guides and Bearings: Cartesian robots rely on linear guides and bearings to facilitate smooth and
accurate movement along the X, Y, and Z axes. Discuss the different types of linear guides, such as ball screws
or linear rails, and how they contribute to precision.
7. Sensors: Introduce sensors used in Cartesian robots for feedback and control. Encoders, proximity sensors,
and vision systems are examples of sensors that provide information about the robot's position, speed, and
the environment. Explain how sensors enhance the robot's ability to adapt to changing conditions.
8. Power Supply: Discuss the power requirements of Cartesian robots. These robots typically require electrical
power to drive motors and controllers. Touch upon considerations such as voltage, current, and power
consumption.
9. Cables and Wiring: Cables and wiring connect various components of the Cartesian robot, ensuring the
seamless transmission of signals and power. Emphasize the importance of organized and well-maintained
wiring for reliable operation.
Linear Actuator for Cartesian Robots:
There are various types of linear actuators used in Cartesian robots, and the choice depends on factors such as
precision, speed, and load capacity. Common types include:
1. Screw-Driven Actuators: These use a screw mechanism to convert rotary motion into linear motion. Ball
screws, lead screws, and acme screws are examples.
2. Belt-Driven Actuators: These use a belt and pulley system to drive linear motion. They are suitable for
applications requiring high speed and moderate precision.
3. Linear Motor Actuators: These actuators use the principle of electromagnetic interaction to produce linear
motion. They are known for high precision and rapid acceleration.
Lead Screw [SDP/SI], Rack and Pinion [QTC Gears], Ball Screw [Reliance Automation], Fixed Belt [Bell-Everman]
DESIGN OF SCREW ACTUATOR FOR CARTESIAN ROBOT
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Designing a screw actuator for a Cartesian robot involves several steps. Here's a general guide:
1. Define Requirements:
Determine the load capacity: Understand the maximum weight or force the screw actuator needs to
handle.
Define travel distance: Specify the range of motion required for your Cartesian robot.
Establish speed and precision requirements: Decide on the desired operating speed and positional
accuracy.
2. Select Screw Type:
Choose between ball screws, lead screws, or roller screws based on your application requirements.
Ball screws are often preferred for high efficiency and precision.
3. Calculate Load and Torque:
Calculate the load on the screw, including the weight of the payload and any external forces.
Determine the torque required based on the load and the desired acceleration.
4. Select Motor and Drive System:
Choose a motor that can provide the required torque and speed.
Select a suitable drive system, considering factors like efficiency, backlash, and resolution.
5. Consider Environmental Factors:
Account for environmental conditions such as temperature, humidity, and cleanliness, as these can
affect the performance and lifespan of the screw actuator.
6. Choose Material and Size:
Select materials for the screw and other components based on factors like strength, durability, and
corrosion resistance.
Determine the size of the screw based on load and torque requirements.
7. Check for Backlash and Efficiency:
Evaluate the backlash in the system, as it can affect precision.
Consider the efficiency of the screw actuator to minimize power losses.
8. Design Support Structure:
Design the support structure for the screw actuator, ensuring it can handle the loads and provide
rigidity.
9. Safety Considerations:
Implement safety features such as limit switches and emergency stops to protect the system and
users.
10. Prototype and Test:
Create a prototype of the screw actuator and test it under various conditions to ensure it meets the
specified requirements.
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Sample Question for design of linear actuator made of steel for cartesian robot
Given:
Load to be lifted: 10 kg
Travel distance: 1 meter
Rpm= 100 rad/s
Efficiency: 90%
Safety factor: 1.5
Assume lead as 2mm
SOLUTION:
Step 1: Calculate all forces
F=ma
F= 10 x 9.81= 98 N
Step 2: Calculate all torques
Torque 1: gravtitaional torque
Torque 2: Frictional torque
T1= F x D = 98 x 0.5 m= 49 N.m
T2= lead / 2 x 3.142 (98 + 0.74 x 98)= 0.054 N.m
T= T1+T2 = 49.1 N.m
Step 3: Motor Selection
T x safety factor = 49.1 x 1.5 = 73.5 N.m
Step 4: Linear Speed
Linear speed = rpm x Distance/
Speed = 100 x (lead x 0.001)/ 2 x π
Linear Speed of actuator = 0.0318 m/s
Linear Speed of actuator =0.0318 m/s/ 0.9
= 0.035 m/s
QUESTIONS:
Q1. Design a linear screw actuator for a Cartesian robot made of aluminum of length 35
cm moving with 220 rpm with lead of 3mm and safety factor 1.5. Choose suitable motor
for the actuator and compute the speed of the actuator. Payload is 1 kg
Q2 Design a linear actuator made of copper for a cartesian robot. The arm needs to
extend to reach objects, and the maximum load it will carry is 2 kg. The extension
distance is 0.4 meters, and the desired speed is 210 rpm. Consider an efficiency of 92%
and a safety factor of 1.2.
Q3. Design a linear actuator made of brass to lift a load of 3 kg over a travel distance of 40
cm. The desired speed is 180 rpm. Assume an efficiency of 85% and a safety factor of 1.3.
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Design and analyze the workspace of a 2-axis Cartesian robot with the following
parameters:
d1=0.2m (length of X-axis),
d3=0.5m (length of Z-axis),
θ=90∘ (rotation angle).
Forward Kinematics:
The forward kinematics equations for this Cartesian robot might be:
X= 0.2 cos theta =0
Y= 0.2 sin theta=0.2 m
Z= 0.5 m
x y
z
STRESSES
The stresses calculated for the actuator of a Cartesian robot typically include:
Axial Stress ϭ = F/A
This is the stress along the axis of the actuator. It occurs when the actuator is subjected to tension or compression
forces due to the load it is moving.
Shear Stress: Shear stress can occur in the actuator if there are forces applied parallel to the cross-sectional area.
However, in many Cartesian robots, the primary stresses are axial, and significant shear forces might be limited.
Shear stress = F/A
Bending stress:
If the actuator is subjected to bending moments, bending stress can be calculated. This is more relevant if the
actuator is not purely axial and experiences bending due to the configuration of the robot.
Ϭb = Mc/I
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Compute stress
Axial force (F): 98 Newtons
Diameter of the screw (D): 0.02 meters
Lead of the screw (L): 0.002 meters (2 mm)
Modulus of elasticity (E): 2.1e11 N/m² (typical for steel)
Step 1: thread area: π (D-L)/4
Step 2: Stress = F/A
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