11.7.1 - Friction Models
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Static Friction
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Today, we're diving into the concept of static friction, or Coulomb friction. Can anyone tell me what static friction is?
Isn't it the friction that prevents two surfaces from sliding against each other when they're not in motion?
Exactly! Static friction acts at low velocities, resisting motion. It’s characterized by a constant opposing force, which we denote with this formula: \( \tau = \tau_f \cdot sign(q̇) \).
What does the \( sign(q̇) \) part mean?
Good question! The \( sign(q̇) \) simply indicates the direction of motion, whether the robot is moving forward or backward.
So that means static friction only comes into play when the robot is trying to start moving from a halted position?
Precisely! And this is crucial during initial movements. Let’s summarize: static friction resists the start of motion and is characterized by a constant force.
Viscous Friction
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Now, let’s talk about viscous friction. Can anyone explain what this type of friction entails?
I think it's related to how fluids resist movement, isn’t it? Like when you try to push a thick liquid?
Exactly! Viscous friction increases with speed and is proportional to the velocity of motion. The formula we use is \( \tau = b \cdot q̇ \), where \( b \) is the viscous friction coefficient.
So, if the robot moves faster, there’s more opposing force due to viscous friction?
Correct! This understanding helps us optimize robot motion at higher speeds. Can anyone summarize how viscous friction influences robotic motion?
It increases the resistance to motion as speed goes up, making it harder for the robot to accelerate!
Well said! Viscous friction indeed makes acceleration harder at higher speeds.
Stribeck Effect
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Now, let’s delve into the Stribeck effect. Who can tell me what happens during the Stribeck effect?
Doesn’t it relate to a drop in friction when the speed is very low, like right before starting to move?
Yes! This occurs when the robot is nearly at rest. Friction decreases significantly, which can lead the robot to start moving more easily.
That sounds like it could create an issue if we’re not careful, right?
Absolutely! This can lead to unexpected motions if not modeled correctly. Combining the effects of static and viscous friction with the Stribeck effect allows for accurate torque calculations.
So, do we use all these components together in our torque calculations?
Correct! The total torque due to friction can be expressed as \( \tau = \tau_f \cdot sign(q̇) + b \, q̇ \). Let's summarize: the Stribeck effect indicates how friction behaves at low velocities, critical for accurate dynamics modeling.
Introduction & Overview
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Quick Overview
Standard
Friction plays a crucial role in robotic systems, impacting the performance and precision of motions. The section examines different types of friction models such as Coulomb (static), viscous, and the Stribeck effect, providing formulas and their implications for torque calculations in robotic actuators.
Detailed
Friction Models in Robotics
In the study of robot dynamics, understanding friction is vital for ensuring accurate and efficient motion control. Friction can manifest in various forms, and the three primary models relevant to robotics include:
- Static Friction (Coulomb Friction): This model describes a constant opposing force that resists the start of motion when the velocity is low. It is characterized by the static friction coefficient and is critical in understanding the initial resistance that a robotic actuator will experience.
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Formula representation:
$$ \tau = \tau_f \cdot sign(q̇) $$
Here, \(\tau_f\) denotes the constant frictional torque. - Viscous Friction: Unlike static friction, viscous friction is proportional to the velocity of the moving parts. As speed increases, the opposing force grows linearly, which is relevant in scenarios where robots operate at faster speeds.
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Formula representation:
$$ \tau = b \cdot q̇ $$
where \(b\) is the viscous friction coefficient. - Stribeck Effect: This describes a phenomenon where friction decreases as the velocity approaches zero, leading to a drop in frictional force. This effect is significant in defining how robots behave when starting or stopping motion.
The overall torque considering friction can be calculated with the combined representation:
$$ \tau = \tau_f \cdot sign(q̇) + b \cdot q̇ $$
This equation indicates that total torque is a function of both static and viscous friction. Understanding these models allows engineers to predict and control robotic movements more effectively, ensuring smoother interactions within various environments.
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Static Friction (Coulomb)
Chapter 1 of 4
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Chapter Content
• Static Friction (Coulomb): Constant opposing force at low velocity
Detailed Explanation
Static friction, often referred to as Coulomb friction, is defined as the force that opposes the start of motion between two surfaces that are in contact and at rest relative to each other. This force remains constant until a certain threshold of applied force is surpassed, at which point the object will begin to move. At low velocities, static friction is able to counteract small forces without movement occurring. Once the applied force exceeds the maximum static friction, motion will begin.
Examples & Analogies
Imagine trying to push a heavy box on the floor. Initially, there's a constant force resisting your push—the static friction—holding the box in place. Only when you push hard enough to overcome this static friction does the box slide across the floor.
Viscous Friction
Chapter 2 of 4
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Chapter Content
• Viscous Friction: Proportional to velocity
Detailed Explanation
Viscous friction is the type of friction that opposes the motion of an object in a fluid (which could be a liquid or gas) and increases with the speed of that motion. Mathematically, it is represented as a force that is directly proportional to the velocity of the moving object. Essentially, the faster you move through a medium (like water or air), the greater the resistive force you encounter due to this type of friction.
Examples & Analogies
When you try to swim through water, you feel a resistance that gets stronger as you swim faster. This is viscous friction; the more quickly you try to move through the water, the more resistance you face, which can make swimming harder.
Stribeck Effect
Chapter 3 of 4
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Chapter Content
• Stribeck Effect: Drop in friction near zero velocity
Detailed Explanation
The Stribeck effect describes a phenomenon where friction decreases as the velocity of an object approaches zero. Initially, as speed reduces, static friction is dominant; however, as the velocity nears zero, the effective friction reduces, transitioning into viscous behavior. This leads to a drop in frictional resistance, which can be observed in lubricated systems where a film of lubricant forms at lower speeds, allowing for smoother operation.
Examples & Analogies
Think of riding a bicycle. When you are moving at speed, you can feel some resistance against the wheels due to friction. However, when you slow almost to a stop, you may notice that it becomes easier to keep the bike rolling. This is because the frictional force decreases when very little motion is occurring, thus resembling the Stribeck effect.
Total Torque Due to Friction
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Chapter Content
Total torque due to friction:
τ = τ_f · sign(q˙) + b · q˙
Detailed Explanation
The total torque exerted by friction is a combination of two components: the first component τ_f, which is influenced by the direction of motion (given by sign(q˙), indicating the direction), and the second component which depends on velocity (b · q˙, with b being a constant related to viscous friction). This equation allows for calculating the net torque experienced by a robot or mechanical system due to frictional forces, considering both static and viscous contributions.
Examples & Analogies
When you pull a drawer, the amount of torque you feel varies with both the speed at which you pull and the resistance of the drawer due to friction. Initially, the static friction holds it in place until you pull hard enough, then moving it encounters both the change in direction and resistance, described by this equation.
Key Concepts
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Static Friction: A constant force opposing the start of motion.
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Viscous Friction: A force opposing motion that increases with the speed of the moving body.
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Stribeck Effect: The phenomenon where friction decreases at very low velocities.
Examples & Applications
A robot arm experiencing resistance when attempting to start moving due to static friction.
An automated vehicle encountering resistance based on its speed due to viscous friction.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
Friction static fights the start, while viscous slows the mover's heart.
Stories
Imagine a robot robotically trying to start moving, but a strong static force holds it back. As it pushes harder, viscous forces increase as it moves faster, but just at the moment it almost stops, it suddenly leaps forward due to the Stribeck effect.
Memory Tools
S-VS: Static, Viscous, Stribeck - remember the types of friction!
Acronyms
F-SVE
Friction consists of Static
Viscous
and Stribeck Effects.
Flash Cards
Glossary
- Static Friction
The frictional force that opposes the initiation of motion between two surfaces at rest relative to each other.
- Viscous Friction
The frictional force that is proportional to the velocity of an object, typically observed in fluid dynamics.
- Stribeck Effect
A phenomenon where friction decreases as the velocity approaches zero, impacting the initial stages of motion.
- Torque
A measure of the rotational force applied at a point, crucial in assessing motion dynamics in robotics.
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