Questions tagged [dynamics]
Questions about the dynamics of a system. Currently there is a very large scope ranging from from dynamics in mechanics, vehicle and flight dynamics, to system dynamics and fluid dynamics.
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Inverted pendulum PID: controller causes cart to move at constant velocity?
I am trying to understand the PID controller of an inverted pendulum on cart system through this MATLAB article: https://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum§ion=...
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Modeling of Wheel Rolling Resistance
I have been working on longitudinal tire model for a while and constantly encounter problems with the formulation of rolling resistance. Consider one wheel model coming down from a damp. It is a 2DOF ...
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Is it possible to design the gain Kp for the system in the image, given it is underdamped and has a settling time of 2 seconds. Thank you
$$G(s) = \frac{K_P}{(s+2)^2}$$
$$H(s) = s+4$$
I keep getting Kp = 0 which leads to a damping ratio of 1 which isn't underdamped. To find Kp = 0, I found the closed loop transfer function and compared ...
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System identification of Blue Robotics Thruster with Simscape multibody
I have CAD design of a Blue Robotics Thruster 200.
The thruster is imported to Simulink.
From data given Blue Robotics Thruster 200 have MATLAB system identification toolbox been used
to generate ...
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Spring constant of angled beam
I'm trying to solve for the dynamics of three blocks, shown below. Two blocks are pushed into a central shuttle, and their force is transmitted through a thin angled beam/pawl. The pawl bends when ...
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Distributed load on a slope/axle
In statics they teach you about distributed beams, how to calculate the total force, the engagement point, etc. I can't find any information anywhere on distributed loads on unevenly sloped surfaces / ...
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How do you go about picking a belt in design?
So when you want to pick a beam to use or determining the thickness of a load bearing beam, or picking bearings, there is some calculations you do to see if its life expectancy or f.s or to see if the ...
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Question about dynamics n-t coordinate system
et = tangential unit vector
en = unit vector in normal direction
I'm currently studying dynamics and I'm having difficulty understanding the process of obtaining det and det/dt in the n-t coordinate ...
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Would the angular acceleration be the same but in the opposite direction?
The acceleration of point B of a on a rigid body would be:
Problem what im confused about is if you were to find the acceleration of A, would alpha be the same magnitude but in the opposite direction?...
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How to calculate the centripetal force along a cartesian axis?
If a centrifuge without a ballast is centered on the origin of an x-y coordinate plane, and starts at the x-axis rotating with increasing velocity counter-clockwise around the origin, how can the ...
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Dynamics of a Releasing Centrifuge?
If 10Nm of torque are applied to a centrifuge with ballast and payload and we assume that the weight of the centrifuge itself is negligible(ignored), then 5Nm go to the payload and 5Nm go to the ...
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Linkage Mechanism Doubt
I am unsure how I would solve this. I have tried to solve it and got -29.1 but my attempt was wrong.
Could someone please lead me in the right direction or show me the way to solve this?
Thank you.
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Why can’t we accelerate a rotating object after some point?
If I push an object in a linear way with constant force bigger than frictional force on ground, the object will accelerate more and more until air drag force matches it. Logically, If I add the same ...
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How does 2nd gear create more thrust than 1st gear?
Let’s analyze a vehicle parallel to velocity and forces applying on it.
The 1st gear has a maximum velocity value after which you can’t accelerate more. It means that thrust force on wheels generated ...
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Torque created at bottom left corner due to torque in centre of 2D box
If I have a 2D box with uniform mass of width $w$ and height $h$. I apply a torque $\tau_O$ to the centre of the box, labeled $O$. The box has a fixed point $A$ at the bottom left around which it may ...
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Effect of Earth's rotation on moving vehicles
The earth rotates at a rate of 460 m/second. I wish to predict the position and approach for landing an UAV (quadcopter) on the vehicle.
I have a free-moving landing platform on vehicle that aligns ...
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Lagrange Mechanics 2 DOF System
Using Lagrange mechanics, how would one define the potential energy of the system? Defining coordinates relative to the system's static equilibrium position would result in there not being a (m1)(g)(y)...
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Minimum torque required to turn a large gear
I want to preface this by saying that this isn't homework, it's just a question I've made up myself (so it could just be impossible to solve), and I am a beginner so apologies if I miss something ...
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Investigation of Body Motion in SolidWorks: Euler Angles Rate or Angular Velocity?
This is my first question in this community.
I decided to demonstrate my problem on simple rigid body, but task may be applied to more complex shapes. So, a cube is built in SolidWorks:
Using the ...
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Intermediate Dynamic Equation of Motion
If I were to determine the equations of motion for a symmetric top that is both spinning and allowed to translate in a single horizontal direction via its contact point.
How would I determine the ...
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Verification of Accelerometer offset calculations occurring due to placement of Accelerometer away from centre of rotation in a rigid body
I have evaluated the Accelerometer offset occurring due to placement of Accelerometer away from the centre of rotation of body. In the below evaluation I am trying to calculate Accelerometer's reading ...
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Where will the load be applied on the beam
In a Newton's cradle, just like the one from the picture, where will the load of the spheres be applied on the right-hand beam?
Will it be a transverse load? The wire is connected laterally, not at ...
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Calculation of Accelerometer offset for Placement of Inertial measurement unit away from centre of mass
I am working on a 6DOF IMU that contains a 3 axis accelerometer and a 3 axis gyroscope, I am building a project to
plot the position and orientation of a vehicle/dirt bike in a 3d plane, However the ...
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Center of gravity offset for accelerometer and gyroscope readings
I am working on a 6DOF IMU that contains a 3 Axis Accelerometer and a 3 Axis Gyroscope.
I am building a project to plot the postion and orientation of the turret/cabin in a crane in 3D space.
The IMU ...
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Tensor of inertia of a curved beam
I need help calculating the inertia tensor for a curved beam.
I found the formulas for this in the article https://hal.archives-ouvertes.fr/hal-01084693/document[page 20, Appendix A] and decided to ...
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Transfer function to get linear velocity from a dc motor system
So I have to create a control system simulation from scratch for the following scenario. For a bicycle-like system, there is a motor attached directly to the rear wheel. From here, the goal of the ...
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Lewis form factor in between teeth
I’ve got total gear ratio of 3.428 but it’s a double step up gearbox. So I have to sq root it get the ratio of the pairs which is 1.851. For the small cog I have to use a min of 18 teeth. So teeth x g ...
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State Space Modeling nonlinear terms of vehicle’s longitudinal motion
My project is to build a software to help drivers achieve ecodriving thanks to optimal control based advices. Consequently, to feed a linear quadratic regulator, vehicle longitudinal equation of ...
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What would the dynamics and measurement operators be in this control theory problem/code, and where can I generate them from?
I'm working on something slightly outside of my scope of work, and I can't figure out if I fully understand what these things mean. Could someone help explain what the dynamics operator and ...
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How to determine which variables are state or input variables in dynamic modeling?
When given a P&ID and a process flow diagram, and asked to determine which of the relevant variables to a process input variables, and which are state variables (eg.: mass flow, temperature, ...
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Running a Dynamic Model as Steady State with Time Varying Inputs
I am attempting to run a dynamic model of a waste heat recovery system (Brayton Cycle with intercooling) on IDAES but I keep getting errors on initilization seemingly no matter what I do. My work ...
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Differences on methods of solution on problem
It is asked to find the velocity and acceleration of the plataform:
Determine the velocity and acceleration of platform $P$ as a function
of the angle of cam $C$ if the cam rotates with a constant ...
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Kinematics of actuated disk with no slip
Given the following kinematic problem, how would one calculate the velocity $v_C$ of point C given a certain horizontal velocity $v_{E}$ in point E? Given is that the disk does not slip and cannot ...
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Analysis of a Beam under Non-static Case
I am interested in the distribution of the beam in nonstatic cases.
Typically we discuss the stress, and moment distribution when a beam is in a static case.
However, I am interested in this ...
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Finding angular velocity through absolute motion analysis
I am seeking help for a textbook question that I am stuck on.
My work is attached below. I broke the velocity vector into two components, one that is perpendicular to the wedge, causing the rod to ...
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Why is the tangential acceleration the same for two gears at the contact point?
Looking at the following question:
The part of the solution I am interested in is as follows
Since the tangential velocities are the same, we could use equation 3 to solve for the angular ...
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Confusion with Measuring Velocities in a Translating/Rotating Reference Frame: Combining Transport Theorem and Homogeneous Transformations
The inertial reference frame is denoted by $I$, the position, velocity, acceleration, angular velocity, and angular acceleration of reference frame $S$ is measured in the inertial frame, reference ...
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How to calculate the degrees of freedom, constraints and the generalized coordinates in this dynamic system
The rope lengths are taken to be constant.
Solution:
$N$ particles with $k$ constraints.
. Then the Degree of Freedom (DOF) is $3N-k$.
In Figure 1, we have two particles $m_1$ and $m_2$, so $N=2$. But ...
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Dynamic Analysis Of A Four-Bar Linkage Powered By A Motor
Below is the dynamic analysis for a single rotating link which is driven by a motor. It shows the 2d front view and the 3d full view. The equations for the analysis require knowing the location of the ...
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How to calculate max load on a custom hitch?
Non engineer here. I'm interested in a conservative calculation of max trailer load for existing frame members for a truck I have. The truck is rated at ~8800lbs towing when stock and with a ...
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Question about engine reaction torque from gas forces
in the figure below the reaction torque equation is given by Fg41.x trying to rock the ground plane about the O2 pivot due to gas forces . My question is if the piston with the cylinder whole assembly ...
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Difference between body-fixed angular velocity and the rate of change of Euler angles?
I'm visualising the motion of a rigidbody in 3D space with MATLAB and Simulink using this library which implements 6DOF equations of motion based on applied forces and moments.
Here is my model so far ...
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Sign Convention for Energy Methods in Vibration Analysis
Find the equivalent spring stiffness of the system below.
I was able to solve it using Newton's second law and got the result below.
$$ k_{eq} = \frac{mgl}{2} - \frac{k_1 l^2}{16} - k_2 l^2$$
However,...
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How to get correct yaw and pitch after rotation
I am trying to come up with a "stabilization" algorithm for an antenna dish. The dish can move in the azimuth (yaw) and elevation (pitch) directions. But the boat it is mounted to, moves in ...
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What is the effect of caster angle in automobiles? What will happen if we use neutral caster?
What is the effect of caster angle in automobiles and what will happen if we use neutral caster?
We study that positive caster makes vehicle more stable at high speeds. It increases lean while ...
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Entrainment Speed in Ball Bearing
Assuming no slip between the inner race and the outer race of a ball bearing, what is the entrainment speed between the balls and the inner race? The inner race is rotating at $\omega_i$ and the outer ...
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Clarification of a piston and crank dynamics question
Yesterday, I had an Engineering Mechanics exam which involved a Piston and a Crankshaft engineering dynamics problem, which I was a bit stumped about. I sought clarification from the teaching staff ...
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Spring and damper in series, equation of motion
For the motion in fig 4.1 (a), please check the description of this system in the images above, everything should be there. I get it, assuming the positive direction is downward, the spring tension is ...
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How to replace these two forces with one force?
Here, $P>Q$. $O$ is the center of mass of the rigid and uniform bar/stick.
As $P>Q$, the resultant is situated to the right of $\vec{P}$ and is parallel to $\vec{P}$. The magnitude of the ...
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Estimating yaw torque and power of HAWTs
I am trying to estimate the amount of torque and power required to rotate a 3 bladed Horizontal Axis Wind Turbine (HAWT) about a vertical axis("yaw" motion). I would like to estimate the ...
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