# What is Dof: Definition and 40 Discussions

DÖF (Deutsch-Österreichisches Feingefühl), (German-Austrian sensitivity), was a 1980s Austrian-German Neue Deutsche Welle pop band, best known for their 1983 single "Codo".

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1. ### I Factors that influence depth of field

I came across a youtube video that discusses some aspects of depth of field in photography/videography. Some things that have been said collided with my understanding of DOF. I then had a long discussion with the creator of the video that unfortunately lead nowhere. I'm no scientist, so I lack a...
2. ### Boundary conditions in Ansys

Hi, I have one question related to the boundary conditions I should apply in a Static Structural simulation for the following support. The support is subjected to the following loading conditions shown below...
3. ### Engineering Mechanical Vibrations - 2 DOF System - Rod with 2 springs

Hi, So the question is to: derive the equations of motion for the following in terms of x1 and x2? The bar is assumed to be light and rigid. (NB. I know I posted another vibrations problem earlier in which I tried to use an energy approach to get to the equations of motion. However, we haven't...
4. ### A Heuristic Approach EFE: Why 10 DOF?

Some sources state we seek 10 dof ( and so ofc this is a symmetric two index tensor.My question is why we seek 10 dof in the first place ?Many thanks
5. ### I Can Fundamental Theorem Algebra be proven by simple DOF?

A monic polynomial of degree N has N number of coefficients. The product of N number of linear factors has N number of free terms. A complex number has 2 DOF. Therefore, both a monic polynomial and the product of free terms have 2N number of DOF of real values. Thus, it must be possible to...
6. ### Inverse Kinematics of a 6 DOF Robotic Arm

Homework Statement Hello. My colleague and I have been struggling with this assignment where we have to: - Given the position and orientation of the end-effector of a robotic arm with 6 degrees of freedom get the joint angle values (inverse kinematics). The robotic arm in question is the...
7. ### Eigenfrequencies of a multiple DOF system

I am confused with this concept. So if a system possesses multiple possible eigenfrequencies (and therefore modes), how does the system "know" which eigenfrequency will it want to vibrate on? Does that depend on the initial condition you give the system? Is there any mathematical relation...
8. ### I Gravity's Degrees of Freedom: Explored

Commonly it is said that the gravitational field has 6 degrees of freedom (a symmetric tensor, that is 10, minus 4 conservation laws). But is this accepted without any dispute? The reason for my question are so called "indirectly coupling" models, where the primary gravitational field is...
9. ### Exact constraint in practice -- Pinned joint with 2 DOF

I've come across this design issue several times, and don't know of any solution in industry. The basic assembly is this: A spherical bearing is fitted to a threaded rod end with a nut to clamp the ball to the rod end. The design intent is to allow angular displacement about the two axes...
10. C

### 2-DoF system characterization with 2 dual axis accelerometers

I've been having some trouble with this problem for a while. (Its not a homework or coursework problem) Its a part of an experimental set up that I'm building and this is a simplified version of it. I have a rigid rod which is hinged at a point and can pitch or heave about that location. There...
11. ### I Energy-time versus time bin DOF

With respect to entanglement, is the energy-time degree of freedom continuous whilst the time bin DOF is discrete or is there some other difference (if any) ?
12. ### Can I Use a Non-Symmetrical Matrix in Simulink for My 2 DOF Vibration System?

Homework Statement I have the following system, I believe I've correctly established the equations. I'm having trouble building a working schematic bloc in Simulink. Homework Equations The Attempt at a Solution In the following equations Ktrain = Ka and Ctrain = Ca I know my matrix should...
13. ### I How many degrees of freedom does a swan's neck have

how many degrees of freedom swan's neck have
14. ### Free vibration of 100 DOF spring

Hi, I have just started reading of "finite element model updating" which is a statistical means of updating the finite element model when there is source of uncertainty in the modelling parameters, modelling error, etc. My question below is NOT related to finite element model updating but to a...
15. ### I Finding eigenvalues for 4 DOF system

Hey all, I've derived a fourth order dynamic system as represented by the following: I need to determine the eigenvalues for this system to check whether they're purely real with no imaginary components. How should I go about doing this? I have done eigenvalue problems in the past, but not to...
16. ### Understanding the four bar linkage DOF

Hello guys, I have a doubt with understanding DOFs. I have taken the example of the four bar linkage. According to Grueblr's condition, the DOF of this mechanism is 1. \mbox{DOF} = 3(l-1) + 2j_1 + 2j_2\\l=4\ j_1=4\ j_2=0\\\mbox{DOF} = 1 In the above figure, the links next to the ground link...
17. ### Dynamic Analysis of a 5 DoF robot

Homework Statement Homework Equations N/A The Attempt at a Solution I am confused as to where the ω3sin(θ)k term disappeared to? It is not included in the very last line? I asked my lecturer and he said it's ''constant'' but he kind of shrugged off the question. I understand everything...
18. ### A Free damped vibration of a system of 2 dof, demostration

Hi,I need help please, i want to know how to solve de differential equation of a system of two degree of freedom using eigenvalues or eigenvectors or if I can use any another way to solve this kind of equations.
19. ### A Free damped vibration of a system of 2 dof, demostration

Hi,I need help please, i want to know how to solve de differential equation of a system of two degree of freedom using Heigenvalues or Heigenvectors or if I can use any another way to solve this kind of equations.
20. ### Equations of motion for 4 dof

Hi all, I'm working on a project to control the angles of a beam(purple) with a quadcopter(orange),see figure below. The angles for both the ground-beam and beam-quadcopter will be measured with joysticks, so only roll and pitch angles will be measured and the yaw rotation is fixed. To obtain...
21. ### How to Solve a Mixed 2 DOF Vibration Problem with Incorrect Free Body Diagram?

I am struggling with the following question, it is a mixed (lever and linear) 2DOF vibration problem, something I never came across before. I am afraid I am missing something on the FBD, thus the differential equations of motions are wrong. Homework Statement Homework Equations...
22. ### Two DOF Anglepoise Spring-balance with Distributed weight

I am designing a a robot arm based on the two degree of freedom anglepoise lamp, like the typical desk lamp or Pixar lamp, that consists of two parallelograms, each balanced with a spring. The goal is to design it so that it remains statically balanced at all positions and let two springs carry...
23. ### Deriving Average Energy Function For A Classical DOF

Hello everyone, The problem I am currently working is exactly what is given in this link: https://www.physicsforums.com/showthread.php?t=554243 However, I do not understand why we integrate between 0 and infinity. What is the motivation for doing so?
24. ### Applying 3 Concurrent Angular Velocities to Vectors

This problem has me stumped. I'm toying with a stabilization platform design which has 3 gyroscopes supplying angular velocity -- one for each axis (x,y,z). The model has units vectors (x,y,z) representing the platform's orientation in space. The question is how do I apply the 3 orthogonal...
25. ### Undamped 2 DOF vibration. What should the eigen vectors be here

Normal modes of vibration, two masses, two spring, arranged vertically with m2 at the top, m1 underneath arranged (top to bottom) m2, k2, m1, k1, rigid support I have solved the first part of an undamped coupled spring problem to give m_1m_2 \omega ^ 4 + ((m_1+m_2)k_2+m_2k_1)\omega ^2...
26. ### Free Vibration of Spring system with two DOF

In some questions I am doing, you set of a pair of simultaneous equations and in the notes we have that . For a non trivial solution of X1 and X2,the determinant of coefficients of X1 and X2 must be zero. An equation might typically look like this (m \omega^2 +k_1)x_1 +k_2 x_2=0 Why must...
27. ### Analysis of mechanism, DOF, repeated bonds of mechanism

Analysis of mechanism, DOF, "repeated bonds" of mechanism Homework Statement The scheme is incomplete, nevertheless it is the way it is. It is required to determine the number of degrees of freedom for the given mechanism. Also, to find the number of "repeated bonds" (my english is poor) in...
28. ### 2 DOF oscillator max force reponse

(NOTE, this is not a homework problem, but it sure seems like one) Hello, I am mounting a component onto structure and I need to determine the maximum force input into the component. My system can be represented by a base driven two degree of freedom oscillator...
29. ### 2 DOF oscillator max force response

Hello, I am mounting a component onto structure and I need to determine the maximum force input into the component. My system can be represented by a base driven two degree of freedom oscillator: http://www.freeimagehosting.net/newuploads/xowmr.png I need to determine the force...
30. ### Automotive Gravity term in simple 2 DOF quarter car model?

Hello all I am trying to derive a quarter car model that i can use Simulink to analyse. The model is 2 DOF and consists of 1 sprung and 1 unsprung mass, suspension spring and damping co-effs, and tyre spring and damping co-effs. Positive is taken as upwards, compression is also taken as...
31. ### Interesting DOF Result: No Matter Focal Length, Ratio is Constant

Perhaps it is known to you, it was something new to me. After Andy confirmed that reasonable circle of confusion for my camera should be about 0.02mm, I did some calculations - and I was surprised by the result. Say you have an object that you want to take a picture of (be it flower, book...
32. ### Is MATLAB's ode45 Suitable for Solving 2D Coupled Nonlinear ODEs?

Can anyone please suggest whether I can use MATLAB ode45 for the numerical solution of the following equations? mx ̈+ c_x x ̇ + k_x x= F_x0+ μ(v_r ) (K 〖VB〗^2 y ̇/v) sgn(v_r ) my ̈+ c_y y ̇+ k_y y= F_y0+ (K 〖VB〗^2 (y/v) ̇ ) Where, m, c_x, k_x, c_y, k_y, F_x0, F_y0, K, v are known...
33. ### Minimizing in the 6 dof of rigid bodies

Hello -- I want to solve a very general type of minimization problem. I have 2 rigid bodies (e.g. molecules) which are exerting forces on each other, and I want to minimize the interaction energy (e.g. from a molecular forcefield with terms for things like Coulomb, van der Waals, etc). In...
34. ### DoF of a Gauge Boson - Why Only 1 for Virtual Photons?

As we know, the number of physical degrees of freedom(DoF) for a photon is 2. I can understand this by gauging away redundant DoF's by gauge fixing. For example, in QED, by fixing the Lorentz gauge \partial_\mu A^\mu = 0 , we could get rid of one DoF, moreover, the residual gauge...
35. ### Lagrangian, 2 DOF (rotation with torsion, springs)

Homework Statement [PLAIN]http://mityaka.com/users/kolodny/img/lagprob.png Homework Equations L = T - V T = \frac{1}{2}*m*U2 Vs = \frac{1}{2}*k*x2The Attempt at a Solution I worked out the equations of motion as: FL = m*\ddot{y}+k*y-k*b*\theta FL*e =...
36. ### How to count on-shell DoF of a gauge theory?

Suppose I have a gauge potential A_{\mu\nu}, which is totally antisymmetric, if, say, the theory is in 6 dimensions, so that there are 6\times5/2 = 15 degrees of freedom. For the action S = \int d^6x F_{\mu\nu\rho}F^{\mu\nu\rho} , where F_{\mu\nu\rho}\equiv \partial_\mu A_{\nu\rho} +...
37. ### Deriving Equations of Motion for Compound Pendulum with 3 DOF

Can anyone help? I have to derive eq of motion of a compound pendulum with 3 rotational dof. I know how to do it, for simple pendulum (using Lagrangian's).
38. ### Equation of Motion for 2 DOF spring damper system

Please guide me towards the "differential equation of motion" for the following 2 DOF Spring-damper system. And furthermore, if above system is in a uniform speed rotating frame, then what can be the effect on this system? Thank you very much.
39. ### Response to a forced 2 DOF system

I have a forced 2 degree of freedom system that I am trying to find the steady state responses to. I have determined the two equations of motions and found the [m], [k], [c], and {f} matrixes. However when i try to use eigen analysis ( q=phi'*[m]*phi ) I am unable to uncouple the two...
40. ### Physical explanation for camera DOF (depth of field)

http://en.wikipedia.org/wiki/Depth_of_field" stands for the range that is sharp on a photograph. The bigger the diafragma (camera opening) the smaller the range that will be sharp on the picture. A bigger diafragma also means a shorter shutter opening (so the picture doesn't become too...