A joint or articulation (or articular surface) is the connection made between bones in the body which link the skeletal system into a functional whole. They are constructed to allow for different degrees and types of movement. Some joints, such as the knee, elbow, and shoulder, are self-lubricating, almost frictionless, and are able to withstand compression and maintain heavy loads while still executing smooth and precise movements. Other joints such as sutures between the bones of the skull permit very little movement (only during birth) in order to protect the brain and the sense organs. The connection between a tooth and the jawbone is also called a joint, and is described as a fibrous joint known as a gomphosis. Joints are classified both structurally and functionally.
I'm trying to understand bolted joints better. For reference, this is from Shigley’s.
Conceptually it makes total sense. And it is obviously right especially because it's in THAT book. But when I try to test it myself some contradictions appear and I can't understand what's happening.
First...
The titular paper can be found here, https://doi.org/10.1088/1751-8121/ac6f2f, and on arXiv as https://arxiv.org/abs/2101.10931 (which is paginated differently, but the text and equation and section numbers are the same). Please see the abstract, but in part this 24 page paper argues that we...
Homework Statement:: This is not a homework, but I want to know how to find the joint reaction force of the 2d elbow flexion, if I know the angular acceleration of the forearm, and the mass of elbow with a known weight on hand. I assume the forearm is a simple cylinder. Suppose the angular...
I want to know how did author derive the red underlined term in the below given Example?
Would any member of Math help board enlighten me in this regard?
Any math help will be accepted.
$$f_{XY}=1$$
$$dzdy=2xdxdy⇒\frac{1}{2\sqrt{z}}dzdy=dxdy$$
$$f_{ZY}=\frac{1}{2\sqrt{z}}\quad \text{on some region S}$$
$$F_{ZY}=\int^y_{g}\int^x_{h}\frac{1}{2\sqrt{z}}dzdy\quad\text{for some}\quad g(x,y),h(x,y)$$
im learning how to find the region S using a change-of variables technique
we haven't learned howw to do parts d-f yest. could you please give me a hand?
(a)
$$E(X)=E(Y)=\int_0^3\int_0^3\frac{1}{9}dxdy=\frac{3}{2}$$
(b)its typoe suppoesed to be W=Y-2
$$E(Z)=E(X-2)=E(X)-E(2)=-\frac{1}{2}$$
$$E(W)=E(Y-2)=E(Y)-E(2)=-\frac{1}{2}$$
(c) i guess joint pdf from ##E(Z)## and...
(a)
$$\int_0^1\int_0^1x+cy^2 dxdy=\int_0^1 [\frac{x^2}{2}+cxy^2]_0^1dy= \int_0^1\frac{1}{2}+cy^2 dy=[\frac{y}{2}+\frac{cy^3}{3}]_0^1=\frac{1}{2}+\frac{c}{3}=1$$
$$\Rightarrow c=\frac{3}{2}$$
(b) The marginal pdf of X is
$$f_X(a)=\int_0^1 f_{X,Y}(a,b)db=\int_0^1 x+\frac{3}{2}y^2...
(a)
The probability mass function of X and Y:
$$p_{X,Y}(1,1)= \frac{1}{2}\cdot \frac{3}{4}=\frac{3}{8}$$
$$p_{X,Y}(1,0)=\frac{1}{2}\cdot \frac{1}{4}=\frac{1}{8}$$
$$p_{X,Y}(0,1)= \frac{1}{2}\cdot \frac{3}{4}=\frac{3}{8}$$
$$p_{X,Y}(0,0)= \frac{1}{2}\cdot \frac{1}{4}=\frac{1}{8}$$
or
$$...
I have this question in my biomechanics class, and the way the teacher has solved it raised some questions with me.
This is the snippet of work from the lecture slides:
But, if we see the red variables acting as 'placeholders' for the value of respective forces, and the value of the force at...
Hi,
If the events A and B are statically dependent then the following formulas are used to calculate conditional probability and joint probability but there is a problem. As I see it both formulas are dependent upon each other. One cannot calculate conditional probability without first...
Hello,
In a piping system connected to the outlet of an crude oil tank, process man has located the expansion joint after the valve which is connected to tank's nozzle. Since this expansion joint is located after the valve, it must be able to withstand the design pressure of the piping system...
Hey everybody, :smile:
I have a joint density of the random variables ##X## and ##Y## given and want to find out ##P(X+Y>1/2)##.
The joint density is as follows:
$$f_{XY}(x,y) = \begin{cases}\frac{1}{y}, &0<x<y,0<y<1 \\ 0, &else \end{cases}$$
To get a view of this I created a plot:
As...
First, a caveat: this is one component of a project, which is difficult to describe without quite a but of digression. If my descriptions seem illogical, it may be because I haven't described the function of the component in its proper context. I assume it will take a little bit of...
Question is : is pivot point is both case at same position...
Useing only external forces (100kg,10kg and 30kg) I can treat joint as fixed conection and still get correct results,in both case pivot point is at same positon,even right case has joint at right side of beam..
How is possible that I...
Hi,
Just a quick question about conditional and marginal probabilities notation.
Question: What does ## p(a|b, c) ## mean?
Does it mean:
1) The probability of A, given (B and C) - i.e. ## p[A | (B \cap C)] ## OR
2) The probability of (A given B) and C - i.e. ## p[(A | B) \cap C] ##
I was...
Summary:: I am doing my structural analysis homework and I can't seem to identify between pin joint and roller.
Please take a look at the following exercises and help me understand:
1) In exercise 6.87, the joint at C is a pin joint whereas in exercise 5.63 the joints at the casters are...
PROBLEM
Here from the conservation of angular momentum I found angular velocity just before impact,
$$ H_1 = 0 $$
$$ H_2 = I_0\omega + mV_0d $$
$$ H_2 = 66\omega + 76.(1.2).(0.87)$$
$$ H_1 = H_2 $$
$$ \omega = 1.202 rad/s $$
But I couldn't solve it to find joint force.
Thanks in advance,
A Hobson's joint is a kind of gearless angled drive. Most often a fixed 90 degree angle, but there is also versions with free moving joints in each axle so it can move to any angle up to a little over 90 degrees. It is today mostly just a novelty and there is very few applications actually...
Below, I have a joint system that consists of a fixed anchor and a moving arm:
What I want is simple: To attach a linear actuator on the moving arm in such a way that the mechanical advantage of the actuator is exactly 1 (Ie the actuator only has to generate exactly the amount of force as the...
John owes Kelly £500.
John and Kelly have a joint account. Each of them pays £200 into the account every month, to spend on joint expenses.
If Kelly pays only half of her monthly contribution into the joint account (so £100), and John pays the usual (£200) how much will John's debt (£500) be...
Hi,
In the question outlined in the images (apologies for the poor quality of the scans), the chosen solution has opted to use a symmetry argument and proceed from there.
Question is from "Structures: theory and analysis" by Williams & Todd
My question is: How could we approach the same...
Hi everyone,
I have a question about sizing a bolted joint. How to calculate the size of the screw? Knowing that the bolt material is 316 stainless steel and the thread material where the bolt will be bolted is 6061 aluminum. This screw will be pulled at 2000N.
Thanks!
How did you find PF?: google
Hi
I have a scenario where I just cannot make up my mind when creating this joint and hinge at the same time.
Obviously yellow is the hinge, red section to the left has two wings hanging off it held there by two hinges, 250 um.
thinking about ultra sonics to...
So I have this word problem as seen below:
Joy and Ethan have agreed to meet for dinner between 8:00 PM and 9:00 PM. Suppose that Ethan may
arrive at any time between the set meeting. Joy on the other hand will arrive at the set meeting under the
following conditions:
• Joy will always arrive...
Hi All,
I think I have some idea of how to interpret covariance and correlation. But some doubts remain:
1)What joint distribution do we assume? An example of uncorrelated variables is that of points on a circle, i.e., the variables ##X ##and ##\sqrt{ 1- x^2} ##are uncorrelated -- have...
There are similar problems with heat conduction only where for example, right side of the bar also has a certain temperature or in-contact with a hot material. However, in this case diffusion and convection occurs on the right side of the bar, more precisely on the Y material. I guess we have to...
For 1) I found two ways but I get difference results.
The first way is I use P(A|B) = P(A and B)/P(B).
I get P(X<1|Y<1)=(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗)/(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗+∫_1^2▒∫_0^(2-x)▒〖3/4 (2-x-y)dydx〗)=6/7
The 2nd method is I use is
f(x│y)=f(x,y)/(f_X (x)...
Homework Statement
Let N denote the number of accidents occurring during one month on the northbound side of a highway and let S denote the number occurring on the southbound side. Suppose that N and S are jointly distributed as indicated in the table.
N/S 0 1...
While working on an old electric iron, I found this joint in the wires:
Any idea what this joint is? Does it have a special name?
The wires are in a horrible condition, so I have to change them. How can I build this joint by myself? Or are such wires readily available in the market?
Homework Statement
Two dice are tossed. Let X be the smaller number of points. Let Y be the larger number
of points. If both dice show the same number, say, z points, then X = Y = z.
Homework EquationsThe Attempt at a Solution
Find the joint probability mass function (X,Y)
For (1,1) = 1/36, I...
Hi!
I'm struggling with the following question:
Show that if n quantum states ρ1, ..., ρn are pairwise perfectly distinguishable, they are also jointly perfectly distinguishable.
Perfect distinguishability means that there is a set of psd matrices \{E_{1}, ..., E_{n}\},\, \sum_{i} E_{i} =...
Hi all,
I was wondering if there exist any theorems that allow one to relate any joint distribution to its marginals in the form of an inequality, whether or not ##X,Y## are independent. For example, is it possible to make a general statement like this?
$$f_{XY}(x,y) \geq f_X (x) f_Y(y)$$...
If X and Y are independent gamma random variables with parameters $(\alpha,\lambda)$ and $(\beta,\lambda)$, respectively, compute the joint density of U=X+Y and $V=\frac{X}{X+Y}$ without using Jacobian transformation.
Hint:The joint density function can be obtained by differentiating the...
Homework Statement
[/B]
Given a group of 100 married couples, let X1 be the number of sons and X2 the number of daughters the couple has.
P(X1 = 0, X2 = 2) = f(0, 2) = 8 /100 = 0.08
2. Homework Equations The Attempt at a Solution
I tried to look for a similar example online, I found this...
Hi,
I'm currently a freshman and I need to choose my program next year! My goal is to pursue physics and go to graduate school for theoretical physics (experimental is still an option). I firstly planned to do a joint honours in mathematics and physics which is offered by the Math department in...
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...
Homework Statement
I am given the following 3 joint probabilities:
p(I am leaving work early, there is a football game that I want to watch this afternoon) = .1
p(I am leaving work early, there is not a football game that I want to watch this afternoon) = .05
p(I am not leaving work early...
Is it possible for me to do cosmology and quantum mechanics as a joint degree at uni? If so where and does it cost extra? I’ve been wondering for a whole and I’m not sure where to look.
Definition 1 The von Neumann entropy of a density matrix is given by $$S(\rho) := - Tr[\rho ln \rho] = H[\lambda (\rho)] $$ where ##H[\lambda (\rho)]## is the Shannon entropy of the set of probabilities ##\lambda (\rho)## (which are eigenvalues of the density operator ##\rho##).
Definition 2 If...
A plate is riveted with a rivet having small rod like projection over the head and the point as shown in drawing.Considering we fix the plate to a vise,and then giving torque to the Rivet Rod;What will be the Maximum Torque the rivet can withstand without getting loosened and how to calculate...
If I were to cut the string and let the board move, I know I would get rotation. But, since the center of mass of the beam is moving as well (in a circle) could I also say that the board is translating once the string is cut?
Hi,
I have homework question that I'm trying to solve. But I can't understand the basis.
Here is a picture of the question and what I have done:
My question is, How do I set the boundaries for the integral? 1. If I want the whole squart. 2. To sum up areas.
Assume I want to sum the areas, I...
Hey folks,
I am doing a structural static analysis in ANSYS Workbench. A problem has troubled me for several days. Here it is: I would like to connect object 2 to object 1 by a revolute joint, which allows 2 to follow the movement of 1 and to rotate around this joint at the same time (under the...
Can someone explain to me why that highlighted force is 0?
Homework Equations
∑Fx = 0
The Attempt at a Solution
I found FDC to be 780lb and I am still trying to solve for FDE
Can anyone recommend a good book on weld design?
I'm not looking for a general textbook on welding. I want something that specifically targets the design of joints and weld choices. Something like the welding chapter of Shigley's Mechanical Engineering Design, just much more in depth.