Go Back   Physics Help Forum > High School and Pre-University Physics Help > Kinematics and Dynamics

Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Aug 8th 2016, 12:52 AM   #1
Junior Member
 
Join Date: Jul 2016
Posts: 17
Whitworth quick return mechanism

See the picture here: https://pl.vc/zk3gn

The transmission behavior defined by the distance a between 2 bearing points and the length b>a of the front-end crank which rotates at constant angular velocity, i.e. β=ω0.t

Express the position B as function of β

Express tanα as function of β

Compute angular velocity ω=α˙(t)of output crank! (I meant it's the derivative of alpha)

I've tried to solve 1st question as:

x = a + OA cosβ

y = OA sinβ

But I have no idea how to answer the 2nd and 3rd question. From the diagram, the relation that I can make is:

Triangle ABO: (OA)^2=a^2 + (BA)^2 − 2 a OB cosα

Triangle AOC (I made my own C): (OA sinβ)^2 = (OA)^2+ (OA cosβ)^2 − 2 (OA) (AB cosα) cosα

Triangle ABC: (BA sinα)^2 = (a + OA sinβ)^2 + (BA)^2 − 2(BA)(a + OA cosβ) cosα

Is it right if I solve tan α with the value of sinα from triangle ABC and the value of cos α from triangle ABO?

Last edited by rndaryam; Aug 8th 2016 at 01:02 AM.
rndaryam is offline   Reply With Quote
Old Aug 8th 2016, 04:43 AM   #2
Physics Team
 
ChipB's Avatar
 
Join Date: Jun 2010
Location: Morristown, NJ USA
Posts: 2,286
It seems you have defined (x,y) as the position of A, but the question asked about the position of B.

You need to clarify how the mechanism is constructed. The drawing makes it look like the points A, B and C are all pivots, but that would mean the mechanism can't turn. Perhaps as crank OA rotates the tip of the AB linkage at B slides along the y-axis, so that the length 'a' varies? But if so, then it makes no sense to ask about the value of y for point B as it is always zero. So clearly I don't understand the mechanism. Also, is the length 'b' the same as the length OA?

Last edited by ChipB; Aug 8th 2016 at 07:30 AM.
ChipB is offline   Reply With Quote
Old Aug 8th 2016, 07:46 AM   #3
Physics Team
 
ChipB's Avatar
 
Join Date: Jun 2010
Location: Morristown, NJ USA
Posts: 2,286
OK, I think I see what you are doing. Points O and B are fixed pivots, and point A slides along the linkage that pivots at B, as in the attached sketch, right? In other words length OB=a and OA=b are fixed, and the length AB varies as the crank OA turns. If so, the value of x and y that you calculated are the coordinate for point A, not B. So then tan(alpha) = y/x = [b sin(beta)]/[a + b cos(beta)]. Then determine the derivative of both sides with respect to time, and solve for d(alpha)/dt.
Attached Thumbnails
Whitworth quick return mechanism-mechanism.jpg  

Last edited by ChipB; Aug 8th 2016 at 11:43 AM.
ChipB is offline   Reply With Quote
Old Aug 9th 2016, 03:01 PM   #4
Senior Member
 
Join Date: Jun 2010
Location: NC
Posts: 388
I don't know why you are working this or what level you are. There is a powerful method available. The plan is to work in two
dimensions with vectors. The mechanism is "constrained." Start with a vector description of the 2-D situation. All else is simply paying attention.

I'm cooking tonight! I wrote some of the equations of your case. See it here.
http://www.thermospokenhere.com/wp/0...ck_return.html

What is the derivative of a time-dependent unit vector?
http://www.thermospokenhere.com/wp/01_tsh/A9820_1.25_vectors_circular/vectors_circular.html


I'll do more upon request... La ti da, JP
THERMO Spoken Here is offline   Reply With Quote
Reply

  Physics Help Forum > High School and Pre-University Physics Help > Kinematics and Dynamics

Tags
crank, mechanism, position, quick, return, velocity, whitworth



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Heat Generation and transfer mechanism ali Advanced Thermodynamics 0 Oct 26th 2014 09:59 AM
Heat transfer mechanism in a stove. ENRIQUESTEFANINI General Physics 4 Jun 23rd 2014 03:16 PM
Photon/QM , Explanation/Mechanism, For Refraction ? morrobay Quantum Physics 0 Dec 10th 2013 06:45 PM
Mechanism in Refraction of Light morrobay Light and Optics 11 Dec 1st 2013 05:52 PM
Four-bar linkage mechanism rementoire Kinematics and Dynamics 0 Jun 11th 2013 02:34 PM


Facebook Twitter Google+ RSS Feed