SOLUTION: Please Help!! I've been trying to work this out but can't seem to figure out how to explain this in any way!! A linkage is a system of rods and joints used to transmit motion. A f

Algebra ->  Parallelograms -> SOLUTION: Please Help!! I've been trying to work this out but can't seem to figure out how to explain this in any way!! A linkage is a system of rods and joints used to transmit motion. A f      Log On


   

Question 934753: Please Help!! I've been trying to work this out but can't seem to figure out how to explain this in any way!!
A linkage is a system of rods and joints used to transmit motion. A four-bar linkage in which opposite links are of equal length is called a parallel-motion linkage. Using the following diagram, explain why the connecting link will always move in such a way that it is parallel to the fixed link.


An example of this kind of linkage is the rod on the wheels of a locomotive. In this case, the two wheels take the place of the driving link and the driven link.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe the driving link rotates in a circle agound the end of the fixed link.
this forces the driven link to do the same.

what you have then are 2 circles being rotated at the same time by the driving link.

the driving link is the radius of the driving circle.
the driven link is the radius of the driven circle.
the circles have the same radius so they are congruent.

since there is always the same distance between them, then they are always in the exact same position relative to each and the distance between the connecting link and the fixed link remain the same.

what you have is a parallelogram that is composed of the driving link and driven link always being equal and parallel to each other, and the connecting link and fixed link always being equal and parallel to each other.

if a quadrilateral has opposite side equal to each other, then the quadraliteral is a parallelogram and the opposite angles will always be equal to each other.

here's a demo on parallelograms that might be helpful.
http://www.mathopenref.com/coordparallelogram.html

this link shows theorems relating to parallelograms.
check out theorem 2.
http://www.sonoma.edu/users/w/wilsonst/courses/math_150/theorems/Parallelograms/default.html

since you know you have a parallelogram because the opposite sides will always be congruent to each other, then it follows that the links will always be parallel to each other.


take the fixed link and mark the left end A and the right end B.

take the connecting link and mark the left end D and the right end C.

your parallelogram is ABCD.

AB is always congruent to CD.
AC is always congruent to BD.