Sunday, November 28, 2010

Roberts straight-line mechanism

Many engineering applications require things move in a linear fashion or "straight-line motion". We can use a linear motion guide that can guide a device accurately along a straight line. Manufacturing know-how of most linear guide manufacturers has let us keep expanding the range of linear guidance. The picture shown here is an example of commercially available linear guides from THK. This Linear Ball Slide is a lightweight, compact, limited stroke linear guide unit that operates with very low sliding resistance. It excels in high-speed responsive performance due to its very small frictional factor and low inertia.

In the late seventeenth century, before the development of the milling machine, it was extremely difficult to machine straight, flat surfaces. For this reason, good prismatic pairs without backlash were not easy to make. During that era, much thought was given to the problem of attaining a straight-line motion as a part of the coupler curve of a linkage having only revolute connection. Probably the best-known result of this search is the straight line mechanism development by Watt for guiding the piston of early steam engines. Although it does not generate an exact straight line, a good approximation is achieved over a considerable distance of travel.

In this post, we show approximated straight-line mechanism discovered by Richard Roberts (1789-1864). He discovered the Roberts' Straight-line mechanism.

Lengths:
O2A = 100
O4B = 100
AB = 100
AC = 100
BC = 100
O2O4 = 200

We can find from the following video clip that point C moves as an approximated straight line. Though it is not an exact straight-line motion, but it's good as a starting point. In later post, we will explore more straight-line mechanisms that can give better straight-line approximation.



Another quick way to create and test Roberts straight-line mechanism is to use design wizard in SAM 7.0 The Ultimate Mechanism Designer. Length of each link can be changed easily and it can display the path of desired node. Watch the following video...




Source:

Sunday, November 14, 2010

3-Position Synthesis with Inversion Method using Unigraphics NX4 Sketch - Part 3

In [3-Position Synthesis with Inversion Method using Unigraphics NX4 Sketch - Part 2], we've shown an example to do three-position synthesis of  a four-bar linkage using inversion method in Unigraphics NX4 sketch.

We can make a quick motion simulation using "animate dimension" command in Unigraphics (UG) NX4 sketch. Just draw lines as per a sketch and add one driving dimension as shown below. Then use animate dimension command to set the lower and upper limits, for this case they're minimum and maximum angles.

Saturday, November 13, 2010

3-Position Synthesis with Inversion Method using Unigraphics NX4 Sketch - Part 2

In previous posts, the fixed pivot points were determined from the moving pivot points. We can get result that can't be fitted in our design due to space limit. The principle of inversion can be applied to solve this problem. The first step is to find the three positions of the ground plan that correspond to the three desired coupler positions.

We start with our desired positions of fixed pivot points.

1) Draw desired fixed pivots (O2 and O4) and moving pivot points. Red lines are three desired positions of links (moving pivots).

2) Draw lines to make fixed relations between the ground plane (O2O4) and the second coupler position.
3) Transfer the ground position to the first coupler position using same relations developed in previous step as shown in dashed lines. Name new ground positions as O'2 and O'4 respectively.

4) Draw lines to make fixed relations between the ground plane (O2O4) and the third coupler position (A3B3).

5) Transfer the ground position to the first coupler position using same relations developed in previous step as shown in dashed lines. Name new ground positions as O''2 and O''4 respectively.

6) Draw lines O2O'2 and O'2O''2, bisect both lines and extend the perpendicular bisectors until they intersect. Label the intersection G.

6) Draw lines O4O'4 and O'4O''4, bisect both lines and extend the perpendicular bisectors until they intersect. Label the intersection H.

7) Draw O2G, GH and O4H. Now we get G and H as inverted fixed pivot points of moving link O2O4.

8) Re-invert the linkage to return to the original arrangement.

Let's see how it moves in [3-Position Synthesis with Inversion Method using Unigraphics NX4 Sketch - Part 3]

Further reading: