## Keywords: Four-bar mechanism, linkage synthesis, pattern-matching, ..

### Kinematic Synthesis of Four Bar Mechanism using …

The basic four-bar linkage is shown at the left. It consists of cranks 2 and 4 rotating on shafts fixed in the frame 1, and connected by link 3. The mechanism itself is shown in configuration space at the left in the diagram. On the right is a of the mechanism, in which the links of the mechanism are represented by the vertices, and the joints by the lines. The problem of determining all possible graphs for a given number of links is an interesting problem in topology, which has received a good deal of attention. This exercise is called . Although interesting and difficult, it is probably not of much practical importance, though it has its enthusiasts. Such matters were not presented in the undergraduate mechanisms course.

### FOUR-BAR MECHANISM - Middle East Technical University

A planar linkage with L links and J joints has F = 3L - 2J - 3 . The number of degrees of freedom is the number of generalized coordinates that must be specified to determine the configuration of the linkage. For the four-bar linkage, L = 4 and J = 4, so F = 12 - 8 - 3 = 1. We will consider here only linkages with one degree of freedom, and the four-bar linkage will be the principal example. One very useful form of the four-bar linkage is the crank and slider mechanism, in which crank 4 is of infinite length, so that the joint has a reciprocating motion.

Similar to the synthesis of rigid body linkages, we first classify kinetostatic synthesis problems into three major categories: function, motion and path generations.

## Four Bar Mechanism | Geometry | Space - Scribd

Consider the four-bar linkage shown at the left. Suppose V_{23} is known, and V_{34} is to be found. From point Q, draw V_{23}. The relative velocity of 34 with respect to 23 must be normal to the link 3, which is in the direction of line a-b. V_{34} must be normal to the crank 4, so a line is drawn in this direction in the vector diagram. These two lines intersect at point b, and so V_{34} is determined. This is as easy as the method of centros, but uses a graphical vector diagram.

## A new dimensional synthesis method is described in the paper

The familiar and important crank-and-slider mechanism is a special case of the four-bar linkage where the radius of one crank is infinite, which means that the joint 34 moves on a straight line, as shown in the figure. Member 2 is the crank, member 3 is the connecting rod, and the slide guiding joint 34 is fixed to the frame, member 1. The path of 34 need not pass through 12, but in most practical mechanisms it does, so that the motion is symmetrical and as simple as possible. It is easy to find the centros 24 and 13 for this mechanism. 24 lies on a vertical line through joint 12, which guarantees that in any case its velocity is parallel to line 12-34, as constrained by the slider. 13 lies on a vertical line through 34. The velocity of 34 can be found either from the motion of centro 24, or from a vector diagram, as shown. V_{23} is drawn from Q. A line parallel to 12-34 gives the direction of V_{34}, and its magnitude is determined by the intersection of this line with a line perpendicular to the connecting rod.

## By using four bar linkages synthesis ..

By extending the five point approximation and the fifth order approximation presented by F. Freudenstein, an analytical method is established for the synthesis of a plane four-bar mechanism to generate approximately a desired founction over a finite interval. This method may be regarded as a general method in the synthesis where the input and output scale factors are specified in advance. Moreover, in order to reduce the structural error of the function generator designed by using this method, a new numerical procedure for respacing precision points is suggested on the basis of the tenth degree polynomial closely approximating the structuralerror.

## Examples range from the four-bar linkage used to amplify ..

The four bar chain can be used to generate an infinite range of curves by adjustingthe two fixed pivot points and the lengths of the links. The curves generated bythe free pivot points are obviously circles with radii = to the length of the links to the adjacentfixed pivot points. The motion of points along the coupler between the two free pivot points is howevercomplex and variable.

The modern method of developing curve motion is to use Numerical control methods combined with hydraulic, or electronic servodrives. There are however opportunities for using direct mechanical systems for low cost components.