In the machine dynamics, there are four basic linkages that are considered more suitable element in the mechanism of this model. In figure 1; there are four linkages of different kinds such as frame link, shortest link, coupler link and rocker links. All the linkages are connected with one another with the help of joint that is used in the connection. It could be moved from one link to another also with the movement of joints. There is rotation in the linkages that are based on the mechanism that is used in measurement of positive axis to the other in the movement of clockwise that shows that the links are connected with each others.

Figure 1. A typical four bar linkage and its position angles

The mechanism is based on the four linkages that are connected with the different devices and it could be found that it works just like movement of bicycle that is working on the principle of loading and lifting and such kind of movement could be seen in the below figure 2.

Figure 2. Applications of a four bar linkage in a bicycle

Four bar linkages have features that could rotate it full capacity that is considered as a remarkable characteristic. Despite from this for doing this, the measurement of all linkages must be chosen to satisfy the Grash of rule. Moreover, if summary of length of the direct and lengthiest links is decrease or equal to the summary of length or some of the other two links and the eccentric would hold the full rotation within the mechanism. As well as it has been taken as in the meaning if the length of other two links has been assumed as S, and the longest link L, and P and Q for the remaining two links then S then S + L ≤ P + Q.

Despite from this better to understand the implementation of these four-bar linkage is original. Moreover, the main purpose of this study is the design and analysis f such walkable mechanism is automatic as it has been given in the figure 3 below. These automatic moves along with two sets of four linkages is the visible side and two sets of four bar linkage in the back. Despite from this motion power gives the set of gear box and set of motor. There are various parameters such as angle, rushing and rapidity of the link which has been calculated for the four bar linkage form back and front of the robot in this assignment.

Figure 3. Four bar linkage in the walkable robot

Description of the process of machine dynamics

The front and back legs of this robot can be compared with the four bar linkages as shown in Figure 4. By comparing the mechanisms shown in this figure with the walkable robot in Figure 3, front and back legs are similar to the blue linkages and the front and back couplers are the same as the green and red linkages, respectively. All linkages in this mechanism moves by the full rotation of driving or crank link in the front leg mechanism. This link with length is the shortest link in the system and is connected to the ground link by joint O in one side and to the front leg link by joint A in another side. The driving link is also connected to the back leg by using the back coupler.

A full rotation of driving link causes the motion of both legs and therefore the motion of the robot. The driving link itself is rotated by a set of motor and gear box. Joints O, O₁and O₂ are fixed and drilled in the both side shells of the robot which have a rectangular shape and are shown in Figure 3 by yellow color. The dimensions of the side shell along with the location of these joints is presented in Figure 5.

Figure 4. Four bar linkage at the front and back part of the robot

The length and corresponding angles of all linkages are shown in Figure 4. It should be noted that the length of both front and back legs are the same (b₁ = c₂ and p₁ = p₂). From Figure 5, it can be seen that the ground links OO₁ and OO₂ are not located in the same line.The angle between this two links together with their lengths d₁ and d₂ can be calculated using the given dimensions forthe locations of joints O, O₁ and O₂. This will be explained more in the following section.

Figure 5. Side shell dimensions in mm

Analysis of machine dynamics

II: Design the parameters of the linkage

Part (a). Finding the lengths

As mentioned earlier, the lengths and angle difference of the ground links are calculated using the details given in Figure 5. With respect to the triangles OO₁Q and OO₂Q it can be written:

The angle between these two links is:

For the front linkage, the lengths of other links are selected based on the Grashof rule since it is required that the driving link have a full rotation. The driving link should be shorter than d₁. So it is selected to bea = 18 mm. Other lengths of front leg and front coupler are selected as: b₁ = 30 mm and c₁ = 35 mm, p₁ = 40 mm. Based on Grashof rule, the summation of the shortest and longest links should be less than the summation of length of other two links:

18 + 35 30 + 27.46

Same process is used for length selection of the back leg linkages. The driving link is common for back leg as well and d₂ = 122.1 mm. The lengths of c₂ and p₂ are the same asb₁ and p₁, soc₂ = 30 mm and p₂ = 40 mm. The length of b₂is then selected to satisfy the Grashof rule. If b₂= 130 mm:

18 + 130 30 + 122.1

Part (b). Drawings of machine dynamics

Two sets of four bar linkages for the front leg and back leg as shown in Figure 4 are drawn with scale in Figures 6 and 7, for the case when the input angle of the driving link is . With respect to figure 5 and the difference between the two ground links, for the back leg mechanism.

Figure 6. Front leg mechanism at

Figure 7. Back leg mechanism at ( , angles are measured from the ground link OO₂)

III: Analyze the four-bar linkage obtained in Section II

Different parameters of the front and back leg mechanisms are to be calculated at driving angles of 30° and 90° for the front leg. Calculations are performed using the vector loop derivation and for open configuration.

For the back leg at :

a = 18mm, b₂ = 130 mm, c₂ = 30 mm, d₂ = 122.1 mm

- Link ratios

- Intermediate parameters

This is the case as drawn in Figure 7.

For the backleg at :

Based on the lengths of links and calculated angles in previous sections:

Part (b). ii. Line velocities of end points M and N

Part (c). Angular acceleration of the legs

Given angular acceleration of driving link and

Using the calculated parameters from the previous sections, angular acceleration of the front leg at is calculated by the following steps:

Conclusion of machine dynamics

The implementation of these four-bar linkage which had been understand in the comprehensive way along by having original analysis of mechanism in the walkable robot. It could be used in four sets of four bar linkages. In these two sets in front and two sets in back.

The movement of the links could be omitted to the driving link which has been allocated in front mechanism which has been done by the set of gearbox and motor. As well as the motion of driving has been caused due to motion of other link in back and front legs and then the motion of robot. In this regard Grashof rule had been implemented in the mechanism in order to attain full rotation of driving link. The summary is based on the theme of length of shortest driving link and the lengthier link had to be shorter than the sum up of length if various two links along with the mechanism of front and back.

In this the analysis of linkages involved the calculation of angle of legs and coupler links as well as line and angular velocities and acceleration angular of the leg link in both back and front mechanism. In this regard there are various equations ad been utilized to calculate above mentioned measurement which has been based on the vector loop derivation and for configuration. There are various parameters that are involving angle, rushing and rapidity of the link which has been calculated for the four-bar linkage form back and front of the robot in this assignment. These automatic moves along with two sets of four linkages is the visible side and two sets of four bar linkage in the back. Despite from this motion power gives the set of gear box and set of motor.