Report on the Four-bar linkage

Table of Contents

List of Figures

Figure 1: Simple pick and place robotic arm.. 5

Figure 2: Automatic Pick and place robotic arm in industry. 6

Figure 3: Pick and place robotic arm in warehouse. 7

Figure 4: Coordinate reference frame for forwarding Kinematics. 9

Figure 5: Kinematic module. 13

Figure 6: Coordinate system for the manipulators. 14

Figure 7: Position & orientation for Joint variables. 15

Figure 8: DH frames parameters & allocation

Project definition of Four-bar linkage

The objective of the project is to design the four-bar linkage of the moving robot and also identify the accurate procedure for constructing an efficient robot design along with to determining the length and width of the links.

Introduction of Four-bar linkage

The purpose of this report is to obtain the analysis for the Four bar linkage to create the model of the robot by using the Robotic Toolbox. Moreover, validate it by the data that is provided through the robot software.

The Four bar linkage robot manipulator is shown that is the compact of the Six (6 DOF) for the industrial manipulators. It is designed for the six revolute and providing the flexible use at the proper accuracy for the suitable wide range of the application, like cutting, welding. 

It can be noted that machines are playing a main role for making our lives easy and comfortable. It is helping to minimize the manpower required in factories. This is because most of the work is done by machines. The human arms are converted into robot arms. The working of pick and place robot arm is extremely simple. Moreover, this robotic arm can be easily designed in different ways according to the requirement of the factory. Such robots are heavily depended on joints. Moreover, all of these joints are used for joining the two consecutive bodes of the robot. These joints are named as linear and rotatory. There are some important components present in the robotic arm.

Figure 1: Simple pick and place robotic arm

Controller of Four-bar linkage

It is considered as the brain of the system. It will help the robot to make different kind of movement properly. It is also keeping proper track of the time, movement of the manipulator and the position of the joints. This control system is divided into three categories that are mechanical, hydraulic and electrical.

The mechanical part is considered as most basic part. The means that it is used in the form of programmable devices that are not existed. The main purpose of the robotic arms is to give proper response on the dynamic movement related to the required objective. This is done by mechanical linkage and cam. On the other hand, for hydraulic system Pascal law is used. It is using the values and pistons to control the movement of the robot. This type of controller is also used for such robot arms that are going to lift heavy and precise loads in the factories. This is because such load requires high precision and accuracy. The last category is related to electrical. It is showing that the type of control is completely convenient, reasonably, quiet, clean and fact. The electrical control is used in such robot arm that requires close tolerance accuracy.

Figure 2: Automatic Pick and place robotic arm in industry

Manipulator of Four-bar linkage

It can be observed that the entire mechanism of the robot that is involved in providing complete support and degree of freedom is manipulator. Moreover, the joints of this manipulator are movable components that will enable pure relative motion between these links. These links are consisted of arm, base and gripper.

The gripper of the robot arm is quite same to the human hand. It is also just like the grip of the hand when it is going to perform any task. Another thing is that the gripper is involved in securing the work piece during the operation.  Moreover, the nature and grip strength is varied according to the object. This shows that its shape is determined according to the given task.

The next point is that in automatic robotic arms there are sensors. These sensors are used to sense the external and internal state of the robot. It will also allow the robot to make required functions smoothly and accurately.

Figure 3: Pick and place robotic arm in warehouse

Literature review of Four-bar linkage

According to Author Constantin & et.al( 2019), the kinematics descriptions of the manipulators as well as their assigned task in the Robotics have used to set up their fundamentals equations for control along with dynamics. For the configuration of the robot, systems the non-linear equation is used the joint parameters map. To write a kinematic equation for the manipulators the DH (Denavit Hartenberg) notations gives the standard methodology. It is significant for the serial manipulators where the matrix is representing their orientation as well as positions. In the Kinematic, analysis of the Robotic, two important aspects “forward kinematics” as well as “Inverse Kinematic” is used. Whereas the forward kinematics is used, the kinematics equations of the robot for the computing of positions of eth end-effectors form the specified values of the joints parameters. In addition, the inverse kinematics permits to utilize the kinematic equation of the robot to calculate the joint parameters, which provide the desired position for the end effector (Constantin & et.al, 2019).

According to the Author Serdar, (2006) it is conducted that in the forward kinematics the manipulators is composed with the serial links;that is affixed by every other prismatic joint for the base of frames by the end effector. For the robot mechanism, the forward kinematics is in the systematic manner that should be suitable for the kinematics model. The DH  method which uses the four parameters that is very common in the robotic kinematics.Whereas the coordinate frame is attached to every joint to calculate the DH parameters,  axes (Serdar, 2006) .According to the author Almaged (2017), it is reviewed that the inverse and forward Kinematic analysis for the validation of the four bar-linkage of the industrial robot. The DH is presented  to write the Kinematics equations. The coordinate system that is matched for every six links of the manipulators. Then all these corresponding links are calculated for every links to construct the six transformation of the  which explains each frame (i)with the relative previuos {i-1}. Calcualte the required angles (in the inverse kinematics for the analytiscal as well as geometerical approches to used the solution of the model. (Almaged, 2017)

Current design of Four-bar linkage
Symbolic form of Forward kinematics

Four bar linkage is the industrial robot manufactured through the FANUC robotics as well as designed the system, or the manufacturing process. Manipulators provide the payload of 5kg capacity in the compact of the modular construction as well as the reach of the 1885.00mm by enough flexibility along with the higher reliability by the harmonic drives in six (6) axes manipulators. Four bar linkage robot is the electric servo-driven in the mini robot offering in the performance of the light that is very efficient and accurate (Balkcom, 2008)

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Now to create a forward kinematics of a four bar linkage, it is the numbered links with the joint of its attached local coordinates reference frames in below figure. Whereas the origin of the frame is chosen in the interaction axis, form the joint by the perpendicular plan that contains the axis of the joint  (Singh & et.al, 2017).;

Figure 4: Coordinate reference frame for forwarding Kinematics

The D-H convention used the product of four basic transformations for the representation of the homogenous transformation is denoted by the. The matrix A is the homogeneous for the  transformation matrix that describe a position of a point in a three dimensional space. By using the DH parameters, the transformation of a homogeneous matrix from one frame to a next frame is derived. Whereas   is represented by the four product of the homogenous transformations;

By using the above equation 2 determine the transformation matrix of this equations to fix the components with its one variable that is theta have the  of the rotational matrix that presents an orientation of an end effector and contain a  type of matrix that presents the position of the end of the effector.

The total 5 transformation between the robot base and a hand is;

By multiplying all these equations we obtained the final equation of the Forward kinematics to compared the value by equation 2 then final obtained the kinematics equations

Inverse kinematics in symbolic form

It is an opposite of the Forward Kinematics analysis. By a given requirements of a locations at the end of the manipulators, the corresponding of the Variable of each joint gives the references of the coordinate systems;

There are various methods to do the inverse kinematics analysis. But in this report, the inverse kinematic is done through multiplying each inverse matrix of T on the left side then equalizing the corresponding the elements

Now comparing these equations

Materials sourcing of Four-bar linkage

There are the various mechanical aspects that are related to the four bar linkage of moving robot for the understanding of this machine.

 Kinematic Model of Four-bar linkage

In this, model represents the DH algorithm as the method through which it is possible for the robotic arm by using a homogeneous transformation matrices .For a study movement of a multi DOF kinematic chain, the robotics kinematic applied the geometry and formed a structure of the robot manipulator

The studies of the robotic kinematics give the relationship among the robot linkage by the orientation, positions as well as acceleration. In addition, the Robotic kinematics analysis is divided into two parts as shown in below figure

·         Forward Kinematic

·         Inverse Kinematics

Figure 5: Kinematic module

Forward Kinematics of Manipulator

In the science of the kinematics the study of velocity, acceleration, position, has a high order of the derivative. Kinematics of the manipulators refers to the time-based properties and the geometrical of the motion. The kinematic equation, as well as joint parameters, is used for the computations of the position at the end of the effector for the specified values for every joint parameter. Calculation of an orientation, as well as opposition of a robotic manipulators in a terms of Joint variable, is defined the forward kinematics

Figure 6: Coordinate system for the manipulators

Inverse Kinematic  of Four-bar linkage

This the opposite of the Forward kinematics that specified the kinematics equations along with the position of the end effectors are utilized for the computation of joint angle form the specified position of an end of the effector. In a below figure a position and orientation of an end effectors for the manipulators is determined all the set of the joint angles which is used to obtain an orientation as well as positions (Jacobsen & et.al, 2004)

Figure 7: Position & orientation for Joint variables

DH Convention for the coordinate reference frame

It is necessary for every link to explain the pose of every link in the relative chain for the preceding link. The formalism of the DH has used only four parameters that describe the spatial relationship among the coordinate frames as well as successive links achieved through the placement of two constraints. The frame axis is  and intersecting the perpendicular for the axis of. The coordinate frame are not unique for the various people to derive the different but have same the coordinate frames (GARCIA & et.al, 2007)

 

Figure 8: DH frames parameters & allocation

By assigning the  axes the standard DH notation; and the two cases are supposed;

If the joint  is revolted,  and the axis of the revolutions of the joint is (. In this above figure 5 each link represented through two parameters; link twist (  and the link length (a) that defines the relative locations foe the two attached joint axes in spaces. The joints are also explained through two parameters: Joint angle, and the link offset that is the distance form one link to another link (Constantin & et.al, 2019)

Conclusion of Four-bar linkage

Summing up all the discussion it is concluded that the report is about the four bar linkage of moving robot which is also identify the accurate procedure for constructing an efficient robot design along with to determining the length and width of the links.