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Modeling and Validation of a Fanuc LR Mate 200iC

M. C. Sabarense; W. S. Fonseca

1. Introduction

The Fanuc LR Mate 200iC is a six degrees of freedom electric servo-driven robot.It has multiple mounting options as floor, tabletop, inside machines, angle andinvert, which maximizes flexibility for small and narrow workspaces. For thesereasons it that can be used for a wide variety of applications as machine tending,material handling, assembly, picking and packing, part washing, dispensing,testing and sampling, education and entertainment.

Figure 1 Fanuc LR Mate 200iC.

It is much important to study and to determine the kinematics of a robot becausethis knowledge can avoid accidents and singularities. A singularity can be definedas a situation that occurs when the robot is moving in a world frame (Cartesian

space) and its axes are redundant (more axes than necessary to cause the samemotion) or when the robot is in certain configurations that require extremely highjoint rates to move at some nominal speed in Cartesian space [3]. The singularityconditions can be determined by the determinant of the Jacobian matrix of therobot and the region of singularity can be showed using Matlab or anothergraphic software [1].

The purpose of this report is to obtain the forward kinematic and the Jacobianmatrix for the Fanuc LR Mate 200iC robot and validate the model usingWorkspace LT for simulation. These information can be use in the future designand production of the robot to make it faster and more accurate.

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Figure 2 Standard dimensions and workspace of Fanuc 200iC and similar models.

2. Reference Papers

I. OLASZ, Attila. SZAB, Tams. Kinematic Analysis of Robot andManipulator Arms. Advanced Logistic Systems, vol.6, n1, 2012.

This paper aims to determine the angles of the joints of the robot and themanipulator for the control system of a Fanuc LR Mate 200iC robot for a workcycle. The prescribed motions of the robot and the manipulator weresimulated by computer. The results show that the curves computed are similarbut not equal for the first three joints of the robot and the manipulator.

II. JACOB, M. G.; LI, Y.; WACHS J. P. A Gesture Driven Robotic ScrubNurse.

In this paper a Fanuc LR Mate 200iC robot is used as a gesture driven roboticscrub nurse (GRSN) reducing the workload of a human scrub nurse. Theaccuracy of the robot was determined experimentally and in 95% of the timesit recognized and repeated the correct gestures and it is only 0.83 seconds

slower than the average of the human performance.

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III. SILVA, S. R. X. et al. Modelagem Matemtica da Cinemtica direta doRob Fanuc LR Mate 200iC com Simulao no Matlab.Congresso

Brasileiro de Educao em Engenharia. 2012.

The authors determined the forward kinematics of a Fanuc LR Mate 200iCrobot to analyze the behavior of the position and orientation of the robot. Thevalidation of the results was performed using Matlab simulation. The authorsalso analyzed and proved the D-H parameters notation.

IV. CURKOVIC, P.; JERBIC, B. STIPANCIC, T. Coordination of Robots

with Overlapping Workspaces Bases on Motion Co-Evolution.

Modern robotics systems development focus on the level of autonomy. Andwhen robots are supposed to work together their workspaces are sharedmeaning that the robots are dynamic obstacles to each other. This paperpresents a solution for the problem of motion coordination of two robots withoverlapping workspaces. The process is evaluated in a simulationenvironment created on Matblab.

V. VALERA, A. et al. Industrial Robot Programming and UPnP ServicesOrchestration for the Automation of Factories.International Journal ofAdvanced Robotic Systems. 2012.

The authors describe and analyse the Plug-and-Play architecture in somerobots as the Fanuc LR Mate 200iC. The validation was made through a testbed specially designed for this experiment.

VI. NUBIOLA, Albert. BONEV, Ilian A. Absolute Robot Calibration with aSingle Telescoping Ballbar. Precision Engineering. 2014.

In this paper a new six degrees of freedom measurement system isintroduced, using a telescoping ballbar and two custom-made fixtures, oneattached to the robot base and one attached to the end-effector. This methodis used to calibrate the robot completely. The robot used is the Fanuc LR Mate

200iC and the experiment showed an improvement in the absolute positioningerror.

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3. Forward Kinematics

The forward kinematics involves the calculation of the position and orientation ofthe end-effector in terms of the joint variables. One easy way to calculate theforward kinematics is to use the D-H parameters. This method uses fourparameters: link length (a), link twist (), link offset (d) and joint angle () todescribe the kinematic model[4]. For the Fanuc LR Mate 200iC the D-Hparameters and the kinematic structure are showed in Table ! and in Figure 3,respectively.

Table 1 D-H parameters of Fanuc LR Mate 200iC.

Jo in t di i ai i

1 330 1 = 0 75 -90

2 0 2 = -90 300 -180

3 0 3 = 180 -75 90

4 -320 4 = 0 0 -90

5 0 5 = 0 0 90

6 -80 6 = 180 0 180

Figure 3 Kinematic Diagram of Fanuc LR Mate 200iC [1]

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Using the D-H parameters and knowing that all joints are rotational ( variable) itis possible to determine the six homogeneous matrices () using Equation 1.

(1)

= 0 75 0 750 1 0 3300 0 0 1 = 0 0 0 00 1 0 3200 0 0 1 =

0 300 0 3000 0 1 00 0 0 1 = 0 0 0 00 1 0 00 0 0 1

=

0 75 0 750 1 0 00 0 0 1 6

=

6 6 0 06 6 0 00 0 1 800 0 0 1

The Forward kinematics model is obtained by the multiplication between the 6homogeneous matrices.6 = . . . . . 6 (2)

Where:

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8/10/2019 Final Project Report - Fanuc LR Mate 200c

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= 0 00 0 1 = 0 0 0 1 0

= 0 0 0 1 0 6 = 6 6 06 6 00 0 1

The rotational and the position matrices related to the base frame were obtainedfrom the Equations 4 as detailed in Equations 5 and 6:

= . . . . . . (4) = 1,1 1,2 1,3 2,1 2,2 2,3 3,1 3,2 3,3 (5)

= 1,4 2,4 3,4 (6)The next step is to determine zi, according to Equation 7.

= . (7)Knowing that = 001, the other zvalues can be determined using Equation 7: = 0 =

0 = .sin + .sin + +

= .sin cos ...cos cos .. .

= .sin. +cos ..sin + ..cos.cos. +cos ..sin + ..cos + . sin ..

To obtain the Jacobian matrix related to the linear velocity it is necessary torealize the vector multiplication as described in Equation 8.

8/10/2019 Final Project Report - Fanuc LR Mate 200c

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= 6 (8)After this it is possible to determine the complete Jacobian matrix applying theequation 8 in the equation 3.

= [ 6 6 6 6 6 6 ] (9)*The complete Jacobian matrix is in the appendix.

5. Workspace LT Simulation and Validation

The evaluation of the robot has been done using the FANUC LR Mate 200iC

Model on the software Workspace LT to create five points and then validatingthese points numerically with Maple Software as described in the followingpictures.

Figure 4 First point determined in Workspace LT and its validation.

Figure 5 Second point determined in Workspace LT and its validation.

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Figure 6 Third point determined in Workspace LT and its validation.

Figure 7 Fourth point determined in Workspace LT and its validation.

Figure 8 Fifth point determined in Workspace LT and its validation.

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6. Conclusions

This work provides information related to the forward kinematics for a FANUC LRMate 200iC and the Jacobian Matrix using the vector multiplication method. Alsoprovides the evaluation of the model validated by Workspace LT software.

Determining those conditions is an important step in the improvement of the robotmodel and the creation of integrated robotic systems for a wide range ofapplications.

7. Other References

[1] ABDERRAHMANE, M. S.; DJURIC, A. M.; CHEN, W.; YEH, C. P. Study andValidation of Singularities for a Fanuc LR Mate 200iC Robot. March, 2014.

[2] DJURIC, A. M. FILIPOVIC, M. CHEN, W. Visualization of the Three CriticalSpaces Related to the 6-DOF Machinery. Fourth Serbian Congresso nTheoretical and Applied Mechanics. Serbia. 2013.

[3] RED, Edward. Robotics Overview. Accessed in 12/08/2014 in:

http://eaal.groups.et.byu.net/html/RoboticsReview/body_robotics_review.html

[4] SERDAR, K. and BINGUL, Z. Robot Kinematics: Forward and InverseKinematics, Industrial Robotics: Theory, Modeling and Control. ISBN: 3-86611-285-8. 2006.

http://eaal.groups.et.byu.net/html/RoboticsReview/body_robotics_review.htmlhttp://eaal.groups.et.byu.net/html/RoboticsReview/body_robotics_review.html

8/10/2019 Final Project Report - Fanuc LR Mate 200c

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8. Appendix Jacobian Matrix

8/10/2019 Final Project Report - Fanuc LR Mate 200c

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