Design Optimization of Robotic Arms

Design Optimization of Robotic Arms

Design Optimization of Robotic Arms

1. Prof. L. S Utpat

   Pro fessor, Mechanical Engineering Dept., MMCOE, Pune -52 Pune University, Maharashtra, India

2. Prof. Chavan Dattatraya K

   Pro fessor, Mechanical Engineering Dept., MMCOE, Pune-52 Pune University, Maharashtra, India

   PhD scholar, JJT University, Ra jasthan

3. Yeolekar N., Sahasrabudhe A, Mandke S.

Graduate Students MMCOE, Pune

1. Abstract: A robot can be defined as a programmable, self-controlled device consisting of electronic, electrical, and mechanical unit.

   The elements which are common to all robots can be considered as the basic elements and are as follows:-

   • Manipulator:-

   • Controller: –

   • End Effecter: –

   • Sensors: –

   • Energy Source: –

   The robot manipulator can be divided into two sections, each with a different function:

   Arm and Body and the Wrist –

   The current design of the robotic arm consists of manipulators that have been over designed to meet reliability requirements. Hence these manipulators have been designed in a way that they do not make best use of material. They have a low payload to weight ratio. This limits the payload capacity and increases the power requirement for movement of the arms. Attempt has been made to optimize the design of the arms using FEA as a tool. Strength and stiffness have been kept as design criteria while optimizing the weight of the moving arms. The results have shown corresponding reduction in power requirement for arms movement..

   \Keywords: Robot, manipulator, topology, optimization,arm,etc

2. PROBLEM DEFINITION:

   The most important characteristic of an industrial robot is the weight to ma ximu m payload ratio. The min imization of

   said ratio can only be achieved by reducing the weight of the robot manipulator. This will also result in increased payload capacity. However this will have to be achieved without severely compromising the static stiffness or the ma ximu m allo wable deflection of the individual linkages.

   Initia lly the components were over-designed to meet the reliability require ments. But in todays economy, the weight of industrial robots and its impact on initial and operating cost are of significant concern for both manufacturers and end users.

   Hence the components of the robot assembly to be taken into consideration for optimization include

   1. The Primary Arm

   2. The Secondary Arm

      CURRENT SPECIFICATIONS OF ROBOT:

      Manipulator Weights

      1. Primary Arm – 3.16 kg

      2. Secondary Arm 4.11 kg Co mbined Manipulator weight 7.27 kg Rated Payload – 2 kg

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3. OPTIMIZATION:

   This analysis shall be based on the finite e le ment method (FEM) and consists of completion of the design model using the dimensional data as design variables.

   Optimized structural design for the structures of the industrial robots have to meet certain criteria regarding dimensional design and shape, materia l consumption and adapt this to the functional require ments.

   To improve the static and dynamic behaviour of the industrial robot structure, the following require ments must be accomplished:

   • M inimu m we ight structure;

   • Ma ximu m static stiffness of structural ele ments;

   • M inimu m deformat ion Ma x. prec ision at the end-effecter. TOPOLOGICAL OR LANDSCAPE OPTIMIZATION:

   Topology optimization is a mathe matica l approach that optimizes materia l layout within a given design space, for a given set of loads and boundary conditions such that the resulting layout meets a prescribed set of performance targets. Using topology optimizat ion, engineers can find the best concept design that meets the design require ments. Topology optimization has been imple mented through the use of finite ele ment methods for the analysis, and optimization techniques based on the method of genetic algorith ms, optima lity criteria method, and level sets. The topological Optimization using FEM methods for Robotics was emp loyed with s hape optimization techniques

   Fig III.1 Visualization of e xisting robot INITIA L DESIGN OF PRIMARY A RM: INITIA L STATUS:

   The Prima ry arm was init ially designed using empirica l approach. The wall thic knesses were decided based on minimu m permissible values for casting process. The box structure was stiffened with the help of a simple cross rib arrange ment.

   INITIA L STUDIES

   For the calculation of initial stresses and deformat ion in the prima ry arm the forces acting were ca lculated.

   The forces for analysis are 1) Comb ined load of the Secondary arm, Secondary arm balancer and secondary arm motor of 98.1 N along the negative Z-axis applied at the face of the upper flange 2) The gravitat ional force act ing globally in the negative Z- a xis.

   Fig III.2 Results for Init ial Design of Prima ry Arm Maximu m Deformat ion: 6.296e-005m = 62.96 mic rons Maximu m Equivalent St ress = 2.412 N/ mm2

   INITIA L DESIGN OF SECONDA RY ARM : INITIA L STATUS:

   The Secondary arm was initia lly designed using empirica l approach. The cross-section of the arm is circula r to account for

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   ma ximu m stiffness. The structure is symmetrical ac ross the XY plane.

   INITIA L STUDIES

   For the calculation of initial stresses and deformat ion in the prima ry arm, the forces acting were calcu lated. The forces for analysis are

   The load of the gripper mechanism and the ma ximu m payload of 29.43N along the negative Y-a xis applied at the face of the front flange. The gravitational force acting globally in the negative Y- a xis.

   Fig III.3 Results for Init ial Design of Secondary Arm Maximu m Deformat ion: = 2.748 mic rons

   Maximu m Equivalent St ress = 0. 222 N/ mm2

   TOPOLOGICAL OPIM IZATION

   The actual optimization of the prima ry and secondary arms was done using the Ansys topological optimization routine.

   The materia l used for the init ial primary and secondary arms is Al Si 12.The same materia l is considered for the topological

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   optimization of the primary and secondary arms. The mate ria l values for the optimization was set for Alu minu m a lloy Al Si 12. Youngs Modulus E = 0.675 X 106 N/ mm2

   Poissons Ratio = 0.34 Density = 2710 kg/ m2

   PRIMARY A RM OPTIM IZATION:

   The basic steps for optimizat ion in Ansys are

   Define the structural problem: The optimization model of the prima ry arm consists of a complete ly solid structure.

   Select the ele ment types : Ele ment type selected is SOLID 95. Specify optimized and non-optimized reg ions : The top and bottom flanges are selected as the non-optimized regions while the rest of the structure is selected as the optimized region. Both these regions are given the element type of SOLID 95.

   Define and control the load cas es or frequency ext raction:.

   For the prima ry arm the completely e xtended position was considered. Forces acting are discussed in init ial studies.

   The fixed support was given on the face of the bottom flange.

   Define and control the optimization process : The mesh size for this given problem is given as 5. This will create e le ments of equal size so as to facilitate measurement of the optimized shape. Figure shows the mesh of the structure.

   The required volume reduction is specified as 50% and the number of iterat ions given are 50.

   Fig III.4 Mesh of Structural Proble m fo r Prmary Arm

   REVIEW THE RESULTS:

   The results obtained by the optimizat ion routine are as seen the following figure. The blue colour represents materia l to be re moved while the red represents materia l to be kept.

   Fig III.5 Optimizat ion for Primary Arm

   The result is then refined as to show only the ele ments that are meant to be kept.

   Fig III.6 Result of Optimizat ion for Prima ry Arm(refined)

   CONCLUSIONS DRAWN:

   The materia l at the back o f the arm can be re moved. The materia l required to be kept increases gradually as we move fro m the upper flange to the lower flange. The materia l at the center of the arm can be re moved keeping the side walls intact.

   SECONDA RY ARM OPTIM IZATION

   Similar steps as used for primary a rm optimization were used. The optimization model of the prima ry arm consists of a complete ly solid structure as shown in the figure.

   Fig III.7 Structural Proble m Definit ion for Secondary Arm The ele ment type selected is SOLID 95.

   The top and bottom flanges are selected as the no n-optimized regions while the rest of the structure is selected as the optimized region. Both these regions are given the element type of SOLID 95.

   For the prima ry arm the completely e xtended position was considered. Forces acting are discussed in init ial studies.

   Fig III.8 Mesh Secondary Arm REVIEW THE RESULTS:

   The results obtained by the optimizat ion routine are as seen the following figure. The blue colour represents materia l to be re moved while the red represents materia l to be kept.

   Fig III.9 Optimizat ion for Secondary Arm

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   The result is then refined as to show only the ele ments that are meant to be kept.

   Fig III.10 Result of Optimization for Secondary Arm(refined)

   CONCLUSIONS DRAWN:

   The proposed section of the secondary arm should b e an I section. The arm should taper towards the front while re ma ining thicker towa rds the boss side of the arm.

4. PRIMA RY ARM RIBS OPTIMIZATION:

   It is has been seen that the thickness of some sections of the prima ry arm are too large to be manufactured by standard casting process. Hence it has been decided that a front face of the prima ry arm shall be ribbed for generating a better design. For generating the ribs of the prima ry arm a 2-D section of the arm shall be considered and same fo rces shall be applied to it.

   An assumption is made that the load is a direct load and not an eccentric load for this optimization process.

   The basic steps for optimizat ion used were:

   Define the structural problem: The optimization model of the prima ry arm consists of a 2-D structure as shown in the figure.

   Fig IV.1 Structural Proble m Definit ion for Primary Arm Ribs

   The ele ment type selected is PLANE 82.

   Specify optimized and non-optimized reg ions : The top and bottom flanges are selected as the non-optimized regions while the rest of the structure is selected as the optimized region. Both these regions are given the element type of PLA NE 82.

   Define and control the optimization process :

   The mesh size for this given proble m is sma rt size super fine mesh. This will create very small ele ments which will generate an optimized rib structure for a given problem. Figure shows the mesh of the structure.

   The required volume reduction is specified as 70% and the number of iterat ions give are 50.

   Fig IV.2 Mesh of Structural Proble m for Prima ry Arm Ribs

   REVIEW THE RESULTS:

   The results obtained by the optimizat ion routine are as seen in the following figure. The blue colour represents materia l to be re moved while the red represents materia l to be kept.

   Fig IV.3 Result of Optimization for Primary Arm Ribs

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   CONCLUSIONS DRAWN:

   This is the approximate shape of the best rib structure for th e give ele ment for the given load condition.

   The best rib pattern is a cross rib pattern.

   The approximate centre of the rib structure should have greater materia l as compared to the rest of the rib structure.

5. FINA L SHAPES BASED ON OPTIM IZATION RESULTS : Based on the optimizat ion results the following dimensions for both the prima ry and secondary arm were finalized. The final shapes were based on the conclusions of the Topological Optimization.

   Basic Design considerations like minimu m c ross -section as well as space for various mountings and electronic components are taken into consideration.

   Manufacturing constraints such as limitations in the pattern ma king process, casting process etc, were also taken into consideration.

   Based on these constraints we managed to reach a optimized shape of the two arms. These shapes were then compared with initia l shapes and difference in weight was calcu lated.

   There was no real change in the manufacturing process of the initia l and final shapes of the primary and secondary arms. However a co mp letely new pattern was required for the casting of the fina l shapes.

   PART NAM E: Primary Arm SIZE: 400 X 120 X 100 1 No.

   Fig V.1 Fina l Shape of Prima ry Arm

   PART NAM E: Secondary Arm SIZE: 350 X 100 X 80 1 No

   Fig V.2 Fina l Shape of Secondary Arm

   ANALYSIS OF FINA L SHAPES :

   The fina l shapes are analysed so as to ensure that the values of stress and ma ximu m have not increased beyond the previous values.

   The analysis of the final shapes shall be done considering the same forces that have been applied for the analysis of the initial shapes. Based on the 3D model, the volume and hence the weight is calcu lated.

   Density of Alu min iu m Alloy Al Si 12 = 2710 kg/m2 Arm 2 In itia l Vo lu me= 1167385 mm3

   Arm 2 In itia l Weight = 1167385 X 2.71 X 10-6 kg = 3.16 kg Arm 2 Final Vo lu me = 966399 mm3

   Arm 2 Final Weight = 966399 X 2.71 X 10-6 kg = 2.61 kg Reduction in Weight = 0.55 kg

   % Reduction in We ight = 15.23 %

   Arm 1 In itia l Vo lu me = 1517165 mm3

   Arm 1 In itia l Weight = 1517165 X 2.71 X 10-6 kg = 4.11 kg Arm 1 Final Vo lu me = 1165229 mm3

   Arm 1 Final Weight = 1165229 X 2.71 X 10-6 kg = 3.15 kg Reduction in Weight = 0.95 kg

   % Reduction in We ight = 23.11 %

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   Fig V.3 Analysis of Prima ry Arm

   RESULTS:

   Maximu m Deformat ion: 2.390e-005m = 23.9 microns

   Maximu m Equivalent St ress = 1.876e +006 N/ m2 =1.876 N/ mm2

   Fig V.4 Analysis of Secondary Arm

   RESULTS:

   Maximu m Deformat ion: 2.427e-006m = 2.427 mic rons. Max. Equ ivalent Stress = 1.590e+005 N/ m2 =0.159 N/ mm2

   ANALYTICA L CA LCULATIONS:

   In order to guarantee that the optimized design has greater stiffness as compared to initia l design the deflection analysis of the initia l and optimized shapes is done analytically.

   The follo wing assumptions are made in order to simp lify the calculations.

   The Load acting on both the arms is static load.

   The load acting on the arm is acting along the centre of gravity of the arm.

   The cross-section of the arm is uniform throughout the length. The arm is comp letely fixed at the support end.

   CA LCULATIONS:

   Bending stress and deflection for un-optimized arm I

   M.I. = 4.50 106 mm4

   Bending mo ment of load acting at free end of cantilever bea m

   M = W L = 98.1 340 = 33354 N.mm

   Bending stress using fle xu ral formu la for pure bending M/I = /y = E/ R

   Where,

   M = Bending Mo ment I = Mo ment of Inertia = Bending stress

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   Y = Distance between extre me fibre to neutral a xis E = Young Modulus

   R = Radius of curvature = 0.44 N/ mm2

   Deflection for cantilever bea m y = Wl3/ 3E I = 0.00423 mm.

   Bending stress and deflection for optimized a rm I

   Moment of inertia = Ixx = 4.54 106 mm4

   Bending mo ment acting at the free end of the cantilever bea m

   M= WL = 98.1 340 = 33354 N.mm

   The bending stress using fle xura l formu la fo r pure bending = M Y/I = 0.367 N/ mm2

   Ca lculation for the deflection of cantilever beam y = Wl3/3E I = 0.00420 mm

   Bending stress and deflection for Un-optimized arm II

   Moment of inertia , I = 267.035 103 mm4

   Bending mo ment acting at the free end of the cantilever bea m

   M= WL = 29.43 300 = 8829 N.mm

   Bending stress using fle xu ral formu la for pure bending = M Y/I = 0.826 N/ mm2

   Deflection of cantilever bea m

   y = 0.01469 mm

   Unoptimized Arm 2 = 0.01469 mm

   Optimized Arm 2 = 0.00868 mm

   VA LIDATION OF RESULTS:

   The effects of optimizat ion have to be checked by imple mentation of the optimized shapes on the system.

   The values of current drawn by the motors for ra ising the payload are observed.

   The graphs of the current drawn by initial design and the current drawn by optimized design are plotted against the payload lifted for both the primary and secondary arm.

   For observations on the primary arm the secondary arm is kept in home position and only the prima ry arm is operated.

   It is to be noted that the current drawn by motors for lowering the load did not vary for in itia l or optimized design.

   Current(Amperes)

   0.4

   0.3

   0.2

   0.1

   0

   0 kg 0.5 1 kg 1.5 2 kg

   Bending stress and deflection for optimized a rm II Moment of Inert ia by using paralle l a xis theore m

   M.I. = 452 103 mm4

   Bending mo ment of load acting at free end of cantilever bea m

   M = W L = 29.43 300 = 8829 N.mm

   Bending stress using fle xu ral formu la for pure bending = M Y/I = 0.488 N/ mm2

   Deflection for cantilever bea m y = Wl3/ 3E I = 0.00868 mm

   Co mparison between Initial and optimized shape deflections Unoptimized Arm 1 = 0.00423 mm

   Optimized Arm 1 = = 0.00420 mm

   8

   kg kg

   PayloaOdp(Ktigm) ized Shape

   Fig V.5 Graph of Current Dra wn by Prima ry Arm Motor

   Current(Amperes)

   0.4

   0.2

   0

   Bibliography.

   1. We ight-optimized Design of a Co mmerc ial Truc k Front Suspension Component – Dana Corporation Testimonia l, www.ansys.com

   2. Topology Optimization in ANSYS – Brian King, IMPA CT Engineering Solutions, www.impactengsol.com

      0 kg 0.5 kg 1 kg 1.5 kg 2 kg

      Payload(Kg)

      Initial Shape

      Fig V.6 Graph of Current Dra wn by Secondary Arm Motor

      CONCLUSION ON OPTIMIZATION:

      Hence we can conclude that the final shapes of the prima ry and secondary arms are lighter in weight than the initial design.

      The reduction in we ight for Primary a rm = 23.11% The reduction in we ight for Secondary arm = 15.23%

      The final shapes also have greater stiffness than the initial shapes at the same given loading conditions.

      For Primary Arm

      Initia l design deflection = 62.96 mic rons Optimized design deflection = 23.9 microns

      For secondary Arm

      Initia l design deflection = 2.748 mic rons . Optimized design deflection = 2.427 microns.

      The power required by the motors of the primary and secondary arms is reduced using the optimized design.

      CONCLUSIONS:

      We succeeded in improving the design of the manipulators and hence reduced their we ight.

      This also in turn improved the performance characteristics of the robot since less power was required by the motors for the same given payload.

   3. Optimization design for the structure of an RRR type industrial robot – Adrian Gh iorghe, U.P.B. Sci. Bull., Series D, Vo l. 72, Iss. 4, 2010

   4. Topology Optimization and Casting – Thorsten Schmidt, Technical Director, He idenreich & Ha rbeck A G, Moelln, Germany, www.ansys.com.

   5. Application of Topology Optimizat ion and Manufacturing Simu lations – Proceedings of the International MultiConference of Engineers and Co mputer Sc ientists 2008 Vo l II, IM ECS 2008, 19-21 March, 2008, Hong KongTruck .

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