Selected aspects of design and modelling of linear actuator based on PM BLDC motor

Transcription

1 Januz HETMAŃCZYK, Tomaz STENZE, Boguław GRZESIK Sileian Univerity of Technology, Faculty of Electrical Engineering, Department of Power Electronic, Electrical Drive and Robotic doi:.599/ Selected apect of deign and modelling of linear actuator baed on PM BDC motor Abtract. The article decribe proce of deign and modeling PM BDC motor operating in a linear actuator. The actuator drive mechanim i implemented on bae of a ball crew. The poibility of applying the implification conequent by the need for the implementation of model realtime calculation wa conidered. The difference in the reult generated uing uch model in comparion to the full model wa alo taken into account. Furthermore, it wa preented the tructure of the real actuator control ytem. The reult of computer imulation were compared with the meaurement waveform, obtained on the tet bench. (Wybrane apekty projektowania i modelowania iłownika liniowego zrealizowanego na bazie ilnika PM BDC) Strezczenie. W artykule opiano proce projektowania i modelowania ilnika PM BDC pracującego w iłowniku liniowym. Mechanizm pouwu iłownika realizowany jet na śrubie kulowej. Rozważono możliwości toowania uprozczeń wynikających z potrzeby realizacji obliczeń w czaie rzeczywitym. W badaniach uwzględniono różnice w wynikach generowanych przy użyciu modeli uprozczonych w porównaniu do modeli pełnych. Ponadto zaprezentowano trukturę układu terowania rzeczywitym iłownikiem. Uzykane wyniki ymulacji komputerowych zetawiono z przebiegami pomiarowymi otrzymanymi na tanowiku badawczym. Keyword: Permanent magnet bruhle, electric drive, linear actuator, modeling Słowa kluczowe: Bezzczotkowy ilnik prądu tałego, napęd elektryczny, iłownik liniowy, projektowanie i modelowanie Introduction The ubject of the paper i the numeric model of a linear actuator deigned for a ix motor drive of a parallel manipulator. Control of the above mentioned manipulator require at firt the development of the ix motor drive control tructure. Another requirement i an implementation of invere kinematic or even, in particular cae, invere dynamic olution. When kinematic decription of the manipulator i ufficient, the reult of algebraic or numeric calculation are etpoint of actuator troke controller. Conidering the acceleration of ix actuator, it might be neceary to calculate invere dynamic olution of parallel manipulator and limit each actuator current in order to achieve appropriate acceleration. Thu the model of ingle actuator i a fundamental component of the parallel manipulator complex numeric model. The development and laboratory verification of uch a model i decribed in the paper. The ancetor of ytem with parallel tructure i a movable platform baed on ix telecopic actuator, which are joined with ball joint. That device wa deigned by Gough in 947. But in 965 the deign known a Stewart platform wa contributed to the theory of machine. In that time Stewart developed parallel tructure with ix degree of freedom for a flight imulator. There exit alo a term Stewart-Gough platform [7, 6]. Mechanical ytem of thi deign are ued for the contruction of aircraft flight or driving vehicle imulator. Another branch of application of the abovementioned ytem i a deign of tet tand for analyi of impact of the vibration and hock on the teted ytem operation. Parallel manipulator like Stewart- Gough deign are alo ued a tabilization ytem in medical conveyance for patient protection in cae of pinal injurie or in neonatal tranport a well a in pecial tranport area for enitive good protection. There are ome advantage of parallel manipulator, tarting from the poibility of ix degree of freedom motion, through the poibility of high acceleration and velocitie due to mall mae of moving part and finihing with high poitioning accuracy reulting from the high rigidity of the mechanim. Beide Stewart-Gough parallel manipulator i characterized by advantageou weight to volume ratio. It i alo worth to mention that all the drive of that ytem are identical, which lead to better efficiency and higher load of the manipulator. There are alo few diadvantage of parallel manipulator like limitation of working pace, which i often much maller than the dimenion of the platform. The other drawback are: poibility of conflict between the kinematic chain element, preence of ingular point within the workpace, the difficulty in determining direct geometrickinematic parameter, complex control ytem, the complexity of the linkage between the moving kinematic chain. Figure a and b how the type of kinematic chain of linear actuator ued in parallel manipulator. Both kinematic chain have three type of joint in different configuration: univeral U, primatic P, and pherical S. Deign principle of primatic joint P baed on ball crew are decribed in detail by [] and []. Beide the claical kinematic platform 6-UPS (Figure 2a) propoed by Gough-Stewart and then [2] or [8] and [5] baed on linear actuator, it i known and ued in modified olution. Such kinematic i hown in Figure 2b. It developed the novel platform 6-PSU, which conit of ix leg with a primatic joint P, pherical joint S, and univeral joint U [4]. The ix primatic joint move vertically with repect to the bae, which appear to be a ignificant improvement over the tandard Gough-Stewart platform. The ame 6-PSU kinematic diagram of the parallel manipulator wa propoed by [5]. In the analyzed cae, each linear actuator conit of a drive and joint: the univeral U, primatic P, and pherical S. Uually, the author do not focu on the modeling of DC drive but the acceleration-baed force-impedance controller. In one cae, claic mini DC motor (5W, 8 V and 53 rpm) were ued [5]. The author preent a dynamic model of the DC drive a an element of the Robotic Controlled Impedance Device (RCID). In another cae, the model of 6-UPS platform wa developed baed on permanent magnet ynchronou motor [8]. Thi type of kinematic i hown in Figure 2a.. PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 9 NR 6/25

2 a) Platform B B n U S P Fig.. Kinematic diagram of linear actuator: a) UPS kinematic chain; PSU kinematic chain A n Platform A The ame kinematic of 6-UPS platform driven by hydraulic linear actuator were ued a a motion imulator [6]. The paper propoe three ytematic optimal deign procedure to olve the practical deign problem of the Gough-Stewart platform and the author focu on the modeling of electrohydraulic linear actuator. There i one article dedicated to modeling of PM BDC linear actuator drive [2], but in the paper [9] decribe model of PM BDC deigned to gear ervo actuator. Quite imilar 6-3 UPS kinematic of parallel manipulator i preented in [8]. It i illutrated in Figure 2c. The 6-3 UPS parallel manipulator conit of ix linear actuator connected to the bae platform in ix point via univeral joint U, and to the motion platform in three point via pherical joint S. Conequently, the conecutive linear actuator are linked to each other in three pair. The linear actuator a an application of a parallel manipulator Parallel manipulator operating in ix degree of freedom (6DOF) conit of a fixed lower bae and movable upper platform. Thee part are connected with ix independent linear actuator (Figure 3a). Each of the actuator, alo called arm of the manipulator, i made up of two main part connected with a crew driven by motor and a ball nut. Thoe part of the whole mechanim enable converion of rotary to progreive motion. The crew i propelled by permanent magnet bruhle DC motor (PM BDC). ower part of the arm i connected with the bae with the Cardan joint, while upper part of the arm i linked to the upper platform with mechanical ytem, which include Cardan joint and rotary univeral joint. Control of the decribed parallel manipulator i baed on an appropriate etting of each actuator length, which lead to achieving ix degree of freedom for the upper platform of the manipulator. PM BDC motor of 4 W were ued in the drive ytem of each actuator. The motor were equipped with integrated control unit controlling the velocity, current, and poition of the motor. The motion parameter including the rotation direction and the number of pule of the encoder can be et uing the CANopen protocol. Control method of parallel manipulator Control method of parallel manipulator can be claified in repect of mathematical decription form and the accuracy of manipulator poitioning derived from that [2, 9]. In thi perpective the parallel manipulator control algorithm can be divided into two categorie: firt-baed on the analytical method, and econd - baed on numerical calculation. Specific algorithm of parallel manipulator motion control differ mainly in poitioning accuracy and computational complexity. Typical decription of the parallel manipulator i baed on the three dimenional Carteian coordinate (X B, Y B, Z B ) and three angle (θ, φ, ψ). It i hown in the Figure 3b. The central point of the manipulator i the center of the local coordinate ytem of the manipulator, while the central point of lower bae Q A i the center of the global bae coordinate ytem. The point from A to A 6 decribe the manipulator bae. The upper platform of the manipulator i defined by point B to B 6. The mentioned two part of the manipulator are linked with ix linear actuator labeled a, 2, 3, 4, 5 and 6. Vector p i the orientation vector of the coordinate Q B with repect to Q A. The poition vector a i (related to Q A ), b i - the poition vector (related to Q B ). The idea of the algorithm of the manipulator control lie in determination of the upper platform tranlation and rotation in three dimenion. Depending of the deired motion parameter, poition and orientation or even acceleration in three dimenion are determined. PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 9 NR 6/25

3 a) of the value of control for each linear actuator drive. In uch approach the torque, inertia and force, preent when the manipulator i in motion, are omitted. In order to achieve accurate value of actuator control, correponding to the value of the real mechanical ytem, it i neceary to olve invere dynamic tak. a) B4 B5 B3 U B2 B B6 S P A4 A5 A3 2 A6 A2 A c) B S B2 B P A4 2 A5 Fig.3. CAD model of 6DOF parallel manipulator: a) deign; kinematic model A3 U A2 Fig.2. Kinematic diagram of Stewart-Gough parallel manipulator: a) the 6-UPS parallel manipulator; the 6-PSU parallel manipulator; c) the 6-3 UPS parallel manipulator. When, tranlation, called alo actuator troke are known, the calculation of motion i decribed a forward kinematic. The invere kinematic algorithm allow to determine troke of all actuator in aumption of deired change of poition of manipulator upper platform. Thi control method require determination of all angular and linear tranlation value, which are poible within certain contraint of linkage and which lead to deired poition of the upper platform of the parallel manipulator. The olution of invere kinematic i the main tak of control and motion programming for parallel manipulator. Thi i important when determining manipulator motion in time. The invere kinematic olution lead to determination A A6 Deign of the linear actuator for parallel manipulator We have ued the SolidWork oftware package for the development of linear actuator deign. Thi engineering Computer Aided Deign (CAD) tool allow not only for three dimenional model deign, but a well allow for examination of deigned mechanical element in repect of the elected iue of kinematic, dynamic and endurance. The deign proce ha been tarted from making the aumption concerning kinematic and manufacturing material. Then three-dimenional model ha been deigned and it ha been ued for determination of elected endurance parameter. The final hape of the deigned actuator i hown in the Figure 5. A the example of computer analyi made in SolidWork environment in the Figure 4 we have hown load force and load torque of the deigned linear actuator during vertical motion cycle of the parallel manipulator. 2 PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 9 NR 6/25

4 a) Fig.4. The waveform of a) ball crew load force of ingle linear actuator; and load torque of thi actuator PM BDC motor drive, during full vertical movement of the parallel manipulator The linear actuator preented in Figure 5 i baed on the cage framework coniting of ix hexagonal aluminum dic, connected with ix connected circular teel rod. Three of thee rod are firmly fixed with both motor body and the ball crew. The pitch of the ued ball crew i p cr = 5 mm. A haft of the PM BDC motor i linked to the ball crew with a clutch. The ball crew i mounted in upper and lower ball bearing. The motor, ball crew and fixing bearing make a complete drive mechanim. ower bearing block conit of two ball bearing, while upper bearing block i made of ingle ball bearing. The tranlation mechanim conit of three remaining leading rod fixed to the ball crew. Poible tranlation of thi mechanim i l= 335mm. Fixing and leading rod are led by linear bearing, which are mounted in the hole in the hexagonal dic. The rod ending are fixed in the appropriate dic with axial and radial crew connection []. Minimal length of each actuator i min = 89 mm. laboratory tand thank to the connection of two computer deign and imulation environment. There i the poibility of control ytem deign and viualization of tatic and dynamic tate of the three-dimenional model of a real object. The drawback of uch approach i the neceity of taking into account accurate parameter of the real object. It require detailed pecification of numeric model deigned in SimMechanic toolbox running in Matlab/Simulink environment. A it come from our analye the initial virtual model i uually an approximation and it could be upplemented with detail after the identification of the real object parameter. Beide, in cae of computer imulation there appear ome problem ariing from numerical method ued in the model, which may lead to the lack of convergence of numerical computation, for example in cae of improper treatment of the mechanical ytem contraint. The overall tructure model of linear actuator drive with PM BDS motor The overall tructure model of linear actuator drive i preented in Figure 6. PM BDC motor model i the primary block of the hown tructure. We have integrated in ingle block the component of motor model and electronic commutator model. Other block are reponible for matching the input circuit parameter and tranforming rotary motion into linear. v 2 T G_lo FQ m J c Fig.6. The block diagram of the linear actuator model drive with PM BDC motor Fig.5. The deign of linear actuator with PMBDC motor For deigning the three-dimenional model of the parallel manipulator (Figure 3a) we have ued the linear actuator model, which we deigned in SolidWork CAD environment. We have deigned the parallel manipulator model in order to make analyi of that electromechanical device and alo in order to make a ynthei of it control ytem tructure and parameter. That approach, baed on integration of CAD oftware with imulation environment wa previouly decribed in a few publication for example in [3]. We have ued Matlab/ Simulink model compatible with SimMechanic toolbox prepared from the data automatically exported from the previouly deigned threedimenional model. The decribed deign proce equence allowed for implifying the implementation of invere kinematic of the deigned parallel manipulator in the Matlab/Simulink environment. We have obtained virtual Output quantitie of the motor are DC power circuit voltage U d, load torque T and moment of inertia of load converted to the motor output haft J. Input quantitie are DC circuit current I d, angular velocity ω and motor torque T. The motor model i connected to the actuator model with a et of matching block, which convert quantitie characteritic for linear crew drive to quantitie pecific for PM BDC motor. The value of input voltage U d i calculated by poition controller (PC). The et point of the mentioned controller i tranlation of linear actuator l, which i determined by mater control ytem. The matching block at the motor model input are reponible for load ma m and force F converion to a ignal proportional to the additional moment of inertia J and load torque T. However, the tak of analogou matching block at the motor output i to convert ignal proportional to angular velocity ω and motor torque T into ignal referring to tranlational velocity of linear actuator v and force F, to which the movable part of that element i expoed. Thee matching block are baed on then following relationhip: block module of converting ma into moment of inertia: PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 9 NR 6/25 3

5 2 v () Jo m Jc block module of proceing load force into load torque: T v F T (2) Q G_lo block module of converting motor torque to linear actuator force: F T T (3) G_lo v where: J c moment of inertia of the drive clutch, J o additional moment of inertia converted to the motor output haft; T motor load torque; T G_lo gear loe torque; F force generated by the actuator, F Q force loading the linear actuator; m - part of the parallel manipulator load ma attributable to ingle actuator. Modified model of PM BDC motor Due to extending imulation time of complete ix-motor drive for parallel manipulator, we have decided to implify one of the main component of the model. The accurate permanent magnet bruhle DC motor model, which i available in Matlab/Simulink environment wa the reference for the new model, which we have created for the purpoe of the project decribed in the paper. The propoed model made poible imulation of tatic and dynamic tate of PM BDC motor. The diagram of three-phae bruhle DC motor main circuit connection i preented in Figure 7. There i one pair of pole in the hown motor and the winding are connected in tar. The electronic commutator tructure i a three-phae bridge. A motor applied in the deign of linear actuator i conitent with the chematic, except for four pair of pole intead of one. Fig.7. Wiring diagram for 3-phae PM BDC motor with electronic commutator The principle of operation and baic propertie of PM BDC motor are widely decribed in literature, for example in [, 2, 22]. The mot important relationhip decribing the motor are lited below: (4) k fk e K T K (5) ek fk k C (6) Te Tek ka (7) lo i T T T dω T J T T (8) dy e dt The following deignation have been ued: e k - phae electromotive force (EMF); K fk - excitation coefficient for k-th phae; T ek electromagnetic torque generated by k-th phae current, T e total electromagnetic torque of the motor; T, T and T lo anti-torque, load torque and motor lo torque; T dy dynamic torque; J total moment of inertia; ω angular peed. The motor with tructure hown in Figure 6 can be brought [2, ] into contant current equivalent model with tructure illutrated by Figure 8. The main aumption of that operation i neglecting the difference between waveform of back EMF, which i variable in PM BDC motor and contant in cae of typical DC motor. The other implifying aumption involve omiion of the reitance and inductance of electronic commutator and motor terminal. Fig.8. PM BDC motor a a pecial cae of a DC motor For circuit with DC voltage controller or pule-width modulation (PWM), the following relationhip are true: (9) Ud Ud* UDC () Id IDC Ud* where U d* i relative voltage value and U DC i ource dc voltage. In cae of ideal motor with negligible inductance impact, the following relationhip are true: Ud 2RId () 2Kfp (2) Te 2KfpId Ud (3) ω 2Kfp Id (4) ω R K fp where K fp i phae excitation coefficient for the flat ection of phae EMF waveform. In real motor, when the winding are witched, the current do not intantly increae in a tep-like manner, but they rie in accordance with exponential curve [2]. Thi caue emergence of additional voltage drop and increae in lope of torque-peed characteritic. What i more, due to energy recuperation into the ource during the time when backward diode conduct current, the current producing electromagnetic torque I e i greater than average input current I d calculated for DC circuit, that i: Te (5) Ie Id 2Kfp The additional voltage drop may be taken into account by introducing the commutation impact coefficient, which provide information on how many time the voltage drop due to commutation i greater than voltage drop acro the reitance. If we refer to [2], we find that commutation coefficient defined a: 4 PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 9 NR 6/25

6 Udx (6) kq UR will be defined a follow, when light implifying aumption have been adopted: mp ω (7) kq 2π 2R The mot important of all implifying aumption i that during commutation motor peed remain approximately contant. When commutation coefficient i ued (6), (4) may be reduced to: Ie (8) ω R kqkfp When commutation coefficient (7) i introduced into (8), we obtain: (9) wherein: (2) T e ω kch R k 2 ch i K fp kch mp Te mp I e 4π Kfp Kfp 4π Kfp Coefficient k ch repreent additional lope of mechanical characteritic, where ω i i angular peed of ideal motor with negligible inductance impact. Baing on the relationhip previouly lited, which decribe ideal PM BDC motor, it i poible to develop a model with the tructure identical to typical DC motor model tructure. Such a model wa denoted a modified model of PM BDC motor [3]. The tructure i hown in the Figure 9b. Verification of numerical model of linear actuator The numerical model of a ingle permanent magnet bruhle DC motor propelled actuator wa created on the bai of contruction data of that element (Figure a). The model implemented in Matlab/Simulink environment ha been ued for development of parallel manipulator model a well a at the tage of PM BDC motor election for parallel manipulator deign [7]. The model calculation ha been accelerated in comparion with the typical PM BDC motor numeric model, thank to the implementation of previouly decribed extenion of DC motor model, baed on the taking into account the lope of mechanical characteritic of the motor. Another application of created model wa the development and implementation of control algorithm. We have performed verification of a ingle actuator deigned for the parallel manipulator on the laboratory tand hown in Figure b. The actuator wa mounted in vertical poition during tet. The PM BDC motor wa mounted in lower part of the actuator. Both imulation and laboratory tet, have been carried out for motor BG75x5PI, manufactured by Dunkermotoren company, with the following catalogue parameter: U n = 24 V, p= 4, R = 2 mω, =,25 mh, P n = 43 W, T n =,9 N.m J M = 43,7-6 kg.m2, T lo =,4 N.m, K m = 52 mn.m/a, K fp = 26 mv./rad. Verification of the elaborated numeric model correctne wa one of the aim of the laboratory tet of ingle actuator, deigned for parallel manipulator. The evaluation of the model wa baed on the comparion of elected quantitie, obtained by imulation reearch and during meaurement of real object. The performed comparative analyi alo gave an opportunity to determine the effect of adopted implification. Beide, we have planned and partially conducted verification of requirement aumed at the deign tage. We have performed the meaurement uing the tet ytem preented in Figure b, equipped with CAN bu for acquiition of meaured quantitie. a) U d U d 2E fp 2E fp 2 R 2K fp 2 R 2K fp Id I e I d I e 2K fp k ch 2K fp Fig.9. Model of PM BDC motor: a) contant current model of PM BDC motor; modified model of PM BDC motor, which take into account mechanical characteritic lope coefficient k Ch At firt we have verified computer model of the PM BDC motor. Figure and how the torque-peed characteritic of the motor obtained by meaurement of real motor in comparion to the characteritic obtained from the imulation reult. The tet have been run for voltage identical to thoe ued during computer imulation. We have carried out the imulation uing the modified contant current model, in which the influence of the inductance, a in real PM BDC motor ha been taken into account. A it come from the diagram below, obtained imulation reult are conitent with mechanical characteritic of real PM BDC motor in range of nominal load torque. Figure 3 how waveform of tranlation l of the linear actuator, velocity n of the motor and current drawn from the voltage ource I DC. There are preented imulation reult (Figure 3a) and meaurement of the real motor (Figure 3. We have obtained the waveform for et troke length l = 33 mm and for rotational velocity 8 rpm. The preented imulation reult were acquired for control ytem tructure, where mater poition controller wa implemented. T lo I d T lo T e T e J T T dy J T T dy i T T PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 9 NR 6/25 5

7 a) Up Spherical Joint w [rad/] Body Ball crew Actuator PM BDC motor Current PWM Angular diplacement Angular velocity Direction of rotation Angular acceleration Angular Velocity T Torque Current PWM Direction of rotation Body Univeral Joint Down Joint enor Velocity Stroke 5 library model 24V modified model 24V 5 contant current model 24V Te [Nm] Fig.. inear actuator a) numerical model; view of the meauring ytem Meaured operational parameter of the motor were acquired by internal built-in enor and tranferred to the hot computer uing CAN bu. The tet reult were tored in a file on the computer controlling the motor alo through CAN interface. During the meaurement the linear actuator wa not loaded with any additional ma. Speed (rpm) S - 24 V 2 - S - 6 V 3 - S - 8V 4 - M - 24 V 5 - M - 6V 6 - M - 8V,, 2, 3, 4, 5, Torque (N.m) Fig.. Torque-peed characteritic of the modified contant current model motor obtained by computer imulation (, 2, 3) for three upply voltage value (24V, 6V and 8V) and meaurement reult (4, 5, 6) obtained for identical voltage. Fig.2. Mechanical characteritic ω = f(t e ) obtained for the motor powered with voltage of 24V for PM BDC model from Matlab/Simulink library and for modified DC model of that motor. Summary and concluion On the bai of performed work in range of computer modelling and on the bai of the laboratory verification of permanent magnet bruhle DC motor, loaded with the ball crew linear actuator, we could tate that numeric model, worked out for the reearch, i correct and allow for calculating acceleration with aumed accuracy. Obtained imulation reult are conitent with laboratory tet meaurement, although ome implification have been applied relative to accurate full PM BDC motor model. The developed model of PM BDC motor with electronic commutator give poibility to determine average rotational velocity and current value, with proper accuracy. The obtained reult are imilar to thoe, which are available in cae of application of library model of PM BDC motor from Matlab/Simulink imulation environment. However, in cae of modified model application, the imulation time are ignificantly reduced. The model that we developed, i uitable for imulation of multi PM BDC motor drive. In order to achieve correct imulation reult, the witching period of commutator valve hould be lower than electromechanical time contant of the motor. In range of PM BDC motor control we have applied the CAN bu a an interface, connecting mater computer control ytem with the motor equipped with built-in power electronic converter and controller. Depite the lack of application of real time operating ytem in the computer controller, we have noted proper operation of the controlled drive ytem. On the bai of the proce and reult of the laboratory reearch, we could tate, that developed control architecture i uitable for digital recording of meaured quantitie through internal motor controller. We have found, that in cae of final control ytem for ix PM BDC motor drive implementation, it i advantageou to apply real time operation ytem. Another olution for that control ytem i baed on the development of dedicated controller with DSP microcontroller or other motion cla controller. Moreover, due to the planned further laboratory tet of multi motor drive for parallel manipulator, it i ueful to carry out the verification of laboratory control ytem baed on abview computing environment, een a an alternative to the currently ued computer control ytem baed on the tool provided by the motor manufacturer. 6 PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 9 NR 6/25

8 a),2, -, -, ,2,4,6,8 Time [] -2,2,4,6,8 Time [],2,4,6,8 Time [] Fig.3. The recorded waveform of tranlation l, rotational velocity n and current I DC of actuator drive for: a) imulation; meaurement REFERENCES [] Bhandari, V. B., Deign of Machine Element, Tata McGraw- Hill Education, (2). [2] Blaie, J., Bonev, I., Monarrat, B., Briot, S., ambert, J., Perron C., Kinematic characteriation of hexapod for indutry, Indutrial Robot: An International Journal, (2), Vol. 37, Iue, pp [3] Březina,., Andrš, O., and Březina, T., NI abview Matlab SimMechanic Stewart platform deign, Applied and computational mechanic, (28), Vol. 2 (), pp [4] Brian, R., Hopkin, Robert,., and William I., Kinematic, deign and control of the 6-PSU platform, Indutrial Robot: An International Journal, (22), Vol. 29, Iue 5, pp [5] Guojun,., Zhiyong, Q., Junwei, H., and Xiaochu,., Sytematic optimal deign procedure for the Gough-Stewart platform ued a motion imulator, Indutrial Robot: An International Journal, (23), Vol. 4 I: 6, pp [6] Guojun,., Zhiyong, Q., Xiaochu,., and Junwei, H., Tracking performance improvement of an electrohydraulic Gough- Stewart platform uing a fuzzy incremental controller, Indutrial Robot: An International Journal, (24), Vol. 4, Iue 2, pp [7] Hetmańczyk, J., Gawleta, Ł., and Krykowki K., A computer model of a parallel multi-drive manipulator of bruhle DC motor (in Polih), Electrical Machine - Tranaction Journal, (23), No. 98/23, pp [8] Hüeyin, A., Elma, A., Ibrahim Ö., Neural network algorithm for workpace analyi of a parallel mechanim, Aircraft Engineering and Aeropace Technology, (27), Vol. 79, Iue, pp [9] Jianwei Ch., Xiaoxian Y., Control of Electric Actuator Uing Bruhle DC Motor and It Performance Evaluation, IEEE Second International Conference on Intelligent Computation Technology and Automation, (29). ICICTA '9, pp [] Kania,., Dziurki, A., and Kaprzycki, A. (22), The Example of the calculation of the baic of machine deign (in Polih), WNT Warzawa. [] Krihnan, R., Electric Motor Drive, Modelling, Analyi and Control, Prentice Hall, New Jerey, (2). [2] Krykowki, K., PM BDC motor in electric drive. Analyi, propertie, modelling (in Polih), Sileian Univerity of Technology, (2) Gliwice. [3] Krykowki, K., and Hetmańczyk, J., Contant Current Model of Permanent Magnet Bruhle Direct Current Motor, Topical Problem in the Field of Electrical and Power Engineering - Pärnu (23), Talin Pärnu Etonia, pp [4] Krykowki, K., Hetmańczyk, J., and Makieła D., Impact of winding witching on torque-peed curve of PM BDC motor, COMPE - The International Journal for Computation and Mathematic in Electrical and Electronic Engineering, (23), Vol. 32, Iue 4, pp [5] ope, A.M. and Almeida, F. G., Acceleration-baed forceimpedance control of a ix-dof parallel manipulator, Indutrial Robot: An International Journal, (27), Vol. 34, Iue 5, pp [6] Merlet, J.P., Parallel Robot, Springer Science & Buine Media, (26). [7] Mutlu, H., Akçali, İ., D., and Gülşen, M., A Mathematical Model for the Ue of a Gough-Stewart Platform Mechanim a a Fixator, Journal of Engineering Mathematic, (26), Vol. 54, Iue 2, February, pp [8] Qiang Meng, Tao Zhang, Jingfeng He, Jingyan Song, and Xuedong Chen, Improved model-baed control of a ix-degreeof-freedom Stewart platform driven by permanent magnet ynchronou motor, Indutrial Robot: An International Journal, (22), Vol. 39, Iue, pp [9] Sajkowki, M., and Krykowki, K., Control ytem deign uing rapid prototyping method on an example of voice controlled mobile robot and 6DOF parallel manipulator, XXIII Sympoium Electromagnetic Phenomena in Nonlinear Circuit - EPNC, (24), Pilen, Czech Republic, pp [2] Sewoong K., Modeling and fault analyi of BDC motor baed ervo actuator for manipulator, IEEE International Conference on Robotic and Automation, ICRA, (28), 9-23 May, pp [2] Stenzel, T., Sajkowki, M., and Grzeik, B., Deign and Implementation of 6-DOF Parallel Manipulator Driven by Permanent Magnet Bruhle DC Motor, 8th International Conference on Method and Model in Automation and Robotic, MMAR, (23), pp [22] Zawirki K., Control of ynchronou motor with permanent magnet (in Polih), Poznań Univerity of Technology, Poznań, (25). Author: dr inż. Januz Hetmańczyk, dr inż. Tomaz Stenzel, dr hab. inż. Boguław Grzeik prof. Pol. Śl., Sileian Univerity of Technology, Faculty of Electrical Engineering, Department of Power Electronic, Electrical Drive and Robotic, Boleława Krzywoutego 2, 44- Gliwice, Poland, Bogulaw.Grzeik@poll.pl; Januz.Hetmanczyk@poll.pl; Tomaz.Stenzel@poll.pl. PRZEGĄD EEKTROTECHNICZNY, ISSN , R. 9 NR 6/25 7