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1

Working area of the helicopter PAD stabilization mechanism

Brewczyński D., Tora G.

Journal of KONES

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2017

|

Vol. 24, No. 1

59--66

EN

Helicopter pad located on the ship significantly increase the operational capabilities of military and civilian ships. During the storm, especially side tilts of the ship hinder or even prevent the safe use of the helicopter pad. It is proposed to apply the system placed between the deck of the ship and landing site plate, driven by four independent cable drives located under the deck. The task of the system will be preventing from transferring to Helicopter pad the tilt of the ship around the longitudinal and transverse axis and the displacement of the deck along the transverse and vertical axis within the limits of the work area. The mechanism consists of four movable links on which the movable helicopter pad platform is located. As the linear actuators, trolleys moving along horizontal guides were used, powered by system of steel cables with four independent electric motors. In folded state the mechanism, take up appropriately little space under the deck area. For the assumed extreme amplitudes of the ship motion, minimum dimensions of the mechanism links that meets the requirement to work in one configuration and lack of collisions were determined. Kinematic relationships were created indicate which mechanical quantities should be measured in real time to determine the momentary drives speeds. For the adopted assumptions simulation was performed, confirming the predicted behaviour of the system. Based on the kinematic equations of system and taking in consideration collisions and geometrical limits, working area for the flat part of the mechanism was determined.

2

Dynamics model of stabilization mechanism for helicopter PAD

Brewczyński D., Tora G.

Journal of KONES

|

2016

|

Vol. 23, No. 2

61--68

EN

Helipad located on ships greatly increases their ability to perform tactical and logistical abilities. They allow performing reconnaissance from the air, transportation of cargos and people to and from the ship. Landing on a moving ship particularly small size during bad weather is not a safe manoeuvre. Article provides an overview of existing solutions that improve safety during the landing manoeuvre of the helicopter to the ship and describes an innovative mechanism with can stabilize helicopter pad in four degrees of freedom. This solution is characterized in that the landing plate is movable and actuated simultaneously by two support plates and two levers. Plates and levers are driven by separate linear motors that move along the guides connected to the base. The main feature of the mechanism is that when the base is not stable, it can reduce the linear movement of the landing platform in the vertical and transverse direction and angular displacement around an axis perpendicular and parallel to the axis of the ship. A preferred feature of the mechanism is that in folded position it occupies relatively little space. In addition, advantageous attribute of the mechanism is its large working area, enabling the reduction of high amplitude vibration. The article contains a calculation of the kinematics for the proposed structure of the mechanism. It also includes speed drives waveforms, which are the result of simulations for the input parameters of the ship movement.

3

Mechanism of a motion platform inducing the movement of the operator’s seat in a heavy machine

Tora G., Trzaska W.

International Journal of Applied Mechanics and Engineering

|

2016

|

Vol. 21, no. 4

1007--1015

EN

One of the major work safety issues involves the investigations of machine vibrations and the way they affect the machine operators. These investigations can be performed in the laboratory conditions in a setup in which the seat vibrations are induced by a motion platform. A complex mechanism is proposed implementing 3 translations and 2 rotation movements, and actuated by three electric motors. This study investigates the design structure of the real motion platform mechanism and provides the synthesis of link dimensioning. Kinematic dependencies are formulated and the Jacobian matrix is derived accordingly to solve the equations of motion. Computer simulation procedure yields the critical seat vibration frequency and amplitudes for the available asynchronous motors.

4

Układ aktywnej stabilizacji lądowiska dla śmigłowców na okręcie

Brewczyński D., Tora G.

Logistyka

|

2015

|

nr 4

2557--2563, CD2

PL

W celu zwiększenia bezpieczeństwa lądowania helikoptera na statku podczas trudnych warunków pogodowych zaproponowano układ aktywnej stabilizacji lądowiska. Wstępne symulacje komputerowe pokazały, że zaproponowany układ może w istotny sposób redukować ruchy wzdłuż osi poprzecznej statku, wzdłuż osi pionowej oraz kątowe wychylenia wokół wzdłużnej osi wywołane kołysaniem okrętu na falach. Wyznaczono pole pracy układu, w którym proponowany układ może skutecznie stabilizować położenie lądowiska. Zaproponowano strukturę układu sterowania, z której wynika potrzeba rozwiązania zadania prostego i odwrotnego kinematyki oraz rozwiązanie zadania odwrotnego dynamiki mechanizmu UASL. W ramach dalszych prac przewidziana jest budowa stanowiska badawczego w celu weryfikacji wyników otrzymanych w symulacjach. Zasadne wydaje się również stworzenie przestrzennego układu aktywnej stabilizacji lądowiska umożliwiającego dodatkowo obrót lądowiska wokół osi poprzecznej statku.

EN

In order to increase the safety of the helicopter landing on the ship during the difficult weather conditions, the paper proposes an active helipad stabilization system. Preliminary simulations have shown that the proposed system can significantly reduce the movement along the transverse axis of the ship, along the vertical axis and tilt angle about the longitudinal axis of the ship caused by rocking on the waves. Designated mechanism field of work in which the proposed system can effectively stabilize the position of the helipad.The structure of the control system is proposed, which shows the need to solve kinematics simple and inverse task and inverse dynamics task of the active helipad stabilization system mechanism. As part of further work planned is the construction of the research model to verify the results obtained in the simulations. It seems reasonable to also create a spatial active helipad stabilization system allowing rotation about the transverse axis of the ship.

5

Stabilization mechanism for helicopter pad with four degrees of freedom

Brewczyński D., Tora G.

Journal of KONES

|

2015

|

Vol. 22, No. 3

7--12

EN

Helipad located on ships greatly increases their ability to perform tactical and logistical abilities. They allow performing reconnaissance from the air, transportation of cargos and people to and from the ship. Landing on a moving ship particularly small size during bad weather is not a safe manoeuvre. Article provides an overview of existing solutions that improve safety during the landing manoeuvre of the helicopter to the ship and describes an innovative mechanism with can stabilize helicopter pad in four degrees of freedom. This solution is characterized in that the landing plate is movable and actuated simultaneously by two support plates and two levers. Plates and levers are driven by separate linear motors that move along the guides connected to the base. The main feature of the mechanism is that when the base is not stable, it can reduce the linear movement of the landing platform in the vertical and transverse direction and angular displacement around an axis perpendicular and parallel to the axis of the ship. A preferred feature of the mechanism is that in folded position it occupies relatively little space. In addition, advantageous attribute of the mechanism is its large working area, enabling the reduction of high amplitude vibration. The article contains a calculation of the kinematics for the proposed structure of the mechanism. It also includes speed drives waveforms, which are the result of simulations for the input parameters of the ship movement.

6

Wpływ opóźnienia czasowego na pracę aktywnego zawieszenia kabiny maszyny roboczej

Brewczyński D., Tora G.

Logistyka

|

2014

|

nr 6

2261--2269

PL

Przejazdy maszyn roboczych po trudnym terenie są przyczyną pojawienia się cyklicznych przechyłów maszyny, negatywnie pływających na poziom koncentracji operatora. Zaproponowano układ aktywnego zawieszenia kabiny, którego zadaniem jest redukcja drgań niskiej częstotliwości w pięciu stopniach swobody. Mechanizm wykonawczy rozpatrywanego układu składa się z platformy podłączonej wahaczami do ramy maszyny. Platforma, na której znajduje się kabina, poruszana jest napędami hydraulicznymi wyposażonymi w sterowniki. Pomiary przestrzennego ruchu ramy maszyny oraz założony ruch kabiny są podstawą do obliczeń w czasie rzeczywistym wartości chwilowych prędkości napędów. Obliczenia zawierają rozwiązanie zadania prostego i odwrotnego kinematyki mechanizmu zawieszenia oraz rozwiązanie zadania odwrotnego dynamiki. Zaproponowano model napędu hydraulicznego z uwzględnieniem siły tarcia. Symulacje pracy aktywnego zawieszenia kabiny wykazały ilościowy wpływ zwłoki czasowej zadziałania napędów na jakość i zakres efektywnej pracy zawieszenia.

EN

Heavy duty machine journey in difficult terrain is causes the appearance of the cyclic machine tilts. It has negative effect on the level of the operator concentration. Active cabin suspension system was Proposed, whose task is to reduce low-frequency vibrations in five degrees of freedom. Enforcement mechanism of the considered system consists of a platform connected by rocker arms to the machine frame. Platform, on which the cabin are located is moved by hydraulic drives equipped with drivers. Measurements of the spatial movement of the machine frame and the planned movement of the cab is the basis for the momentary drives speed calculation in real time. The calculations include the solution of simple and inverse kinematics tasks of a suspension mechanism and solution of the inverse dynamics task. Proposed drive model taking into account the hydraulic frictional force. Simulation of the active cab suspension has shown an quantitative impact drives response time delay on the quality and range of effective suspension work.

7

Identification of joints positions of the landing gear mechanism using laser measurements

Brewczyński D., Tora G.

Logistyka

|

2014

|

nr 6

2270--2276

EN

The article contains a description of the noncontact method of geometry measurement using handheld 3D laser scanner REVscan with a step-by-step guide. The test object is MIG-29 aircraft landing gear. During the analysis performed a complete scan of the landing gear with a resolution of 2.0mm (accuracy of 0.05 mm) and a scan of critical points with a resolution of 0.2mm (0.05 mm accuracy). Subsequently an attempt to determine the position of characteristic points of connections, joints and links dimensions by editing the resulting cloud of points. During measurements has been shown the advantages, disadvantages and limitations in the use of non-contact method using 3D laser scanners. Influence of type and color of the object surface on the measurements was observed. Additional research were performed to examine this phenomenon. Collected data was used to find characteristic point of landing gear in main reference system. VXelements software was used for calibration, configuration of the scanner and collecting data. Geomagic 3D software was used for extensive data processing.

PL

Artykuł zawiera opis bezkontaktowej metody pomiarów geometrycznych przy użyciu ręcznego laserowego skanera 3D REVscan wraz z opisem procedury pomiaru. Obiektem badanym było podwozie samolotu MIG-29. Podczas analizy wykonano kompletny skan podwozia lotniczego z rozdzielczością 2.0mm (dokładność podana przez producenta 0.05mm) oraz skan kluczowych punktów z rozdzielczością 0.2mm (dokładność podana przez producenta 0.05mm). Następnie podjęto próbę ustalenia pozycji charakterystycznych punktów połączeń oraz długości ogniw przez edycję chmury punktów. Podczas pomiarów wykazano zalety, wady oraz ograniczenia w stosowaniu bezkontaktowej metody pomiaru z użyciem laserowego skanera 3D. Został zaobserwowany wpływ rodzaju i koloru badanej powierzchni na pomiary. Dodatkowe badania zostały wykonane w celu zbadania tego zjawiska. Zebrane dane posłużyły do znalezienia charakterystycznych punktów mechanizmu podwozia lotniczego w głównym układzie odniesienia. Oprogramowanie VXelements zostało użyte do kalibracji, konfiguracji skanera oraz zapisu danych. Oprogramowanie Geomagic 3D zostało użyte do szerokiej obróbki danych.

8

Dynamic positioning system of helicopter pad on the ship

Brewczyński D., Tora G.

Journal of KONES

|

2014

|

Vol. 21, No. 4

21--27

EN

Helicopter pad located on the ship significantly increase the operational capabilities of military and civilian ships. During the storm, especially side tilts of the ship hinder or even prevent the safe use of the helicopter pad. It is proposed to apply the system placed between the deck of the ship and landing site plate, driven by three independent linear drives located under the deck. The task of the system will be preventing from transferring to Helicopter pad the tilt of the ship around the longitudinal axis and the displacement of the deck along the transverse and vertical axis within the limits of the work area. The mechanism consists of the three movable pillars with the plate on top, which is the movable helicopter pad platform. As the linear actuators, plates moving along a horizontal guide were used, powered by system of steel cables with three independent electric motors. In folded state the mechanism, take up appropriately little space in the deck area. For the assumed extreme amplitudes of the ship motion, minimum dimensions of the mechanism links that meets the requirement to work in one configuration and lack of collisions were determined. Kinematic relationships were created indicate which mechanical quantities should be measured in real time to determine the momentary drives speed. For the adopted assumptions simulation was performed, confirming the predicted behaviour of the system. Based on the dynamics equations of system, drives loads, their power and individual links and joints load were determined.

9

Motion planning of a novel 2-DOF parallel manipulator applied as driving simulator of the wheel loader

Knapczyk J., Tora G.

International Journal of Applied Mechanics and Engineering

|

2014

|

Vol. 19, no. 3

599--608

EN

A novel parallel manipulator with 3 legs (2 actuated by linear actuators and one supporting pillar),which is applied in a wheel loader driving simulator, is proposed in this paper. The roll angle and the pitch angle of the platform are derived in closed-form of functions of the variable lengths of two actuators. The linear velocity and acceleration of the selected point and angular velocity of the moving platform are determined and compared with measurement results obtained in the respective point and in the body of the wheel loader. The differences between the desired and actual actuator displacements are used as feedback to compute how much force to send to the actuators as some function of the servo error. A numerical example with a proposed mechanism as a driving simulator is presented.

10

Analysis of links positions in landing gear mechanism

Brewczyński D., Tora G.

International Journal of Applied Mechanics and Engineering

|

2014

|

Vol. 19, no. 3

503--512

EN

This article contains a kinematic analysis of an aircraft chassis mechanism in a range of positions. The mechanism of the chassis is made up of several smaller subsystems with different functions. The first mechanism is used to eject the chassis before landing (touchdown) and fold it to hatchway after the lift off. The second mechanism is designed to perform rotation of the crossover with the wheel, in order to adjust the position of the wheel to fit it in the limited space in the hold. The third mechanism allows movement of the chassis resulting from the change in length of the damper. To determine the position of the following links of the mechanism calculus of vectors was applied in which unit vectors were used to represent the angular position of the links. The aim of the analysis is to determine the angle of convergence and the angle of heel wheels as a function of the variable length of hydraulic cylinder, length of the shock absorber, length of the regulations rods.

11

Optimal service term of the bridge cranes

Kovalenko V., Vishnevetsky S., Brewczyński D., Tora G.

Journal of KONES

|

2013

|

Vol. 20, No. 4

169--176

EN

The questions of the rational/optimal service term of the warehouse bridge cranes on the exploitation and projection stages are observed. The method of the residual crane resource’s definition by the criterion of the specific reduced responses is suggested. On the stage of the crane projection, the forecasting of the warehouse cranes’ resource in coordination with their constructive parameters is expedient. The existing task has main aspects: recognition of the residual crane resource and definition of the project crane resource. In course of time in the massive of the sample from the low carbon steel occur changes: grows firmness, equalize the internal tensions, little internal cracks “overgrow”, sometimes the groups of little cracks create macrocracks. This are a diffusion action. The definition of the rational constructive parameters is being carried out on the base of the work processes’ mathematical modelling. On the base of modelling is defined the size of the residual deflection of the main beam that is formed during one work crane cycle considering the action of the main beams’ free vibrations in the processes of start and braking considering the factor of the attenuation of those vibrations. In result of the modelling, we receive the microscopic size of the residual deflection, formed during one work cycle. On the base of the multisession modelling is noticed that the crane resource can be prolonged on 20-50%.

12

Dimensional synthesis of active suspension cab mechanism links

Brewczyński D., Tora G.

Journal of KONES

|

2013

|

Vol. 20, No. 4

47--53

EN

One of the directions of the heavy duty machine is the operator cabin construction, which provides a high level of comfort. Adequate control of active suspension drives can reduce low frequency and large amplitude vibrations occurring in a number of cabin degrees of freedom. The main link of the mechanism is the platform with cab suspended on two rockers and one actuator. Article proposes methods for determining the length of suspension arms, the width of the platform and centres of the joints, which are connected to the suspension. It has been proved for the flat case that if the momentary centre of rotation of the platform relative to the machine frame is located inside the road roughness zone is a single drive can effectively reduce transverse vibration and angle vibration around the longitudinal machine axis. Further conditions that determine links size are to prevent from peculiar positions, to avoid collision between cab wall and suspension joints. Presented relations between the height of the waist rough roads, wheelbase machine, cab mounting height on the machine and the dimensions of the link suspension mechanism. Presented dimensional calculation results cab suspension links dedicated to Caterpillar 924 GZ loader. Assuming the vertical driving cab calculated inaccuracy of its transverse displacements. Presented the results showing influence of the cab assembly height on the cabin mounting links dimensions.

13

Analysis of the wheel orientation angles in lockheed F-104S starfighter aircraft

Brewczyński D., Tora G.

Journal of KONES

|

2013

|

Vol. 20, No. 3

79--87

EN

This article contains kinematic analysis of the chassis mechanism used in Lockheed F-104S Star fighter aircraft, which is recently used by the NATO military aviation as an interceptor. The mechanism of the chassis is made up of several smaller subsystems with different functions. The first mechanism is used to eject the chassis before landing (touchdown) and fold it to hatchway after the lift off. The second mechanism is designed to perform rotation of the crossover with the wheel, in order to adjust the position of the wheel to fit it in the limited space in the hold. The third mechanism allows movement of the chassis resulting from the change in length of the damper. To determine the position of the following links of the mechanism was used calculus of vectors in which unit vectors were used to represent the angular position of the links. Often used equation, which describes a polygon vector, and the equation of unknown unit vector possible to determine if the other two and the angles between them are known. Calculations were performed in the three local systems of reference, thus were obtained the simplest forms of solutions for links positions. The corresponding scalar products of unit vectors are elements of two transition matrices. These matrices are needed for the vectors calculation in each of the three coordinate systems. The result of the analysis is to determine the angle of convergence and the angle of heel wheels as a function of variable length of hydraulic cylinder and the length of the shock absorber. It has been shown that length of the shock absorber has little effect on angle of convergence, but has a significant effect on the angle of the tilt-wheel landing gear.

14

Simulations of the active cab suspension

Tora G.

Journal of KONES

|

2012

|

Vol. 19, No. 1

455-464

EN

In the context of growing ergonomic concerns and pressing competition on the market, designing machines and vehicles offering a better operator comfort has become a major trend in development of heavy-duty machines and vehicles. During the ride over the rough terrain, the cab is subjected to excitations in the form of low frequency and high-amplitude vibration. This study investigates the vibration reduction strategy whereby the machine structure should incorporate an active suspension of the cab. An actuating mechanism is incorporated, connected to the machine frame and the cab, and placed in between. The main system component is a mobile platform to which the cab is attached. Respective drives set in motion the passive links in the actuating mechanism. The drives are equipped with cylinders capturing the instantaneous velocities derived in the control sub-system. The machine frame, subjected to kinematic excitations, performs a movement in space, which has to be measured with a set of sensors to support the control process. Basing on the measured movements of the machine frame, the control sub-system calculates the realtime values of the anticipated load and the required drive velocities. This study focuses on the development of a mechanical model of the actuating mechanism operating in several degree of freedom options. Solving the direct and inverse problems involving the position and velocity of the mechanism allows the Jacobean matrix to be applied in Newton-Euler’s equations. The purpose of the active suspension system is to stabilise the cab in the vertical position and to reduce its lateral vibrations and seat vibrations in the vertical. This study summarises the results of simulations performed to evaluate the system's performance and its power demand.

15

Simulation of control drives a tower crane

Solarz W., Tora G.

Transport Problems

|

2011

|

T. 6, z. 4

69-78

EN

The design of a control system for a tower crane is investigated. Underlying the controller design is the theory of optimal linear control. Computer models of a crane and the control systems for the crane drives are developed. Simulation data reveals that the motion of the load can be effectively controlled so that it should follow a predetermined trajectory.

PL

Artykuł przedstawia budowę układu sterowania żurawia wieżowego. W regulatorze układu wykorzystano teorię optymalnej regulacji liniowej. Zbudowano komputerowe modele żurawia oraz układu regulacji napędów. Na podstawie symulacji wykazano, że można efektywnie sterować ruchem ładunku żurawia zgodnie z założoną trajektorią.

16

Study operation of the active suspension system of a heavy machine cab

Tora G.

Journal of Theoretical and Applied Mechanics

|

2010

|

Vol. 48 nr 3

715-731

EN

This study is a part of research on active suspension systems of cabs in heavymachines and trucks, used for suppressing low-frequency and large- amplitude vibrations. The suspension system incorporates two platform mechanisms placed one upon the other. The lower mechanism is responsible for maintaining the cab in the vertical position whilst the upper mechanism controls the cab movements in the vertical direction. Motion of the cab is described using versors associated with the mechanism links. Relationships are derived that yield the instantaneous velocities of the drives that lead to reduction of the cab vibrations in selected DOFs. The procedure is shown for calculating the loads acting on the drives of the active suspension during the specified movement of the machine frame. The mathematical model is further utilised in simulations of the suspension operation.

PL

Artykuł stanowi etap prac dotyczących aktywnego zawieszenia kabiny maszyny roboczej, służącego do redukcji drgań niskoczęstotliwościowych o dużej amplitudzie. Zawieszenie składa się z dwóch mechanizmów platformowych umieszczonych jeden na drugim. Dolny mechanizm jest odpowiedzialny za utrzymanie kabiny w pionie. Górny mechanizm odpowiada za ruch kabiny w kierunku pionowym. Do opisu ruchu wykorzystano wersory związane z ogniwami mechanizmu. Wyprowadzono zależności na chwilowe prędkości napędów, powodujących redukcję drgań kabiny maszyny w wybranych stopniach swobody. Przedstawiono sposób obliczania obciążeń napędów aktywnego zawieszenia kabiny dla znanego ruchu ramy maszyny. Na podstawie matematycznego modelu wykonano symulacje pracy zawieszenia.

17

Aktywne zawieszenie kabiny maszyny roboczej

Tora G.

Problemy Maszyn Roboczych

|

2009

|

Z. 33

67-76

PL

Artykuł zawiera propozycję aktywnego zawieszenia kabiny maszyny roboczej, redukującego drgania, wynikające z przejazdu maszyny w warunkach terenowych. Mechanizm zawieszenia, umieszczony pomiędzy ramą maszyny a kabiną, działa w wybranych czterech stopniach swobody. Sformułowano model kinematyki i dynamiki mechanizmu zawieszenia. Wyprowadzono zależności na chwilowe prędkości napędów, powodujące redukcję drgań kabiny. Opracowano układ regulacji i współpracujący z nim układ pomiarowy.

EN

An active suspension is proposed to control the cab vibrations in a heavy machine during the ride in rough terrain. The suspension, placed between the frame and cab, is able to handle 4 selected DOFs. The kinematic and dynamic model of the suspension is developed. Relationship are derived that yield the instantaneous drive velocity, leading to vibration suppression. The control system and the supporting measurement system are designer.

18

Application of a hydraulic - linkage mechanism to balance the excavating equipment in heavy machines

Tora G.

Archive of Mechanical Engineering

|

2008

|

Vol. LV, nr 3

247-253

EN

The author suggests that a mobile counterweight mechanism could be introduced to the excavator structure for coupling the hydraulic system with the excavating equipment. It is shown that the mobile counterweight mechanism reduces power demand, at the same time improving stability of the excavator.

PL

Artykuł zawiera propozycję umieszczenia w koparce mechanizmu ruchomej przeciwwagi, sprzęgniętego poprzez układ hydrauliczny z osprzętem. Wykazano że mechanizm ruchomej przeciwwagi zmniejszy zapotrzebowanie na energię, potrzebną do napędów osprzętu oraz polepszy stateczność koparki.

19

Symulacja sterowania optymalnego napędami żurawia wieżowego

Solarz W., Tora G.

Problemy Maszyn Roboczych

|

2006

|

Z. 28

71-78

PL

Artykuł przedstawia budowę układu regulacji żurawia wieżowego. W regulatorze układu wykorzystano teorię optymalnej regulacji liniowej. Zbudowano komputerowe modele żurawia oraz układu regulacji napędów. Na podstawie symulacji wykazano, że można efektywnie sterować ruchem ładunku żurawia zgodnie z założoną trajektorią.

EN

The paper presents a stucture of regulation system of tower crane. The regulator is based at optimal linear regulation. The paper presents a computer models of tower cranes and a system of drives regulation. The results of simulation show that there is a possibility of effective control of crane load.

20

Sterowanie napędami żurawia wieżowego

Solarz W., Tora G.

Transport Przemysłowy

|

2005

|

nr 4 (22)

10-12

PL

Przedstawiono model odwrotnej kinamatyki i dynamiki żurawia wieżowego, który będzie użyty do wstępnego wysterowania napędów żurawia jako etapu syntezy procesu regulacji. Zadaniem sterowania będzie zapewnienie przemieszczania ładunku wzdłuż zadanej trajektorii. W celu sprawdzenia poprawności modelu przeprowadzono numeryczną weryfikację.

EN

The paper presents a model of inverse kinematic and inverse dynamic of an tower crane. This model is the base for initial control of tower crane drives and it's a part of regulation system. The goal of regulation is the load motion control at the specific trajectory. The model was modeled using PC software, and there are shown results of simulations.