Yu-yang JIN，Ming-u ZHANG，Jin-bo YAO，Chang-juan YU（Hebei University of Technology，Tianjin 30030，China）（Robotics Institute，Civil Aviation University of China，Tianjin 300300，China）

Dynamics analysis and simulation for aircraft surfaces cleaning manipulator based on ADAMS

Yu-yang JIN1，2*，Ming-1u ZHANG1，Jin-bo YAO2，Chang-juan YU1
（1Hebei University of Technology，Tianjin 300130，China）
（2Robotics Institute，Civil Aviation University of China，Tianjin 300300，China）

Focusing on the 5-DOF（Degree-of-Freedom）serial robot for cleaning aircraft surfaces，the dynamic model of the cleaning manipulator is established by using Lagrange’s equations，Solidworks was utilized to establish the virtual model of the cleaning manipulator，then，the model was imported into ADAMS to generate the virtual prototype，and through carrying on the dynamic simulation and analysis，we obtained the relation curves of joint angles and joint torques，and determined the input joint torque required，which provides a reliable basis for the control and types of joint driving.

Robot，Kinematics，Dynamics，ADAMS，Lagrange’s equations

Hydromechatronics Engineering

http：//jdy.qks.cqut.edu.cn

E-mail：jdygcyw@126.com

1 Introduction

Cleaning robot for aircraft surfaces is an important daily maintenance equipment of the fuselage，the cleaning manipulator as the core component of cleaning robot for aircraft surfaces，which is a typical jib system，so the rationality of its whole structure and dynamic performance will directly influence the working performance of the whole robot.In recent years，due to the development of control technology and new materials，the manipulators develop toward lightweight，high precision and high-speed，therefore，dynamics analysis of manipulator has become a very important content.

There are many methods for generating the dynamic equations of a manipulator.Although the forms of the equations may be different，yet each method generates equivalent sets of the equations［1］，and it is difficult to realize real-time control.For example，the literature［2-4］studied the structure design and dynamic problems of serial manipulator.The literature［5］established the dynamics equation of the reconfigurable robot based on screw theory by using Lagrange’s equations，which has realized the conversion of the torque in different coordinates systems，and the conversion of the force of the end-effector and the torque of each joint.Literature［6］calculated the relative kinetic energy of the crane ship by using Lagrange’s equations，and obtained dynamics equation of the boom and payload in the non-inertial coordinate frame fixed on the crane ship.Literature［7］established the dynamics equation，and obtained the torque of each joint by simulation of ADAMS.Literature［8］established the dynamics model coupled rigid and flexible system of flexible joint manipulator including 1P5R，and discussed the feedback linearization control of the kind of manipulator.Dynamics model established by these methods are complex，and large amount of calculation.While the application of dynamic simulation software can improve design efficiency of the robot，and reduce development time and design cost，which lays a foundation for the control of manipulators.

At present，there are a lot of dynamics simulation softwares，such as ADAMS，DADS，DISCOOS etc.，where ADAMS is a modeling method based on Lagrange’s equations，because it does not involve the forces of constraint acting between the link，can directly establish the relationship between the active force and motion，and also can be directly connected with many other softwares，so ADAMS has obvious advantages in dynamic analysis of the robot system. Therefore，according to the design requirements of the cleaning manipulator，we analyzed the angular velocity and angular acceleration of the cleaning manipulator，obtained the dynamic characteristics in the process of movement by using ADAMS，which provides a theoretical basis for the further optimization design.

2 Dynamics model

Let θ∈Rnbe the joint angles for a serial manipulator.The Lagrangian is of the form

Where M（θ）∈Rn×nis inertia matrix of the manipulator，which is defined as M（θ）If miis the mass of the ithlink and g is the gravitational constant.The total potential energy of the manipulator can be written as V（θ）

The equation（1）is substituted into Lagrange’s equations，where rirepresent the actuator torque generalized forces acting on the ithjoint，a second-order differential equation in terms of the manipulator joint variables can be written as

Where Γijkis given by

It consists of three terms：inertial forces，which depend on the acceleration of the joints；centrifugal and Coriolis forces，which are quadratic in the joint velocities；potential forces of the form?V/?θ.

3 Establishment of virtual model of the cleaning manipulator

The virtual model of the cleaning manipulator established by Solidworks was imported into ADAMS/View in Parasolid format.After setting the work environment，in order to reduce the modeling complexity and simulation time，motors，connecting pins，screws and other parts were ignored，and Boolean operations on certain components.Then after editing parts imported and defining name，material，color and other attributes，the system will automatically calculate the mass and moment of inertia of the components.In order to simulate the motion process of the cleaning manipulator，each part needs to be defined the relative moving property through adding joint mechanism.The moment of inertia and joint mechanism of parts are shown in Table 1.

TabIe1 The type of joint mechanism and the moment of inertia

4 Kinematics simulation

After defining relative constraints between joint mechanisms，the virtual prototype has physical characteristics similar to the actual test prototype through the driving function defining drive types.Then we can set up the simulation environment of the virtual prototype after verificating the model correctly.The driving function of each joint is set，as shown in Table 2.

TabIe2 The driving functions of joints

The simulation time is 30 seconds，the step size is 0.02，that is，a total of 1500 step simulation.Then we created the terminal trajectory of the cleaning manipulator by using“Create Trace Spline”relative to the earth，as shown in Fig.1.

Fig.1 The terminaI trajectory of the cIeaning manipu-Iator

The Y directional displacement，the Z directional displacement and the total displacement of the terminal end can be measured by selecting Y，Z or mag in the“Component”options group，as shown in Fig.2 to Fig.4.

The velocity curve and acceleration curve of the terminal end can be obtained in a similar manner，as shown in Fig.5 and Fig.6.

Fig.2 The X directionaI dispIacement of the terminaI end

Fig.3 The Y directionaI dispIacement of the terminaI end

Fig.4 The Z directionaI dispIacement of the terminaI end

Fig.5 The veIocity curve of the terminaI end

Fig.6 The acceIeration curve of the terminaI end

5 Dynamics simulation

To choose the type of driving motor，we should consider whether the power of the driving motor exceed the instantaneous power of the load.So analysis on the relation between the torque and the joint angle has important reference value to how to select the motor torque，which is great value to optimize the structure of the cleaning manipulator.So we considered maximum actuator torque of joints and maximum angular velocity of the motor.In order to calculate the drive torque rifor selecting the appropriate drive system，several limit postures of its travel are summarized in Table 3.The simulation time is 30 seconds，the Step Size is 0.01 seconds，thus the spatial motion path of the cleaning manipulator is determined.Fig.7 shows the motion process of the cleaning manipulator.

TabIe3 The driving function of joints

The joint angle and torque of each joint are measured in ADAMS/PostProcessor，abscissa means time and ordinate means the torque of each joint，the relationship between the torque and the desired configuration is shown in Fig.8.

Fig.8 The reIationship between each joint torque and each joint angIe

Fig.8 obviously shows the changes of each joint torque when several configuration of the virtual prototype change.The simulation results show that the simulation curves depend on the spatial configuration and the motion process of links.The maximum torque of joint 1 is close to 40 N·mm，which occurs at the start of 20 seconds，in this case，the configuration of manipulator can be determined by the each joint angle.The maximum torque of joint 2 closes to 28 N·mm，which occurs at the start of 17.5 seconds. The maximum torque of joint 3 closes to 7.5 N·mm，which occurs at the start of 25 seconds.The maximum torque of joint 4 closes to 45 N·mm，which occurs at the start of 10 seconds.The maximum torque appears in the joints of the upper arm and the forearm，the maximum value is 3 596 N·mm，which occurs at the start of 0 seconds.And during the 20-30 seconds，the torque is relatively high，close to starting torque.

6 Conclusions

1）The faster the end-effector moves，the more driving torque each joint requires.Due to the existence of static friction of each joint，the change trend of the angular velocity and angular acceleration curve is steep in a relatively short period of time.So as long as the corresponding parameters of the cleaning manipulator are adjusted，the cleaning manipulator can achieve better control performance.

2）According to the relationship between the torque of each joint and each configuration，we get the change trend of the driving torque and its maximum value.So based on considering the efficiency of driven system，we should ensure that the drive capability of the drive system can meet the requirements，and ensure that the cleaning manipulator can have sufficient strength and rigidity，which provides a reference for the motion planning and control of the manipulator.

3）Through the simulation，the accuracy of the model and the feasibility of the design scheme have been verified.It is necessary to make further verification using actual prototype.The simulation results provide theoretical basis for the optimal design and control of robots.

Acknowledgements

This paper is supported by Special Funding for Basic Scientific Research in Colleges and Universities Operating Costs of the Central（20001833）.

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基于ADAMS的飛機(jī)表面清洗臂動(dòng)力學(xué)仿真與分析

金玉陽(yáng)1，2*
，張明路1，姚錦博2，于常娟1
1.河北工業(yè)大學(xué)，天津 300130；
2.中國(guó)民航大學(xué)機(jī)器人研究所，天津 300300

針對(duì)五自由度的飛機(jī)表面清洗機(jī)械臂，利用Lagrange方程建立了清洗臂的動(dòng)力學(xué)模型，采用Solidworks建立了該清洗臂的實(shí)體模型，將其導(dǎo)入到動(dòng)力學(xué)分析軟件Adams中生成了虛擬樣機(jī)，并進(jìn)行了動(dòng)力學(xué)仿真與分析，由此得出各關(guān)節(jié)轉(zhuǎn)角和關(guān)節(jié)力矩的關(guān)系曲線，確定了關(guān)節(jié)所需的輸入力矩。這為機(jī)械臂的控制、關(guān)節(jié)驅(qū)動(dòng)形式的確定提供了可靠依據(jù)。

機(jī)器人；運(yùn)動(dòng)學(xué)；動(dòng)力學(xué)；ADAMS；拉格朗日方程

10.3969/j.issn.1001-3881.2015.12.007Document code：A

TP242

15 November 2014；revised 20 January 2015；accepted 7 March 2015

*Corresponding author：Yu-yang JIN，Ph.D.，

E-mail：149276047@qq.com