1. Introduction
The space manipulator is a high level of integrated space of mechanical and electrical systems in mechanical, electrical, thermal, and control fields. The space environment is harsh and it is a zero-gravity condition. Thus, a space manipulator must be completely analyzed and pass all the verification tests in a zero-gravity simulation system on the ground before it operates on-orbit.
The simulation systems should simulate the zero-gravity condition and allow motions of the space manipulator. They can be divided into five types according to their working principles [
1,
2]: (1) Free fall: It uses gravity acceleration to realize a zero-gravity environment. A drop tower designed by the University of Stuttgart and Baylor University, which can provide 1.5 s in free fall duration a quality of
g [
3]; (2) Parabolic flight: It uses gravity to perform a parabolic trajectory and achieve microgravity condition. A specially-modified Airbus A310-300 aircraft is flied by The European Space Agency for a total of 10 min of weightlessness per flight [
4]; (3) Neutral buoyancy: The manipulators are placed in a water environment, such as the neutral buoyancy facility at University of Maryland [
5]; (4) Air-bearing system. It is the most widely used method to achieve zero-gravity. The air bearing pads support the manipulator and balance the gravity force. The main arm of the Japanese Experiment Module Remote Manipulator System (JEMRMS) has been tested on an air bearing test bed [
6]; and (5) suspension system. The suspension force compensates the gravity force. Carnegie Mellon University designed a gravity compensation system for their Self Mobile Space Manipulator (SM
) [
7]. Each zero-gravity system has advantages and disadvantages, and scholars should select the testing system carefully according to the actual situation.
Because of the large motions and the multiple Degree of Freedom (DOF) of the manipulator, an active compensation suspension system is used as the zero-gravity simulation system in this study. A constant-tension suspension for space manipulators was developed by Fujitsu Laboratories (Fujitsu Ltd. Kawasaki, Japan) first [
8]. The tension force was provided by a motor instead of the counterweight mechanism. Liu et al. [
9] used a single wire to achieve the gravitation of the moon for the Rocker-bogie Rover. The Gravity compensation model is established as well. Shen et al. [
10] designed a system for physically simulating human walking in microgravity using such a method. The suspension system can be divided into two distinct parts [
11]: a constant tension force system and a follow-up system. The tension force system affords vertical constant forces, which can be controlled to balance the gravity force. The follow-up system guarantees the tension force is vertical whatever the attitude of the manipulator. However, in an actual experiment, the tension forces cannot be always constant. Thus, the gravity of the manipulator cannot be balanced completely, causing additional torques to be exerted in the joints. To ensure the reliability of the experiments, it is necessary to analyze the additional torques of the joints.
Several experiments must be conducted to verify the zero-gravity simulation system after the primary design of the system. It is costly and unreliable to use the actual space manipulator directly. Consequently, it is essential to design a simulated manipulator is designed to replace the space manipulator for the initial experiments. When the system is tested completely, the space manipulator can be experimented in it. Equivalent test models are widely used in the aerospace field. We can predict the conditions of the actual ones by testing on the models. Kuroda et al. [
12] produced two experimental models of the planetary rover to test in a low-gravity flight. Yao et al. [
13] presented a method to solve the added mass of a robot tested in neutral buoyancy, which made the model and the actual robot be similar. In our study, the structures and masses of the joints of the simulated manipulator differ from the space ones. To assure the consistency in the kinematics and dynamics, the mass, barycenter, and inertia of the simulated manipulator must be matched [
14]. Hou et al. [
14] proposed a dynamic programming to match the barycenter of a microsatellite, which can guarantee the dynamic balance of the satellite. You et al. [
15] used the genetic algorithm (GA) to optimize the mass-matching on a reentry vehicle. It can ensure the complex requirements of mass parameters by using the least counterweight. However, most of the present researches consider the barycenter only, and the mass of the counterweight can be changed. In this study, the total mass of the joint is constant, which increases the difficulty of mass-matching. Moreover, the errors that are inevitably introduced after matching should be evaluated. Ijar et al. [
16] indicated that the spacecraft is sensitive to any reaction force and torque for its zero-gravity operating condition. They established the dynamic equations of a spacecraft by using Lagrange’s formulas. Alepuz et al. [
17] derived the kinematic and dynamic equations of a free-floating satellite-mounted robot (FFSMR), which contains a series manipulator and a satellite. Masuya et al. [
18] proposed a novel technique to estimate motion of the barycenter for a biped robot based on its torque equilibrium. In a similar way, the torque can becalculated based on the motion of the barycenter.
In this study, a method is designed to match the mass and barycenter of the joint of the simulated manipulator. The counterweight components are used to adjust the masses and barycenters of the simulated joints for agreement with the space ones. In addition, the equivalence relationship between the mass and inertia of the simulated and actual space manipulators is analyzed. The results can contribute to future experiments involving the space manipulator.
The paper is organized as follows. In
Section 2, the kinematics and dynamics of the manipulator is established. The optimized design of the joints is presented in
Section 3. The mass and inertia parameters of the joints affected by mass-matching is derived as well. The simulation results are in
Section 4.
Section 5 is the measurement results of the mass parameters of the joints. Conclusions are drawn in
Section 6.
6. Conclusions
In this study, counterweight components for matching the mass and barycenter of the joint of a simulated manipulator to those of an actual space manipulator is presented. Combined numerical derivation with computer programming, an optimization result of mass-matching, is achieved. The deviation of barycenter is <2 mm, which is greatly superior to the required indices. Then, the torque of each joint of the simulated manipulator in different suspension force error is calculated. With the increase of the force error, the torques increase fast, especially those of the 3rd and 4th joints. Furthermore, the torque deviations of simulated and space joints are calculated as well. The results show that the deviation is 25 times less after mass-matching. It confirms that the research is effective and significant. The results contribute to future experiments involving the actual space manipulator.
However, in this study, we consider the manipulator as a rigid object and ignore the elastic deformations and frictions. Actually, the slenderness ratio of two arms are large and the elastic deformations are obvious; when the manipulator operates, the frictions are existing between joints. To improve the accuracy of the model is part of our future work.