Chapter 1 Introduction Introduction
2.1 Overview
2.2 Spherical Motion Platform I Based on Three Spherical Wheels ... 13 2.2.1 Mechanical Structure and Design ... 13 2.2.2 Spherical Wheel Mechanism ... 13 2.2.3 Kinematic Model ... 15 2.2.4 Dynamic Model ... 19 2.3 Spherical Motion Platform II Based on Four Spherical Wheels ... 22 2.3.1 Mechanical Structure and Design ... 23 2.3.2 Compliant Spherical Wheel Mechanism ... 23 2.3.3 Kinematic Model ... 25 2.3.4 Dynamic Model ... 29 2.4 Geometric Stability ... 30 2.5 Active Driving Control ... 32 2.6 Kinematic Control for Four Rolling Contacts ... 33 2.7 Slip Estimation for Rotational Motion ... 34 2.8 Numerical Simulation and Experimental Validation ... 36 2.8.1 Validation for SMP I ... 36 2.8.2 Validation for SMP II ... 46
2.1 Overview
Motion platforms capable of controlling multi-DOF motion have been rising in popularity to motion simulation for virtual experience industries such as ride simulation [13], [14], flight simulators [15], micro-positioning [16], solar tracker [17], and medical manipulators [18], [19]. In particular, the motion platform is also effective in training a pilot or operator of unmanned systems by providing VR [20].
*This chapter includes the following published contents: [3], [10], [11], [12], [36].
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Recently, VR systems offer not only visual information as a first-person view but also perception ability so that humans can realize virtual operating conditions and environments.
Two designs of mechanisms for the motion platform have been widely explored. One is a serial manipulator, and the other is a parallel. The serial mechanism connects an end effector and a base serially with several linkages. It has the advantages of planning the position and velocity of an end- effector from each joint of linkages to a large workspace. However, it has the disadvantages of low stiffness and accumulated errors in each linkage. On the other hand, the parallel mechanism has been widely applied to many industries due to the advantages of rigidity, accuracy, and fast response. The Stewart platform [21] is a representative parallel platform driven by six prismatic actuators connected by spherical joints from the base to the end-effector. Although the parallel mechanism, in general, provides a small range of motion compared to the serial mechanism due to geometrical limitations of the design, constraining acceleration, The Stewart platform provides better ranges of six DOFs motion.
Various mechanisms based on the parallel platform, such as parallel cable drive [22], new geometric approach [23], and other mechanisms [24]–[28], have been proposed to overcome the limitations of the range of motion. In addition, a singularity in motion control and a closed-loop (CL) control system have been still investigated for better performance in accuracy as well as robustness under various disturbances [26]–[31].
The motion platform using an omnidirectional wheel (Omni-wheel) named Atlas has been developed in [32]. Atlas, composed of perfectly independent rotational and translational systems based on Omni-wheels, can provide unlimited rotational motion, as shown in Table 2.1. An Omni wheel has attractive features to move toward any desired direction as well as desired orientation at the same time.
It has been applied to many applications: mobile manipulators [33], mobile vehicles [1], and robots [34].
However, platforms based on Omni wheels have disadvantages such as large size compared to the SPW, control complexity, and discontinuity of small wheels, causing defective rotational motion and less accuracy. Furthermore, small rollers on the Omni wheel may not transmit completed motion and torque smoothly, resulting in vibration and discontinuity in motion control, as shown in Fig. 2.1. In order to improve the rigidity, Omni-ball [1] (see Fig. 2.1(c)), which has two orthogonal rotations as active and passive rotations, is developed. However, the direction of the passive rotation axis continuously changes according to active rotation, increasing complexity. In addition, a partially sliding roller [35] (see Fig.
2.1(d)) is proposed to rotate a ball, where it consists of four moving parts generating free rolling and enables the ball to rotate smoothly. However, the thin surface of the roller has a rigidity problem, and it is limited in translational motion. Thus, the SPW is proposed to generate active and passive rotation with continuous motion transfer and translational motion.
11 Table 2.1. Comparison of SMP and Atlas.
Type SMP (proposed) Atlas [9], [32]
DOF 6 6
Motion range Unlimited rotation (360 deg) Unlimited rotation (360 deg) Number of
motors 6 9
Rigidity High Low
Motion
continuity Continuous Discontinuous
Diriving
mechanism Spherical wheel Omni wheel
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(a) (b)
(c) (d)
Figure 2.1. Comparison of spherical driving mechanisms. (a) Spherical wheel. (b) Mecanum wheel [9]. (c) Omni-ball [1]. (d) Partially sliding roller [35].
In this chapter, the novel SPW mechanism and design are analyzed to generate two rotation orthogonal each other. The developed SPW is implemented to design SMP for unlimited rotational motion as well as translational motion. When the cockpit sphere linearly moves, the corresponding rotation occurs to escape slippage. Thus, a control strategy, active driving control, is proposed to compensate for the coupled rotation. Moreover, two types of design, SMP I and II, are analyzed, and the motion capabilities of the two platforms are compared from the perspective of geometric stability.
The SMP II are four SPWs achieving higher geometric stability and torque transmission capability but causing failure of one rolling contact and slipping motion. For this, a compliant SPW mechanism and strategy of slip estimation and kinematic control are developed to achieve full rolling contact. Finally, full-scale SMP I and prototype SMP II are developed to validate the novel mechanism and design.
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