Parallel Manipulators Applications—A Survey

In this paper, approaches for the solution of parallel manipulators forward kinematics have been addressed. Current research on this topic has been analyzed to determine the status and unresolved issues of the research field. Articles on parallel manipulators forward kinematics were reviewed, and numerous approaches for resolving forward kinematics in particular have been identified and published, which may assist researchers in selecting the most appropriate technique for solving the problem in this domain. Researchers have also attempted to apply these methods to a variety of other parallel manipulator-related problems, such as inverse kinematics and dynamics. In robotics, serial manipulators were invented before parallel manipulators. Hence, methodologies for solving forward kinematics were first developed for serial manipulators and many methods are ineffective for parallel manipulators. In this paper, all identified methods can be used for solving forward kinematics of parallel and serial manipulators.

Parallel manipulators have been proposed to overcome accuracy problem in the end effector positioning, exhibited by serial manipulators(Stewart, 1965)(Reboulet, 1988)(Merlet, 2000). These parallel robots are primarly used in the applications for which the considered processes require a high degree of accuracy, high speeds or accelerations. Aircraft simulator (Stewart, 1965), machining tools (Neugebauer et al., 1998)(Poignet et al., 2002), and various other medical applications (Merlet, 2002)(Leroy et al., 2003)(Plitea et al., 2008) constitute some of the many possible applications of parallel robots. The computation of the inverse dynamic model is essential for an effective robot control. In the field of parallel robots, many approaches have been developed for efficient computation of the inverse dynamics. The formalism of d’Alembert has been used to obtain an analytical expression of the dynamics model (Fichter, 1986)(Nakamura & Ghodoussi, 1989). The principle of virtual works has been applied in (Tsai, 2000) for solving the inverse dynamics of the Gough-Stewart platform and in (Zhu et al., 2005) for a Tau parallel robot. Lagrangian formalism is applied in (Leroy et al., 2003) for the dynamics modeling of a parallel robot used as a haptic interface for a surgical simulator. These various approaches do not seem effective for a robot dynamic control under the real time constraint. A better computational efficiency can be achieved by the development of approaches using recursive schemes, in particular, based on the Newton-Euler formulation. Gosselin (Gosselin, 1996) proposed an approach for the computation of the inverse dynamic model of planar and spatial parallel robots, in which all the masses and inertias are taken into account. This proposed method is difficult to generalize for all the parallel architectures. Dasgupda et al (Dasgupta & Choudhury, 1999) applied this method to several parallel manipulators. Khan (Khan, 2005) has developed a recursive algorithm for the inverse dynamics. This method is applied to a 3R planar parallel robot. Bi et al (Bi & Lang, 2006) use the Newton-Euler recursive scheme for the computation of the articular forces of a tripod system. Khalil et al (Khalil & Guegan, 2004) proposed a general method for the inverse and direct dynamic model computation of parallel robots, which is applied to several parallel manipulators (Khalil & Ibrahim, 2007). Despite the large amount of contributions in this field, there is still a need for improving the computational effeciency of the inverse kinematic and dynamic model clculation for real-time control. In this paper, a parallel robot is considered as a multi robot system with 17

Zeroing dynamics (ZD), as a powerful method proposed for time-varying problems solving, has found successful applications in motion control of serial manipulators. Compared with serial manipulators, parallel manipulators possess some attractive advantages such as high carrying capacity and high operation accuracy. However, the inherent differences between parallel and serial manipulators set great difficulties on the applications of ZD to the control of parallel manipulators. Making progress along this direction, the first ZD based motion controller of parallel manipulators is proposed and the design procedure of the ZD based scheme is presented. As a typical application, the proposed scheme is utilised to control a Stewart platform for tracking a quatrefoil-shaped path, which illustrates the effectiveness of the ZD based scheme.

A method has been developed that successfully represents the workspace of a parallel manipulator within a finite twist image space. A point in this space represents a unique position and orientation of the end effector. The method of analysis is based upon the established technique of simplifying the parallel manipulator, by modelling each leg as an independent serial manipulator. The workspace corresponding to each serial manipulator is mapped onto the image space to produce a hyper-volume. The intersection of the individual hyper-volumes represents the workspace of the complete parallel manipulator. Since the hyper-volume corresponds to all possible positions attainable by the end effector, this represents the reachable workspace. Within the reachable workspace there lies subsets of volumes in ⮲3 that correspond to all possible orientations attainable. Such volumes represent the dextrous workspace. Although the method is illustrated by the use of a Stewart platform, it is equally applicable to the general parallel manipulator. The method is demonstrated successfully by the use of a 3 legged, 3-DOF planar parallel manipulator.

Optimal path planning for a new type of 6RSS parallel robot based on virtual displacements expressed through Hermite polynomials

Multioperation capacity of parallel manipulators basing on generic kinematic chain approach

In this paper, a novel random matrix approach is utilized to characterize the uncertainty propagation in the articulated robotic systems. This method permits the probabilistic formulation to take into account the complexity and structural inter-dependencies of the kinematic manipulators. However, conventional random variable/vector based approaches are unable to address this issue. The kinematic Jacobian matrix of the manipulator is probabilistically formulated so that it adopts a random symmetric positive definite perturbation matrix. The density function of the perturbation matrix is constructed using maximum entropy principle that yields a Wishart distribution with specific parameters. The only information used in the construction of the Jacobian matrix probability model are mean and a scalar value dispersion parameter. We propose to use this framework to study the propagation of the uncertainties in both serial and parallel manipulators. Parallel architecture manipulators offer superior manipulation accuracy and structural rigidity compared to serial chain manipulators but feature more complex physical layout and limited workspace. Therefore, for the design purposes, a trade off between two different architectures is required. This necessitates the mathematical characterization of their capability with respect to the uncertainty propagation. As a case study, the developed random matrix method is implemented on a planar RRR serial and a planar 3-RRR parallel manipulator, that are performing an identical task. A Monte Carlo analysis is conducted and the statistics of the response of both systems provides appropriate measures to compare their dexterity dealing with the uncertainties. The final results verify superiority of the parallel architecture.

A parallel manipulator provides an alternative design to serial manipulators, and can be found in many applications such as mining machines (Arai et al., 1991). Through the design of active joints such that actuators are fixed to the manipulator base, the mass of moving components of the parallel manipulator is greatly reduced, and high speed and high acceleration performance may be achieved. Parallel manipulators, comprised of closed-loop chains due to multiple linkages of the parallel structure, also provide high mechanical rigidity, but adversely exhibit smaller workspace and associated singularities. Considerable research has focused on kinematic analysis and singularity characterization of these devices (Gosselin & Angeles, 1990, Merlet, 1996). Planar parallel manipulators typically consist of three closed chains and a moving platform. According to the arrangement of their joints in a chain, these mechanisms are classified as PRR, RRR etc. where P denotes a prismatic joint and R denotes a revolute joint respectively. An assembly industry, such as the electronic fabrication, demands high-speed, high acceleration placement manipulators, with corresponding lightweight linkages, hence these linkages deform under high inertia forces leading to unwanted vibrations. Moreover, such multiple flexible linkages of a parallel manipulator propagate their oscillatory motions to the moving platform where a working gripper is located. Therefore, such vibration must be damped quickly to reduce settling time of the manipulator platform position and orientation. A number of approaches to develop the dynamic model of parallel manipulators with structural flexibility have been presented in the literature(Fattah et al., 1995, Toyama et al. 2001), but relatively few works related to vibration reduction of a parallel manipulator have been published. Kozak (Kozak et al., 2004) linearized the dynamic equations of a two-degree-of-freedom parallel manipulator locally, and applied an input shaping technique to reduce residual vibrations through modification of the reference command given to the system. Kang (Kang et al., 2002) modeled a planar parallel manipulator using the assumed modes method, and presented a two-time scale controller for linkage vibration attenuation of the planar parallel manipulator. Since both the input shaping technique and the two-time scale control scheme, applied to parallel manipulators,

Photolithography is one of the core technologies of micro-nano fabrication. Recently, lithography technology is applied to diverse field of technologies. These technologies include MEMS (micro electro mechanical system) devices, FPD (flat panel display), and semiconductor industry. When it comes to the typical exposure process of lithography technology, photomask costs is occupying large portion of the optical system. So, how to reduce the cost of the mask and employing maskless lithography technology has become an important issue to engineers. Although there being both advantages and disadvantages, maskless lithography is a receiving substantial attention from engineers in the fileds of micro-nano fabrication. With the development of technology, low cost, flexibility, efficiency in the fabrication of device are in high demand in maskless lithography technology. How to generate line/space patterns is gaining considerable attention in terms of maskless lithography exposure process. In order to achieve the accurate alignments of numerous optical heads within a reasonable amount of tack time, installing autonomous position align micro parallel manipulator system in each optical heads required. Applied parallel manipulator that consists of four 2-DOF (degree of freedom) decoupled actuator gives chances to provide 6-DOF independence motion, and has strength in high accuracy. It is thus, this parallel manipulator is suitable for the experiment. This paper covers the follows: First, we reported the DMD (Digital Micro mirror Device)-based makless lithography system to introduce spot array method in maskless digital exposure process. Second, applying a redundant parallel micro manipulator and analyzing kinematic characteristic of the 4-[PP]PS parallel manipulator is described. After that, comparing benefits and drawbacks of 4-[PP]PS parallel and 4-DOF serial manipulator is covered. Third, proposing a suitable error model of the system and applying the genetic algorithm to alignment spot array concerning position correction. Finally, we designed experiment which has vision sensor and align unit to verify positioning algorithm. Simulation and experimental result will be shown with the regard to parallel manipulator can find the optimal solution based on genetic algorithm and carry out the problem of spot array alignment by reducing the position error of the system.

Dimensional synthesis of a spherical parallel manipulator based on the evaluation of global performance indexes

In comparison to classical serial mechanisms parallel kinematic machines (PKM) provide a higher accuracy, a higher stiffness, and higher dynamic properties. However, parallel robots suffer from the presence of singularities within their workspace (Gosselin & Angeles, 1990). In such configurations the moving platform gains at least one degree of freedom (DOF) and the actuation forces become (in theory) infinite. As a result, the kinematic structure can be damaged or even destroyed. Additionally, several performance indices, e.g. the achievable accuracy, are directly related to the singularity loci (Kotlarski, Abdellatif & Heimann, 2008). The closer the endeffector (EE) is ’located’ to a singularity the higher is the pose error resulting from the influence of active joint errors, e.g. from limited encoder resolution. In order to minimize the singularity loci of parallel mechanisms and to increase their performance, e.g. their achievable accuracy, redundancy can be used (Merlet, 1996). Two redundancy approaches are established for PKM, actuation redundancy and kinematic redundancy (Kock & Schumacher, 1998; Wang & Gosselin, 2004). Actuation redundancy can be realized whether by adding a kinematic chain to the mechanism or by actuating a passive joint. Amongst others, it reduces singular configurations and leads to internal preload that can be controlled in order to prevent backlash (Kock, 2001). However, the control of such mechanisms is a challenging task (Muller, 2005). Furthermore, an additional kinematic chain mostly reduces the total workspace. Therefore, kinematic redundancy is proposed realized by adding at least one actuated joint to one kinematic chain (Cha et al., 2007; Mohamed & Gosselin, 2005). It is well known that the singularity loci as well as the achievable accuracy are greatly affected by the geometrical parameters of a mechanism (Kotlarski, de Nijs, Abdellatif & Heimann, 2009; Merlet & Daney, 2005), and are therefore highly dependent on the mechanism’s actual configuration. In this chapter, as examples, kinematically redundant versions of the well known planar 3RRR and 3RPR mechanisms (Gosselin & Angeles, 1988; Zein et al., 2006) are considered. In each case, an additional prismatic actuator is added to an arbitrary base joint. The introduced mechanisms are denoted as 3(P)RRR and 3(P)RPR. Thanks to the additional prismatic actuator, the inverse displacement problem has an infinite number of solutions (Ebrahimi et al., 2007). Hence, reconfigurations of the mechanisms can be performed selectively in order to avoid singularities and to affect their performance directly (Kotlarski, Do Thanh, Abdellatif & Heimann, 2008). It is important to note that with respect to the work of Arakelian et al. (Arakelian et al., 2008), kinematic redundancy can be used to rather change the geometrical parameters of a mechanism than its basic structure. This can be done at the 19

At present, parallel robots show a great progress in their development due to their behaviour in multiple applications. In this sense, the Stewart-Gough platform with proper mechanical adaptations could be used for a climbing parallel robot. A climbing parallel robot with 6 degrees of freedom has been proposed and analysed. Parallel robots have great advantages compared to serial robots with legs using as climbing robots. Some advantages can be cited as the high weight payload capacity, robustness, simplicity of its mechanical design, etc. However, some difficulties have to be resolve too as the adaptation to the structure meanwhile the robot accomplishes the task or the singularities that can be produced in the movement on the structure. In this paper several options of a climbing parallel robot based in the S-G platform have been presented and analysed. First of all, an initial prototype to climb along tubular structures as pipes or palm trunks has been shown. The main features of this robot are the pneumatic actuators and the external control loop that allows centring the robot to the tubular structure. Taking into account this first prototype, another parallel robot to resolve the problem of displacement and climbing along metallic structures has been presented. The main features of this robot are the electrical actuators and the clamping device developed with the purpose of reducing possible collisions between the movement ring of the robot and the environment. The results achieved with both prototypes show the validity of these platforms to undertake tasks in which are necessary to climb on. In short, this paper tries to show the big potential of using parallel robots as climbing robots. Also, we are working in introducing teleoperation techniques to manage these parallel robots. So, the robots will be controlled in a semi-automatic way when it displaces along the tubular or metallic structures.

This thesis explores the fundamentals of a new class of parallel mechanisms called parallel mechanisms with configurable platforms as well as the design and analysis of parallel robots that are based on those mechanisms. Pure parallel robots are formed by two rigid links, the base and the end-effector, connected in parallel by independent serial chains, called legs. The novel concept behind parallel robots with configurable platforms is that the rigid end-effector is replaced by a closed-loop chain, the configurable platform. Some of the links of this closed-loop chain are attached to the legs so its configuration can be fully controlled from the actuators located on the base. The use of a closed-loop chain instead of a rigid end-effector allows the robot to interact with the environment using multiple contact points on the platform. This results in a robot that can combine motion and grasping capabilities into a structure that provides an inherent high structural stiffness. All the actuators are grounded on the base requiring no additional motor at the end-effector location to provide the grasping. High-speed pick-and-place robots and haptic interfaces are examples of devices that can benefit from this new type of architecture.

Double-cylinder parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-cylinder parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a critical role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to apply this type of parallel manipulator.

This research presents a new spatial Parallel Manipulator (PM) with pure translational motion in a plane or 2-DOF PM for pickand-place operation. This spatial 2-DOF PM is constructed by the 2(RRR)-2(PRRR) kinematic chain and is named Ψ2. This Ψ2 PM offers simplicity in its architecture because each limb applies a 1- DOF joint. The applicability of Ψ2 for pick-and-place operations was investigated by performing kinematic and singularity analyses at the preliminary stage. The singularity of Ψ2 was determined by relying on its Jacobian matrices, where three kinds of singularity can be evaluated. Next, the singularity and Jacobian matrix hold a key to identifying the workspace in a regular geometrical shape required for the operation of such an application. The identified operational workspace must be free of singularity and good conditioning workspace. In this study, two predetermined values of Ψ2 kinematic parameters were used to evaluate the kinematic characteristics and singularity of the manipulator as well as to identify its operational workspace. According to the results, Ψ2 has a good prospect of being applied to high-speed pick-and-place operations.