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

This paper presents the kinematic analysis of a new type of 6SS parallel manipulator with six degrees of freedom. The parallel manipulator consists of a fixed plate and a mobile platform connected through six independent kinematic chains. Each of the six kinematic chains has an actuator revolute joint and two spherical joint. The kinematic analysis was done by applying the restriction method. The motion equations for the six kinematic chains of the parallel mechanism have been defined when it performs a certain technological function. Also kinematic analysis was done using a CAD softwere and the variation of the angular speeds of the actuating arms were obtained.

In this work, we shall present a novel design of a 3-translational-DOF in-parallel manipulator having 3 linear actuators. Three variable length legs constitute the actuators of this manipulator, whereas two other kinematic chains with passive joints are used to eliminate the three rotations of the platform with respect to the base. This design presents several advantages compared to other designs of similar 3-translational-dof parallel manipulators. First, the proposed design uses only revolute or spherical joints as passive joints and hence, it avoids problems that are inherent to the nature of prismatic joints when loaded in arbitrary way. Second, the actuators are chosen to be linear and to be located in the three legs since this design presents higher rigidity than other. In the second part of this paper, we addressed the problem of kinematic analysis of the proposed in-parallel manipulator. A mixed geometric and vector formulation is used to show that two solutions exist for the forward kinematic analysis. The problem of singularities is also investigated using the same method. In this work, we investigated the singularities of the active legs and the two types of singularity were identified: architectural singularities and configurational singularities. The singularity of the passive chains, used to restrict the motion of the platform to only three translations, is also investigated. In the last part of this paper, we built a 3D solid model of the platform and the amplitude of rotation due to the deformation of the different links under some realistic load was determined. This allowed us to estimate the “orientation error” of the platform due to external moments. Moreover, this analysis allowed us to compare the proposed design (over constrained) with a modified one (not over constrained). This comparison confirmed the conclusion that the over constraint design has a better rigidity.

Parallel manipulators (PMs) are often used as parallel kinematic machines (PKMs), which are more accurate and have more payload capacity compared to their serial counterparts. Spherical joints are frequently used in the construction of PKMs; however, spherical joints have a unique physical constraint, known as cone angle limit, around their axis of symmetry. The present work investigates the effect of changing the orientation of the spherical joint symmetry axis (SJSA) on the kinematic performance of PMs. Workspace index, global conditioning index, kinematic conditioning index and global stiffness index are chosen as performance indices. It is found that changing the orientation of SJSA has a remarkable impact on the kinematic performance of PMs. Also, it is shown that considering the cone angle limits considerably affect the kinematic performance of PMs. To demonstrate the results, two PMs, namely 3-PRS (P, R, and S denote prismatic, revolute, and spherical joints, respectively) and 3-RPS manipulators with spherical joints with adjustable axis of symmetry orientation, are used. The effect of changing SJSA orientation on various performance indices is carried out, and optimal orientation values are determined. Genetic algorithm (GA) optimization technique and traditional method are used. The results obtained using the two methods matched very well. It is found that orientation of the SJSA is one of the important PMs optimization parameters that should be considered during the design process.

This paper presents the comparison between serial and parallel manipulators. Day by day, the applications of the parallel manipulator in various field is become apparent and with a rapid rate utilized in precise manufacturing, medical science and in space exploration equipments. A parallel manipulator can be defined as a closed loop kinematic chain mechanism whose end effector is linked to the base by several independent kinematic chains. The classification of various parallel manipulators is presented herewith. The prime focus of the paper is to realize the parallel manipulators applications for industry, space, medical science or commercial usage by orienting manipulator in the space at the high speed with a desired accuracy.

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 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.

Multioperation capacity of parallel manipulators basing on generic kinematic chain approach

A spatial redundantly actuated parallel mechanism (RAPM) constrained by two point contact higher kinematic pairs (HKPs) has been designed, arising from the inspiration of mastication in human beings: the end effector is the lower jaw, the six kinematic chains are the primary chewing muscles, and the constraints at HKPs are the temporomandibular joints. In this paper, firstly, the constrained motions of the mechanism are described in detail; thereafter, five models are formulated by the well-known Newton-Euler's law, the Lagrangian equations, and the principle of virtual work, to explore its rigid-body inverse dynamics. The symbolic results show that the model structures based on these approaches are quite different: the model via the Newton-Euler law well reflects the nature of the mechanism in terms of the constraint forces from HKPs with six equations and eight unknowns, and the existence of reaction forces at the spherical joints is tightly dependent on the number of kinematic chains. In comparison, from the latter two methods, the constraint forces and the reaction forces at spherical joints do not appear in the four models in which there are only four equations and six unknowns. Further, by using the dynamics model of the non-redundantly actuated counterpart as the core in both the second models from the energy and virtual work-related methods, their computational cost is only about 16.7% and 36.63% of the two first models, respectively. Finally, the comparisons between the dynamics models of the RAPM and its counterpart clarify that the HKP constraints greatly alter the model structures and raise the technical difficulties.

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

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.

Chapter 4 - Free Motion of the End Effector of a Robot Mechanism

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,

A parallel spherical manipulator can provide three degrees of freedom of pure rotation around the virtual center of its platform. Parallel manipulators, where all actuators are fixed to the base of the manipulator, provide better load-carrying capacity and better dynamic properties. This advantage makes it possible to use a parallel spherical manipulator as an additional tool for rotating the end-effector in robots with an incomplete set of degrees of freedom or compensate rotation/position error of the master robot. This solution can be used in precise machining operations and other problems where external forces have great influence or other sources of position errors are significant.Under the influence of external forces robot's end-effector could have an offset in the positioning. In this work, we propose to use a specially designed parallel robot that mounted on the master robot flange between the master robot and its tool. In order to compensate position errors following steps is performed: 1) Estimation of master robot stiffness model; 2) Estimation of spherical parallel robot stiffness model; 3) Estimation of external forces; 4) Estimation of compliance errors for both robots; 5) Trajectory modification for spherical parallel robot; 6) Trajectory execution.In this way, the overall accuracy of the system could be greatly improved, without any modification to the master robot program.

The cantilever structure of serial manipulator leads to bending under high load and vibration at high speed which affects precision and creates other problems. Parallel manipulator offers alternative to serial manipulator with higher precision and high payload capacity. Parallel manipulator with less degrees of freedom are used for drilling, contour milling, welding and tapping application with better accuracy and faster repeatability. In this paper a 3DOF parallel kinematic machine is proposed for drilling applications. The configuration of proposed PKM (Parallel Kinematic Machine) is 2PUS+PRR. The moving platform is connected with fixed platform using two links with Prismatic-Universal-Spherical (PUS) joints and one link with Prismatic-Rotational -Rotational joints (PRR). Rotational, Universal and Spherical joints are passive joints whereas prismatic joints are actuated by screw pairs with stepper motor. This paper derives Kinematic analysis, velocity equations mathematically.

Design and analysis of novel 2R1T generalized parallel mechanisms with large rotational angles