Workspace Analysis of the 4RRR Planar Parallel Manipulator with Actuation Redundancy

The objective of this paper is to determine whether a planar parallel manipulator with redundant actuation has better tracking accuracy than a planar parallel manipulator without redundant actuation. The effects of the redundant actuation on tracking accuracy of parallel manipulators are studied by using two different experimental platforms. The first platform is the planar five-bar parallel manipulator with normal actuation, and the other one is the planar parallel manipulator with redundant actuation. The dexterity pictures and the kinematic configurations of the two platforms validate the kinematic advantages from the redundant actuation. In order to study the dynamic advantages of the redundant actuation further, a nonlinear adaptive controller is presented for the two platforms. The experimental comparison is implemented on two actual parallel manipulator platforms, and from the experimental results, one can find the tracking accuracy of the parallel manipulator with redundant actuation can be improved above 38% than that of the five-bar parallel manipulator without redundant actuation.

This paper deals with the performance analysis of a 3-degree-of-freedom (3-DOF) planar parallel manipulator with actuation redundancy. Closed-form solutions are developed for both the inverse and direct kinematics about the redundant parallel manipulator. In performance analysis phase, the dexterity is analyzed, three kinds of singularities are investigated, and the stiffness is estimated. Compared with the corresponding non-redundant parallel manipulator with the redundant link removed, the redundantly actuated one has better dexterity, litter singular configurations and higher stiffness. The redundantly actuated parallel manipulator was applied to the design of a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.

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,

Geometric isotropy indices for workspace analysis of parallel manipulators

SUMMARYThe workspace is often a critical parameter for optimum design of parallel manipulators. Workspace shape and area are two important considerations under this. In this paper, 5-R and 3-RRR planar parallel manipulators having symmetric link lengths are considered for workspace analysis. Here, symmetric means that the lengths of the first and second links of the legs are the same in all branches. Workspace analysis for such manipulators is normally done in a nondimensional way. The determination of the workspace area is one of the important parameters in the optimum design of a manipulator, and the determination of the area in terms of nondimensional parameters is extremely difficult in the case of 3-DOF and higher-DOF manipulators. In this paper, a geometric method is presented to determine different workspace shapes and areas. Based on this, all possible shapes of workspace are presented for both 5-R and 3-RRR planar parallel manipulators. For each case, a geometrical relationship between the link lengths is determined. The geometric approach gives a closed-form expression for the area calculation, which is not possible when adopting a nondimensional approach. In addition, this approach provides relationships between workspace shape and area and link lengths.

Robogami structures are employed for many purposes, including miniature parallel manipulators. Parallel manipulators require accurate joint position feedback, underlining the open problem in robogami structures for providing sophisticated feedback with 2D, fully embeddable, down-scalable, flexible sensors. Existing studies include only on-off control applications, excluding any parallel mechanism implementations and continuous proportional control signals. We implement silver inkjet printed angle sensors for the first time into a robogami structure and use this class of sensors for control. For the first time, a parallel manipulator is controlled with a 2D sensor, and printed sensors are tested for continuous control. Performances are analyzed with set-point and tracking control tasks using a paper Delta mechanism, compared with on-off control and encoder feedback control cases for better evaluation. A detailed comparison with the existing studies both for robogami parallel mechanisms and other sensor-embedded flexible hinges is provided. Encoder-like control performances are achieved in a wide range of the joint space and down to ~1 mm. RMS task space accuracy is recorded. Sources and potential improvements for the less accurate regions are stated. We conclude that printed sensors are promising for parallel mechanisms and continuous signal control applications.

This paper introduces a family of statically balanced five-degree-of-freedom (5DOF) parallel mechanisms (PMs) with kinematic and actuation redundancy. Moving platforms of this family of PMs can provide 4DOF Schönflies motion. Three applications are considered in this work. The first and second applications use kinematic redundancy to avoid parallel singularities and perform an auxiliary grasping task in sequence. The third application incorporates actuation redundancy into a kinematically redundant manipulator to increase the load-carrying capacity. Screw theory was used to derive the Jacobian of the 5DOF PM with kinematic and actuation redundancy. Parallel singularities can be completely alleviated by controlling the orientation of the redundant link, thereby obtaining a large rotational workspace, and actuation redundancy increases the load-carrying capacity. Using a commercially available multibody dynamic simulator, an example of trajectory was performed to illustrate the large rotational workspace of the first and second applications and compare the Euclidean norm of the vector of actuation torque of nonredundant and redundant PMs. Three prototypes were also developed to demonstrate the output motion and static balancing property.

In the design of a mechanism, the quality of effort transmission is a key issue. Traditionally, the effort transmissivity of a mechanism is defined as the quantitative measure of the power flowing effectiveness from the input link(s) to the output link(s). Many researchers have focused their work on the study of the effort transmission in mechanisms and diverse indices have been defined. However, the developed indices have exclusively dealt with the studies of the ratio between the input and output powers and they do not seem to have been devoted to the studies of the admissible reactions in passive joints. However, the observations show that it is possible for a mechanism to reach positions in which the transmission indices will have admissible values but the reaction(s) in passive joint(s) can reach excessively high values leading to the breakdown of the mechanism. In the present paper, a method is developed to ensure the admissible values of reactions in passive joints of planar parallel manipulators. It is shown that the increase of reactions in passive joints of a planar parallel manipulator depends not only on the transmission angle but also on the position of the instantaneous center of rotation of the platform. It allows the determination of the maximal reachable workspace of planar parallel manipulators taking into account the admissible reactions in its passive joints. The suggested method is illustrated via a 5R planar parallel mechanism and a planar 3-RPR parallel manipulator.

SUMMARYIn this paper, a new family of 3-degree-of-freedom planar parallel manipulators (PPMs), namely U-shape fixed base PPMs starting with an active prismatic joint on each leg, is proposed. In order to identify the best manipulators of this family, comparative kinematic and dynamic performance studies are performed. The kinematic performances are quantified through the local performance index, namely the kinematic isotropy. From the kinematic isotropy analysis results, it is observed thatPPR-PRP-PRP,PRP-PRP-PRP andPRR-PRP-PRP configurations have better kinematic design aspects compared to other configurations of this family of U-shape fixed base parallel configurations. Further, from the workspace analysis, it is observed that thePPR-PRP-PRP configuration has a higher value of workspace to the total area required ratio compared to other configurations. This paper also presents a comparative dynamic performance analysis of these top-three U-shape fixed base configurations in terms of dynamic driving performance measures, and energy requirements for three different (fixed base size of the manipulators) aspect ratios under two different loading conditions. From the analyses results, it is perceived that thePRP-PRP-PRP configuration is requiring lower energy and dynamic driving performances than others. These analyses are done with the help of multi-body dynamic software, namely MSC ADAMS, and the results are validated through the help of real-time experiments conducted on in-house fabricated prototypes of these three PPMs. In specific, the energy consumption is measured and compared in this study. Experimental results demonstrated that thePRP-PRP-PRP manipulator displays a considerably better performance in terms of minimum energy requirement.

This paper addresses the kinematic and dynamic models of a 3-PPR parallel manipulator, which are the foundation of parallel manipulator dynamic control. Then, based on the Udwadia-Kalaba equation, a three-step procedure is exploited to realize the perfect trajectory tracking of 3-PPR parallel manipulator involving the known uncertainty. In addition, when the initial conditions are incompatible and system parameters are uncertain, we adopt the adaptive robust control method to realize approximate trajectory tracking of the planar parallel manipulator. The controller consists of three parts. The first part is the perfect control of dynamic model based on the Udwadia-Kalaba equation. The second part deals with the incompatibility of initial conditions. The third part is the robust control for system uncertainty regulated by adaptive law. Finally, on the basis of theoretical analysis, the adaptive robust control algorithm is demonstrated by simulation.

Typical parallel mechanisms suffer from parallel singularity due to kinematic coupling of multichains. This paper investigates how to remove parallel singularities by using redundant actuations. First, actuation wrenches and constraint wrenches forming the full direct kinematic Jacobian matrix are derived. After briefly addressing conditions for their constraint singularities, Grassmann–Cayley algebra is employed to identify parallel singularities. Then, employing Grassmann line geometry, the locations and the minimum number of redundant actuators are identified for the parallel mechanisms to have parallel singularity-free workspace. Three different types of 3-degree-of-freedom parallel mechanisms such as planar, spherical, and spatial parallel mechanisms are given as exemplary devices.

Topology design of (3T-1R) parallel mechanism (PM) based on POC equations is discussed in detail as an example to illustrate the systematic method for topology design of PMs proposed in Chap. 9. The design process includes two stages. The first stage involves traditional structure synthesis, which results in 18 structure types of (3R-1R) PMs that contain no P pairs. The second stage includes topological performance analysis and classification of the obtained PM structure types which may help designer to select the most suitable structure type. Its core contents include: (1) Key steps of topology design for (3R-1R) PMs include: (a) Determine structure types of the SOC branch containing only R and P pairs according to the method for structure synthesis of SOC branch described in Chap.8. Then obtain corresponding HSOC branches through topologically equivalent principle in Chap.9. (b) Determine the geometrical condition for assembling branches between two platforms according to corresponding basic formulas in Chap. 9. Then determine different assembling schemes for the same geometrical condition. (c) Performance analysis and classification of the obtained PM structures are conducted based on topological characteristics of PMs in Chap. 9. The result can be used for assessment and optimization of (3R-1R) PM structure types. (2) 18 types of (3T-1R) PM structures containing no P pair are obtained, two of which have already been used in existing SCARA parallel robots. The other structure types may potentially be used in new SCARA parallel robots. (3) These 18 structure types of (3R-1R) PMs are classified into four types: Type-1 include four PMs containing only SOC branches; Type-2 include six PMs containing only HSOC branches; Type-3 include seven PMs containing both HSOC and SOC branches; Type-4 include three PMs with partial motion decoupling property. (4) According to topological performance analysis and classification of these PMs based on topological characteristics, the type-3 PM has a higher rigidity than a type-1 PM and a larger workspace than a type-2 PM. So, special attentions shall be paid to type-3 PMs.

Prescribed flexible orientation workspace and performance comparison of non-redundant 3-DOF planar parallel mechanisms

This paper describes the research results on telemicromanipulation systems for microlevel tasks. Because of its better manipulation precision, stiffness and speed characteristics, the parallel mechanism micromanipulator was chosen to compose our systems. First, the kinematic analysis of our original manipulator mechanism is performed. Then, the structure of our parallel manipulator, control scheme, and experimental results are shown. Position accuracy and device control characteristics are analyzed and the feasibility of the use of parallel mechanisms for micromanipulator is then discussed. A parallel manipulator motion is restricted by 3 factors: mechanical limits of the passive joints, collision between links and actuators limitations. Results of the numerical workspace analysis considering the above factors are shown. We are proposing the use of dual manipulators for implementing improved real manipulation systems. The first kinematics and workspace analysis of dual systems using the VR simulator are also shown.

The change of position and orientation of workpieces is often required in CNC machining, workpiece conveying and product testing. A novel practical planar parallel mechanism with three sliders driven on two parallel guide rails is presented. The direct and inverse kinematic solutions are deduced. The workspace analysis on the end-effector is conducted under given position and orientation. The simulation of motion characteristics of three sliders is completed when it is in given orientation. The virtual prototype is demonstrated. This paper is useful to real-time control and industrial application of this 3-DOF parallel manipulator.KeywordsParallel mechanismKinematicsWorkspace