Singularity analysis of a new spatial rotation 3-DOFs parallel manipulator based on actuating performance index

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.

This paper concerns the proposal and analysis of a novel spatial parallel manipulator. The parallel manipulator consists of a base plate, a movable platform, and three connecting legs. The moving platform has three degrees of freedom (DoFs), which are two degrees of translational freedom and one degree of rotational freedom, with respect to the base plate. The inverse and forward kinematics problems are described in closed forms and the velocity equation of the new parallel manipulator is given. Three kinds of singularities are presented. The workspace for the manipulator is analyzed systematically. Especially, the indices to evaluate the rotational capability of the moving platform of the manipulator will be defined and discussed in detail. Due to the high rotational capability performance, the proposed manipulator has wide application in the fields of industrial robots, simulators, micromotion manipulators, and parallel kinematic machines.

SUMMARYThis paper presents the computation of the safe working zone (SWZ) of a parallel manipulator having three degrees of freedom. The SWZ is defined as a continuous subset of the workspace, wherein the manipulator does not suffer any singularity, and is also free from the issues of link interference and physical limits on its joints. The proposed theory is illustrated via application to two parallel manipulators: a planar 3-R̲RR manipulator and a spatial manipulator, namely, MaPaMan-I. It is also shown how the analyses can be applied to any parallel manipulator having three degrees of freedom, planar or spatial.

The workspace of a spatial 6-DOF electro-hydraulic parallel manipulator is strongly coupled, due to its multi-closed-loop kinematic structure and the coupling complicates motion planning and control of the parallel manipulator. This paper clearly analyses the strong dynamic coupling property in the workspace of a spatial 6-DOF parallel manipulator, using modal decoupling theory and a frequency responses characteristics analysis method. The dynamic model of a spatial 6-DOF electro-hydraulic parallel manipulator is expressed with the Kane method and hydromechanics principles. The modal analysis method is used to establish the map between strong coupling workspace and decoupled modal space and the dynamic coupling relationship and coupling strength between workspaces are exactly revealed. The quantitative evaluation index of dynamic coupling is presented. Moreover, the relationship between dynamic coupling effects and input is discussed through applying frequency characteristics analysis. Experimental results show the workspace of the parallel manipulator is strongly coupled and the coupling property is coincident with theoretical results.

A new 2R1T (R: rotation, T: translation) parallel manipulator (PM), called Tex3, is proposed. The Tex3 PM is a 2PUR-PRU PM consisting of 9 joints with 12 DOFs (degrees of freedom), and can be actuated by fixed linear actuators. Mobility analysis shows that it is an RPR-equivalent PM whose finite motion is the product of a rotation (R) followed by a translation (P) and another rotation (R). Inverse position and velocity analyses are discussed. Furthermore, the local transmission index and good transmission workspace are used to evaluate the motion/force transmissibility of the proposed PM. The singularity loci of the proposed PM are obtained according to the motion/force transmissibility, corresponding to the inverse, forward and combined kinematic singularity. The constraint singularity is also discussed. Finally, link parameters are optimized to obtain an improved good transmission workspace. Because of its minimum DOF of joints and fixed linear actuators, the Tex3 PM has good kinematic performance and is suited to the high-speed machining of workpieces with curved surfaces.

Parallel manipulators with less than six degrees of freedom (DOF) have been increasingly used in high-speed hybrid machine tools. The structural features of parallel manipulators are dynamic, a characteristic that is particularly significant when these manipulators are used in high-speed machine tools. However, normal kinematic control method cannot satisfy the requirements of the control system. Many researchers use model-based dynamic control methods, such as the dynamic feedforward control method. However, these methods are rarely used in hybrid machine tools because of the complex dynamic model of the parallel manipulator. In order to study the dynamic control method of parallel manipulators, the dynamic feedforward control method is used in the dynamic control system of a 3-PSP (prismatic-spherical-prismatic) 3-DOF spatial parallel manipulator used as a spindle head in a high-speed hybrid machine tool. Using kinematic analysis as basis and the Newton-Euler method, we derive the dynamic model of the parallel manipulator. Furthermore, a model-based dynamic feedforward control system consisting of both kinematic control and dynamic control subsystems is established. The dynamic control subsystem consists of two modules. One is used to eliminate the influence of the dynamic characteristics of high-speed movement, and the other is used to eliminate the dynamic disturbances in the milling process. Finally, the simulation model of the dynamic feedforward control system of the 3-PSP parallel manipulator is constructed in Matlab/Simulink. The simulations of the control system eliminating the influence of the dynamic characteristics and dynamic disturbances are conducted. A comparative study between the simulations and the normal kinematic control method is also presented.The simulations prove that the dynamic feedforward control method effectively eliminates the influence of the dynamic disturbances and dynamic characteristics of the parallel manipulator on high-speed machine tools, and significantly improves the trajectory accuracy. This is the first attempt to introduce the dynamic feedfordward control method into the 3-PSP spatial parallel manipulator whose dynamic model is complex and provides a study basis for the real-time dynamic control of the high-speed hybrid machine tools.

Singularity analysis is one of the basic problems for parallel manipulators. When a manipulator moves in a singular configuration, the motion and transmission performance are poor. In certain serious cases, the normal operation could be damaged. Based on the topology structure and kinematics analysis of a 2(3HUS+S) parallel manipulator, the Jacobian matrices were established. Then, the singular locus surface was obtained by numerical simulation. In addition, the relationship between the motion path curve and the singular locus surface was analyzed. In this study, α, β, and γ are the attitude angles that describe the motion of moving platforms. There is a nonsingular attitude space in singular locus surfaces, and the singular locus surface is a single surface in a small attitude angle range. The nonsingular attitude space increases as the absolute value of γ increases, and singularity could be avoided when γ is large. Furthermore, the motion path curve passes through the singular locus surface two times, and the two intersection points are consistent with the positions where the motion dexterity is equal to zero. This study provides new insights on the singularity analysis of parallel manipulators, particularly for the structure parameter optimization of the nonsingular attitude space.

Geometric isotropy indices for workspace analysis of parallel manipulators

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.

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

The parallel manipulators with n<6 spherical joint-prismatic joint-spherical joint (SPS) type active legs and one passive constrained leg have attracted more attention and been used in many practical applications. This kind of parallel manipulator has a larger capability of load bearing and a simple structure of active leg. The paper used 4-SPS/PS four degree-of-freedom (DOF) parallel manipulator for the simulation of ship's heave and swing motion. Mobility property of the 4-SPS/PS parallel manipulator is analyzed by screw theory. The inverse position kinematics model is established and the analytical solution is obtained. It uses extra sensor and Sylvester resultant elimination to derive analytical solutions of forward position kinematics including two real solutions and two imaginary solutions, and uses vector cross product to derive the Jacobian matrix of 4-SPS/PS parallel manipulator. Furthermore, it introduces three performance indicators to analyze the singularity. In order to obtain accurate analysis results of singularity, it calculates the minimum singular value, condition number and manipulability degree of Jacobian matrix for different combination of pose, respectively.

Topology of serial and parallel manipulators and topological diagrams

A methodology is proposed for unified solving active wrench of the limited-degree of freedom (DOF) parallel manipulators (PMs). First, the geometric constraints and the inverse displacement kinematics are analysed. Second, the formulae for unified solving the inverse/forward velocity and the translational/rotational Jacobian matrices and inverse/forward Jacobian matrices are derived. Third, the analytic formulae for unified solving the active wrench of limited-DOF PMs are derived based on the principle of virtual work. Finally, a 3-DOF PM with linear/rotational active legs is presented to illustrate the use of the methodology.

The establishment of an elastostatic stiffness model for over constrained parallel manipulators (PMs), particularly those with over constrained subclosed loops, poses a challenge while ensuring numerical stability. This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis (MSA) and independent displacement coordinates (IDCs) extraction techniques. To begin, the closed-loop PM is transformed into an open-loop PM by eliminating constraints. A subassembly element is then introduced, which considers the flexibility of both rods and joints. This approach helps circumvent the numerical instability typically encountered with traditional constraint equations. The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix, utilizing multipoint constraint theory and singularity analysis, all unified within a single coordinate frame. Subsequently, the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix, alongside its elastostatic model. The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix, eliminating the need for additional equations. An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method. In conclusion, the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

In this paper, an optimal design methodology for three-degree-of-freedom planar or spatial parallel manipulators is presented. In particular, cuspidal manipulators, which own the ability of performing non-singular transitions, are addressed. The design procedure incorporates the transitioning ability into the design criteria. An initial stage of the procedure comprises the analysis of different designs by means of characterizing configuration space entities. This gives an overall insight into the capacities of the robot. Then, the dimensional synthesis focuses on cuspidal designs in order to find the set of optimum design parameters such that the operational workspace is as larger as possible having also a regular shape. So as to illustrate the methodology, the 3-SPS-S spatial orientation manipulator is used.Keywordsparallel manipulatornon-singular transitionconfiguration spacedimensional synthesis