Inverse Velocity Analysis Research Articles

Velocity and Singularity Analysis of a 5-DOF (3T2R) Parallel-Serial (Hybrid) Manipulator

This article presents the velocity and singularity analysis for a five-degree-of-freedom (5-DOF) parallel-serial manipulator. The hybrid structure of the manipulator combines a tripod-like parallel part and a serial part, represented as two carriages moving in perpendicular directions. This manipulator provides its end-effector with a 3T2R motion pattern, which includes three independent translations and two independent rotations. First, the study briefly discusses the manipulator design and the results of the position analysis. These results form the basis for the subsequent velocity and singularity analysis, performed by screw theory. The screw coordinates of the unit twists are written for each manipulator joint, and then through the reciprocal screw approach, the actuation and constraint wrenches of the manipulator are obtained by simple inspection. Based on these twists and wrenches, the paper forms the velocity equation and shows an example of the inverse velocity analysis for a given end-effector trajectory. The same example is solved by numerical differentiation to verify the proposed approach. Next, the paper investigates singular configurations by analyzing the wrench system of the manipulator and presents several conditions for serial and parallel singularities. Each condition has both a symbolic representation, given by an equation for screw coordinates of certain wrenches, and a visual representation, which shows the manipulator in a singular configuration.

Manipulator Kinematics and Dynamics on Differentiable Manifolds: Part II Dynamics

Abstract The manipulator differentiable manifold kinematics formulation presented in Part I of this paper is employed for forward and inverse kinematic analysis and formulation of ordinary differential equations of motion on disjoint, maximal, singularity free, path-connected components of regular configuration space, for a broad spectrum of manipulators. Existence of forward and inverse configuration mappings throughout maximal singularity free manifold components yields analytical forward and inverse velocity mappings. Efficient computational algorithms for forward and inverse configuration and velocity analysis on a time grid are derived for each of three manipulator categories. Manifold parameterizations are used to transform variational equations of motion in manipulator coordinates to second-order ordinary differential equations of manipulator dynamics, with both input and output coordinates as state variables, eliminating the need for ad hoc derivation of equations of motion. Criteria that define manipulator differentiable manifolds are shown to guarantee that the equations of motion derived are well-posed on maximal singularity free components of manipulator configuration space. This process is illustrated by presenting terms required for the evaluation of equations of motion for three model manipulators. It is shown that computation involved in the evaluation of equations of manipulator kinematics and dynamics can be carried out in real-time on modern microprocessors, supporting the in-line implementation of modern methods of manipulator control.

Kinematic analysis of overconstrained manipulators with partial subspaces using decomposition method

SUMMARYOverconstrained manipulators in lower subspaces with unique motions can be created and analyzed. However, far too little attention has been paid to creating a generic method for overconstrained manipulators kinematic analysis. This study aimed to evaluate a generic methodology for kinematic analysis of overconstrained parallel manipulators with partial subspaces (OPM-PS) using decomposition to parallel manipulators (PMs) in lower subspaces. The theoretical dimensions of the method are depicted, and the use of partial subspace for overconstrained manipulators is portrayed. The methodology for the decomposition method is described and exemplified by designing and evaluating the method to two overconstrained manipulators with 5 degrees of freedom (DoF) and 3 DoF. The inverse kinematic analysis is detailed with position analysis and Jacobian along with the inverse velocity analysis. The workspace analysis for the manipulators using the methodology is elaborated with numerical results. The results of the study show that OPM-PS can be decomposed into PMs with lower subspace numbers. As imaginary joints are being utilized in the proposed methodology, it will create additional data to consider in the design process of the manipulators. Thus, it becomes more beneficial in design scenarios that include workspace as an objective.

Inverse and forward dynamics of a 4RSS+PS parallel manipulator with one infinite rotational motion

ABSTRACT Modelling and dynamic analysis of a novel four degrees of freedoms (DOFs) parallel manipulator (PM) with 4RSS+PS topology is conducted in this paper. The letters R, S and P denote revolute joint, spherical joint and prismatic joint, respectively, and underline denotes an actuated joint. The proposed manipulator has three rotational and one translational DOF (3R1T), while one of the rotational DOFs around the direction of translational DOF is free of limitation. In addition to the inverse kinematic, velocity and acceleration analyses, a computationally efficient scheme based on the principle of virtual work is presented to derive a closed-form dynamic equation of the 4RSS+PS PM. Then, the dynamic equation is applied for the inverse and forward dynamic analyses of the manipulator. Numerical examples are also studied with Matlab software and its SimMechanics toolbox to demonstrate correctness and efficiency of the presented dynamic modelling.

Kinematic and Singularity Analysis of PRoM-120 – A Parallel Robotic Manipulator with 2-PRU/PRS Kinematic Chains

PRoM-120 was a parallel robotic manipulator which constructed by 2-PRU/PRS kinematic chains. The mobility of this manipulator was 3 DOF, i.e. 1 translational DOF, and 2 rotational DOF (1T2R). The objective of this research was to analyze kinematic, and singularity of PRoM-120 based on its geometrical configuration. Inverse kinematics and velocity analysis were carried out by applying loop vector equation. Meanwhile, all screw systems existed in PRoM-120 were derived using screw theory. Singularity analysis revealed that PRoM-120 had no constraint singularity within its workspace. The kinematic singularity of PRoM-120 showed similar condition to transmission singularity. Three types of both singularities were examined and presented for general condition and selected numerical value of kinematic constants having by PRoM-120. The selected numerical values of those kinematic constants showed only one pose for the singular condition, which was the direct kinematic or the output transmission singularity.

Use of an integrated finite/discrete element method-discrete fracture network approach to characterize surface subsidence associated with sub-level caving

The LKAB Kiruna sub-level cave mine, located in Kiruna, Sweden, is one of the most well studied sub-level cave mines. Due to proximity of the city to the hanging wall, the mine has developed a comprehensive surface deformation monitoring program which is perhaps unparalleled in the mining industry. This surface monitoring scheme provides an excellent data source with which to constrain numerical modelling. In this study, a finite/discrete element modelling approach coupled with a discrete fracture network (FDEM-DFN) is utilized to analyse the Kiruna hanging wall surface subsidence with an emphasis on investigating the influence of discontinuity persistence and spacing. The FDEM-DFN data interpretation uses a variety of novel approaches including time-displacement hanging wall deformation characterization, numerical inverse velocity analysis and virtual hanging wall inclinometer simulation to improve our understanding of the extent and mechanism of hanging wall failure with mine advance. The simulated displacements correspond closely to the actual field data, illustrating the ability of the proposed approach to reproduce sub-level cave behaviour. Three distinct time-displacement phases namely: regressive, progressive and steady state are observed in the FDEM-DFN models. The paper also reviews the potential application of the inverse velocity method and virtual inclinometers in characterizing sub-surface brittle failure associated with sub-level caving.

Tex3: An 2R1T Parallel Manipulator with Minimum DOF of Joints and Fixed Linear Actuators

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.

Mobility, Kinematic Analysis, and Dimensional Optimization of New Three-Degrees-of-Freedom Parallel Manipulator With Actuation Redundancy

Parallel manipulators (PMs) with redundant actuation are attracting increasing research interest because they have demonstrated improved stiffness and fewer singularities. This paper proposes a new redundantly actuated parallel manipulator that has three degrees-of-freedom (DOFs) and four limbs. The proposed manipulator is a 2UPR-2PRU parallel manipulator (where P represents an actuated prismatic joint, R represents a revolute joint, and U represents a universal joint) that is actuated using four prismatic joints; two of these joints are mounted on the base to reduce the movable mass. Mobility analysis shows that the moving platform has two rotational DOFs and one translational DOF. First, the inverse displacement solution, velocity, and singularity analyses are discussed. Next, the local transmission index (LTI) and the good transmission workspace are used to evaluate the motion/force transmissibility of the 2UPR-2PRU parallel manipulator. Finally, the parameter-finiteness normalization method (PFNM) is used to produce an optimal design that considers the good transmission workspace. It is thus shown that the motion/force transmission of the proposed manipulator is improved by optimizing the link parameters.

Lagrangian Dynamics Analysis of a XY-Theta Parallel Robotic Machine Tool

Dynamics of a highly stiff parallel machine tool is the subject of this paper. High stiffness, good accuracy, relatively large workspace and free of singularities on the whole workspace makes the manipulator suitable for machining applications as an XY-Theta precision table. First, obtaining kinematics constraints, inverse kinematics analysis and velocity analysis are performed. Next, using six redundant generalized coordinates, we obtain Lagrangian of the manipulator. Also, a Lagrangian approach is proposed to obtain dynamics equations of the machine tool using three Lagrangian multipliers. This method allows elimination of constraint forces and moments at the joints from the motion equations. Dynamic equations of the manipulator are formed as inverse dynamics and direct dynamics problems. Finally, two examples are presented that confirms the obtained dynamics equations.

Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses

Predicting the time of failure is a topic of major concern in the field of geological risk management. Several approaches, based on the analysis of displacement monitoring data, have been proposed in recent years to deal with the issue. Among these, the inverse velocity method surely demonstrated its effectiveness in anticipating the time of collapse of rock slopes displaying accelerating trends of deformation rate. However, inferring suitable linear trend lines and deducing reliable failure predictions from inverse velocity plots are processes that may be hampered by the noise present in the measurements; data smoothing is therefore a very important phase of inverse velocity analyses. In this study, different filters are tested on velocity time series from four case studies of geomechanical failure in order to improve, in retrospect, the reliability of failure predictions: Specifically, three major landslides and the collapse of an historical city wall in Italy have been examined. The effects of noise on the interpretation of inverse velocity graphs are also assessed. General guidelines to conveniently perform data smoothing, in relation to the specific characteristics of the acceleration phase, are deduced. Finally, with the aim of improving the practical use of the method and supporting the definition of emergency response plans, some standard procedures to automatically setup failure alarm levels are proposed. The thresholds which separate the alarm levels would be established without needing a long period of neither reference historical data nor calibration on past failure events.

Inverse kinematic and dynamic analysis of planar path generating adjustable mechanism

Path generating adjustable mechanisms with continuous adjustment have been studied in literature, wherein the synthesis has been commonly based on the position kinematics of the mechanism. Many real life applications would, however, demand that the coupler point traces the path at specified velocity and acceleration, thus necessitating development of inverse velocity and acceleration analyses. Further, the inverse dynamic analysis needs to be carried out from the viewpoint of mechanical design and motion control of the mechanism. In this paper, inverse kinematic and dynamic analysis of a path generating four-bar mechanism with continuous one-parameter adjustment is presented. The kinematic analysis is presented for both, the non-singular and singular configurations of the mechanism. Newton's equations of motion are solved by introducing a set of generalized unknowns, resulting in explicit formulae for all the unknowns. The dynamic analysis approach is general and is applicable to any multi-degree-of-freedom single-loop planar mechanism with revolute joints. Results are presented for illustrative examples and future extension of the presented work is discussed.

Design and Analysis of 3R2T and 3R3T Parallel Mechanisms With High Rotational Capability

This paper describes the design, kinematics, and workspace analysis of 3R2T and 3R3T parallel mechanisms (PMs) with large rotational angles about three axes. Since the design of PMs with high rotational capability is still a challenge, we propose the use of a new nonrigid (or articulated) moving platform with passive joints in order to reduce the interference between limbs and the moving platform. According to the proposed nonrigid platform and Lie subgroup of displacement theory, several 3R2T and 3R3T PMs are presented. Subsequently, the inverse kinematics and velocity analysis of one of the proposed mechanisms are detailed. Based on the derived inverse kinematic model, the constant-orientation workspace is computed numerically. Then, the analysis of rotational capability about the three axes is performed. The result shows that even if interference and singularity are taken into account, the proposed mechanisms still reveal the high continuously rotational capability about the three axes, by means of actuation redundancy.

Inverse jerk analysis of symmetric zero-torsion parallel manipulators

In this work the inverse velocity, acceleration and jerk analyses of a class of three-degrees-of-freedom parallel manipulators are approached by means of the theory of screws. The concept of reciprocal screws allows to obtain simple and decoupled expressions to compute the joint rates, up to the third time derivative, of the class of manipulators under study given the instantaneous kinematic properties of the center of the moving platform. The interdependency between the angular and linear kinematic properties of the moving platform is also derived. A case study is included.

Realization and Simulation of Motion Trajectory of a 2-DOF Planar Parallel Manipulator

A kind of 2-DOF parallel manipulator driven by two sliders moving along two parallel guides is analyzed. Based on the explicit expression of inverse position, velocity and acceleration analyses, the mobile trajectory of this manipulator is investigated and simulated. In trajectory planning, the trajectory profiles are assigned to be accelerated and decelerated at the first and last few seconds, respectively, and keep at constant speed for the remainder of time, where the forth-order polynomial is fitted during acceleration and deceleration, and clothoid curve is applied around the corner of axis. Then the mobile rule exerted on the actuator sliders is obtained using inverse position based on the desired end-effecter trajectory. Finally, the virtual prototype of this mechanism is modeled using Solidwork and the kinematics and dynamics simulation is performed using Cosmostion. The result shows that both velocity, acceleration of the sliders and the driving force exerted on the sliders are continuous curves, which can fully satisfy the demand of high-accuracy and real-time processing of the high-speed Manipulator.

Inverse velocity analysis for line guidance five-axis robots

In this paper, inverse velocity problem for five-axis robots is investigated. The conventional method for a five-axis robot is to pseudo-inverse the 6×5 Jacobian matrix. The solution, primarily based on six freedoms inverse velocity analysis, is just an approximation with a least-square error. A five-axis robot can exactly guide an axis-symmetrical tool in 3-D space. Two exact solutions are provided for five-axis robots. One is based on the screw motion of the tool. The other is based on spherical angles of the tool to derive a 5×5 Jacobian matrix. A new type of singular configuration is discovered and is called the task singularity. The moving path of the line shaped tool is constructed as a ruled surface. Analysis of the angular acceleration shows the surface constructed based on the spherical angle representation has better characteristic. It is concluded that for five-axis robots, the tool position is better represented by five parameters rather than six parameters in order to get better solutions for inverse velocity as well as the motion planning.

Design and analysis of a new singularity-free three-prismatic-revolute-cylindrical translational parallel manipulator

A new three-prismatic-revolute-cylindrical (three-PRC) translational parallel manipulator (TPM) with orthogonally arranged fixed actuators is proposed in this paper. The mobility of the manipulator is analysed via screw theory. The inverse kinematics, forward kinematics, and velocity analyses are performed and the singularities and isotropic configurations are identified afterwards. Moreover, the mechanism design rules producing a singularity-free manipulator have been generated. Under different cases of physical constraints subject to mechanical joints, the reachable workspace of the manipulator is geometrically determined and compared. In particular, it is illustrated that the manipulator has a regular shape workspace with a maximum cuboid defined as the usable workspace inscribed and one isotropic configuration involved. Furthermore, to obtain a large usable workspace, the architecture design of a three-PRC TPM is carried out and the singularity property within the usable workspace is verified. Simulation results show that there are no singular configuration within the workspace, which reveal the validity of design rules for a singularity-free three-PRC TPM.

Kinematics of a Hybrid Manipulator by Means of Screw Theory

In this work the kinematics of a hybrid manipulator, namely a fully parallel-serial manipulator, with a particular topology is approached by means of the theory of screws. Given the length of the six independent limbs, the forward position analysis of the mechanism under study, indeed the computation of the resulting pose, position and orientation, of the end-platform with respect to the fixed platform, is carried out in closed-form solution. Therefore conveniently this initial analysis avoids the use of a numerical technique such as the Newton-Raphson method. Writing in screw form the reduced acceleration state of the translational platform, with respect to the fixed platform, a simple expression for the computation of the acceleration of the translational platform is derived by taking advantage of the properties of reciprocal screws, via the Klein form, a bilinear symmetric form of the Lie algebra e(3). Following a similar procedure, a simple expression for the computation of the angular acceleration of the end-platform, with respect to the translational platform, is easily derived. Naturally, as an intermediate step, this contribution also provides the forward and inverse velocity analyses of the chosen parallel-serial manipulator. Finally, in order to prove the versatility of the expressions obtained via screw theory for solving the kinematics, up to the acceleration analysis, of the proposed spatial mechanism, a numerical example is solved with the help of commercial computer codes.

Kinematic Analysis and Design of a New 3-DOF Translational Parallel Manipulator

A new three degrees of freedom (3-DOF) translational parallel manipulator (TPM) with fixed actuators called a 3-PRC TPM is proposed in this paper. The mobility of the manipulator is analyzed via screw theory. The inverse kinematics, forward kinematics, and velocity analysis are performed and the singular and isotropic configurations are identified afterward. Moreover, the mechanism design to eliminate all singularities and generate an isotropic manipulator has been presented. With the variation on architectural parameters, the reachable workspace of the manipulator is generated and compared. Especially, it is illustrated that the manipulator in principle possesses a uniform workspace with a constant hexagon shape cross section. Furthermore, the dexterity characteristics are investigated in the local and global sense, respectively, and some considerations for real machine design have been proposed as well.

Inverse Velocity and Singularity Analysis of Low‐DOF Serial Manipulators

AbstractThis paper presents a method for exact inverse velocity analysis of low‐DOF (degrees of freedom n<6) serial manipulators. For a low‐DOF serial manipulator, the number of independently controllable variables in the Cartesian space is equal to the number of joint variables in the joint space, and the remaining 6−n variables are linearly dependent on these independent variables. This paper employs the theory of reciprocal screws to determine a mapping between the independent velocity components in the Cartesian space and the joint rates in the joint space. It is shown that singular conditions of a low‐DOF manipulator depend on choice of independent variables. A 5‐DOF and a 4‐DOF manipulator are analyzed, and a numerical example in which the end effector of a 4‐DOF manipulator is commanded to follow a straight line is used to demonstrate the methodology. © 2003 Wiley Periodicals, Inc.

Forward and Inverse Acceleration Analyses of In-Parallel Manipulators

Simple expressions for the forward and inverse acceleration analyses of a six degree of freedom in-parallel manipulator are derived. The expressions are obtained by firstly computing the “accelerator” for a single Hooke-Prismatic-Spheric, HPS for short, connector chain in terms of the joint velocities and accelerations. The accelerator is a function of the line coordinates of the joint axes and of a sequence of Lie products of the same line coordinates. A simple expression for the acceleration of the prismatic actuator is obtained by forming the Klein form, or reciprocal product, with the accelerator and the coordinates of the line of the connector chain. Since the Klein form is invariant, the resulting expression can be applied directly to the six HPS connector chains of an in-parallel manipulator. As a required intermediate step, this contribution also derives the corresponding solutions for the forward and inverse velocity analyses. The authors believe that this simple method has applications in the dynamics and control of these in-parallel manipulators where the computing time must be minimized to improve the behavior of parallel manipulators. [S1050-0472(00)01303-9]