Jerk analysis of a six-degrees-of-freedom three-legged parallel manipulator

In this work the jerk analysis of a 3-RRPS parallel manipulator to realize six degrees of freedom is approached by means of the theory of screws. The input/output equations of velocity, acceleration and jerk of the moving platform with respect to the fixed platform are obtained systematically by resorting to reciprocal-screw theory. A numerical example is included in order to show the application of the method of kinematic analysis. Furthermore, the numerical results obtained via screw theory are satisfactorily compared with simulations generated with the aid of commercially available software.     

A new spatial hyper-redundant manipulator

This work presents a novel hyper-redundant manipulator. Such a manipulator is built with a variable number of tandem-assembled modules. Each module consists of a 3-dof parallel manipulator with asymmetric extremities in which moving platform possesses mixed motions with respect to the base platform. The manipulator's architecture is so simple that the forward position analysis is presented in closed-form solution, more specifically, in echelon-form solution. On the other hand, the velocity and acceleration analyses are carried out using the theory of screws. Finally, a case study consisting of solving the kinematic analysis of a 30-dof hyper-redundant manipulator is presented.     

The kinematics of modular spatial hyper-redundant manipulators formed from RPS-type limbs

This study addresses the kinematics, including position, velocity and acceleration analyses, of a modular spatial hyper-redundant manipulator built with a variable number of serially connected identical mechanical modules with autonomous motions. First, the kinematics of the base module, a three-legged in-parallel manipulator, is formulated using the theory of screws. After that, the results thus obtained, are applied recursively for accomplishing the kinematic analyses of the hyper-redundant manipulator at hand. A numerical exampled is included.     

Position,Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator

This paper investigates the problems of kinematics, Jacobian, singularity and workspace analysis of a spatial type of 3-PSP parallel manipulator. First, structure and motion variables of the robot are addressed. Two operational modes, non-pure translational and coupled mixed-type are considered. Two inverse kinematics solutions, an analytical and a numerical, for the two operational modes are presented. The direct kinematics of the robot is also solved utilizing a new geometrical approach. It is shown, unlike most parallel robots, the direct kinematics problem of this robot has a unique solution. Next, analytical expressions for the velocity and acceleration relations are derived in invariant form. Auxiliary vectors are introduced to eliminate passive velocity and acceleration vectors. The three types of conventional singularities are analyzed. The notion of non-pure rotational and non-pure translational Jacobian matrices is introduced. The non-pure rotational and non-pure translational Jacobian matrices are combined to form the Jacobian of constraint matrix which is then used to obtain the constraint singularity. Finally, two methods, a discretization method and one based on direct kinematics are presented and robot non-pure translation and coupled mixed-type reachable workspaces are obtained. The influence of tool length on workspace is also studied.     

A New Approach to the Architecture Optimization of a General 3-PUU Translational Parallel Manipulator

This paper presents a new approach to the architecture optimization of a general 3-PUU translational parallel manipulator (TPM) based on the performance of a weighted sum of global dexterity index and a new performance index-space utility ratio (SUR). Both the inverse kinematics and forward kinematics solutions are derived in closed form, and the Jacobian matrix is derived analytically. The manipulator workspace is generated by a numerical searching method with the physical constraints taken into consideration. Simulation results illustrate clearly the necessity to introduce a mixed performance index using space utility ratio for architectural optimization of the manipulator, and the optimization procedure is carried out with the goal of reaching a compromise between the two indices. The analytical results are helpful in designing a general 3-PUU TPM, and the proposed design methodology can also be applied to architectural optimization for other types of parallel manipulators.     

Kinematic analysis of the 3-CUP parallel mechanism

This paper investigates the kinematics of a parallel mechanism that is composed of three identical CUP legs evenly distributed on the fixed base. The platform of the mechanism has three degrees-of-freedom, namely: two rotations and one translation along the axis perpendicular to the base. The paper obtains closed form solutions for the inverse and forward kinematics problems. Furthermore, the Jacobian matrix is determined in order to solve the instantaneous kinematics analysis. It is used for the identification of the singular configurations of the mechanism, which are investigated by applying screw theory. The parasitic motions of the platform are determined by means of a workspace analysis. This paper uses several simulations and numerical examples to prove the accuracy of the analytical results.     

Mobility analysis and kinematics of the semi-general 2(3-RPS) series-parallel manipulator

This work reports on the kinematics of a series-parallel manipulator built with two zero-torsion tangential parallel manipulators assembled in series connection. Although this mechanism has been widely studied, there are some topics that must be revised, e.g. the mobility analysis here reported shows that the robot under study is not precisely a six degrees of freedom spatial mechanism as it has been commonly considered. Furthermore, the traditional hexagonal coupler platform is replaced with a three-dimensional platform which yields a mechanism with a more general topology. The forward and inverse displacement analyses of the robot are obtained in semi-closed form solutions based on simple closure equations which are generated upon the coordinates of three points embedded to the moving platform while the input–output equations of velocity and acceleration of the semi-general series-parallel manipulator are easily derived by resorting to reciprocal-screw theory. A case study is included in order to show the application of the method of kinematic analysis.     

An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory

This paper analyzes the mobility and stiffness of a three-prismatic-revolute-cylindrical (3-PRC) translational parallel manipulator (TPM). Firstly, the original 3-PRC TPM is converted into a non-overconstrained manipulator since there exist some practical problems for the overconstrained mechanism. By resorting to the screw theory, it is demonstrated that the conversion brings no influences to the mobility and kinematics of the manipulator. Secondly, the stiffness matrix is derived intuitively via an alternative approach based upon screw theory with the consideration of actuations and constraints, and the compliances subject to both actuators and legs are taken into account to establish the stiffness model. Furthermore, the stiffness performance of the manipulator is evaluated by utilizing the extremum stiffness values over the usable workspace, and the influences of design parameters on stiffness properties are presented, which will be helpful for the architecture design of the TPM.     

Inverse dynamics of a parallel manipulator

Presented is an analysis of the kinematics and the inverse dynamics of a proposed three degree of freedom (dof) parallel manipulator resembling the Stewart platform in a general form. In the kinematic analysis, the inverse kinematics, velocity, and acceleration analyses are performed, respectively, using vector analysis and general homogeneous transformations. An algorithm to solve the inverse dynamics of the proposed parallel manipulator is then presented using a Lagrangian technique. In this case, it is found that one should introduce and subsequently eliminate Lagrange multipliers to arrive at the governing equations. Numerical examples are finally carried out to examine the validity of the approach and the accuracy of the numerical technique employed. The trajectory of motion of the manipulator is also performed using a cubic spline. © 1994 John Wiley & Sons, Inc.     

Orientation-Singularity and Nonsingular Orientation-Workspace Analysis of the Semi-Regular Stewart–Gough Platform Manipulator

This paper addresses the orientation-singularity analysis and the nonsingular orientation-workspace computation of the semi-regular Stewart–Gough platform manipulator (SRSGPM). Based on the half-angle transformation, a polynomial expression that represents the orientation-singularity locus of the SRSGPM when the mobile platform of the platform manipulator is fixed to a constant position is derived. It is shown that the orientation-singularity locus of the SRSGPM at a fixed position is a polynomial expression of degree 13 in the mobile platform orientation parameters and graphical representations of the orientation-singularity locus of the SRSGPM are illustrated with examples to demonstrate the theoretical result. Using this half-angle transformation, a new discretization method is proposed for computing the nonsingular orientation-workspace of the SRSGPM in consideration of singularities, limitations of active and passive joints, and link interference. Examples of a SRSGPM are given to demonstrate the results.     

高低频复合驱动的并联调姿隔振平台的运动分析

针对现有扰动补偿装置调姿和隔振功能分离的缺陷,研制了高低频复合驱动并联平台．通过多种复合驱动方式的性能比较,选用RRPRP构型的平面五杆机构作为复合驱动单元,并将机构构型确定为3-RRPRP-4S．运用约束螺旋理论来分析高低频复合驱动单元的等效形式以及机构的自由度．进而分别建立高频和低频2种驱动形式下的位置反解模型,其中对高频驱动形式下的分析应用逐步迭代法．基于旋量理论,构建2种驱动形式下的动平台与广义输入之间的1阶影响系数和2阶影响系数,进而得到从广义输入到动平台速度和加速度的线性映射．基于运动学分析结果,提出了瞬时锁定法作为机构的驱动策略,通过在高低频驱动下的数值算例对理论分析进行仿真验证,并进行了样机实验．结果表明,仿真曲线和理论曲线几乎完全重合,样机实验的复现率在93%～96%之间．因此,该平台应用高低频复合驱动的形式实现了调姿隔振的混合输出,突破了驱动器频率带对扰动补偿装置的限制,可对频率范围跨度较大的干扰信号进行补偿．     

Synthesis on forward kinematics problem algebraic modeling for the planar parallel manipulator: displacement-based equation systems

Based on a proven exact method which solves the forward kinematics problem (FKP) this article investigates the FKP formulation specifically applied to planar parallel manipulators. It focuses on the displacement-based equation systems. The majority of planar tripods can modeled by the 3-RPR parallel manipulator, which is a tripod constituted by a fixed base and a triangular mobile platform attached to three kinematics chains with linear (prismatic) actuators located between two revolute joints. In order to implement the algebraic method, the parallel manipulator kinematics are formulated as polynomial equation systems where the number of equations is equal to or exceeds the number of unknowns. Three geometrical formulations are derived to model the difficult FKP. The selected proven algebraic method uses Gröbner bases from which it constructs an equivalent univariate system. Then, the real roots are isolated using this last system. Each real solution exactly corresponds to one manipulator assembly mode, which is also called a manipulator posture. The FKP resolution of the planar 3-RPR parallel manipulator outputs six complex solutions which become a proven real solution number upper bound. In several typical examples, the resolution performances (computation times and memory usage) are given. It is then possible to compare the models and to reject one. Moreover, a number of real solutions are obtained and the corresponding postures drawn. The algebraic method is exact and produces certified results.     

Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms

By a mobile manipulator we mean a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator fixed to the platform. A taskspace of the mobile manipulator includes positions and orientations of its end effector relative to an inertial coordinate frame. The kinematics of a mobile manipulator are represented by a driftless control system with outputs. Admissible control functions of the platform along with joint positions of the manipulator constitute the endogenous configuration space. Endogenous configurations have a meaning of controls. A map from the endogenous configuration space into the taskspace is referred to as the instantaneous kinematics of the mobile manipulator. Within this framework, the inverse kinematic problem for a mobile manipulator amounts to defining an endogenous configuration that drives the end effector to a desirable position and orientation in the taskspace. Exploiting the analogy between stationary and mobile manipulators we present in the paper a collection of regular and singular Jacobian inverse kinematics algorithms. Their performance is evaluated on the basis of intense computer simulations.     

Hyper-Jerk Analysis of Robot Manipulators

In this work the hyper-jerk analysis of robot manipulators is addressed by means of the theory of screws. The reduced hyper-jerk state of a rigid body as observed from another body or reference frame is obtained as a six-dimensional vector by applying the concept of helicoidal vector field. Moreover, this contribution demonstrates that the reduced hyper-jerk state of a rigid body can be considered, similar to the velocity state, as a twist about a screw. Furthermore, the reduced hyper-jerk state is systematically obtained in pure screw form. Finally, a case study, which is verified with the aid of commercially available software, that consists of solving the kinematics, up to the hyper-jerk analysis, of a zero-torsion parallel manipulator is included in order to show the application of the method of kinematic analysis.     

Kinematics analysis of an offset 3-UPU translational parallel robotic manipulator

The parallel robotic manipulator has attracted many researchers’ attention and it also has growing applications to different areas. This paper proposes a 3-UPU (universal–prismatic–universal) translational parallel robotic manipulator with an equal offset in its six universal joints, based on the zero offset 3-UPU parallel manipulator. The kinematics of the new manipulator is analyzed and its inverse and forward kinematics solutions are provided. The conclusion is that its forward kinematics has 16 solutions instead of two in the zero offset manipulator.     

Dynamics of the 6-6 Stewart parallel manipulator

Recursive matrix relations in kinematics and dynamics of the 6-6 Stewart–Gough parallel manipulator having six mobile prismatic actuators are established in this paper. Controlled by six forces, the manipulator prototype is a spatial six-degrees-of-freedom mechanical system with six parallel legs connecting to the moving platform. Knowing the position and the general motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each manipulator’s link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Finally, compact matrix relations and graphs of simulation for the input velocities and accelerations, the input forces and powers are obtained.     

An analysis of the inverse kinematics for a 5-DOF manipulator

This paper proposes an analytical solution for a 5-DOF manipulator to follow a given trajectory while keeping the orientation of one axis in the end-effector frame. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analyzed systemically. The singular problem is discussed after the forward kinematics is provided. For any given reachable position and orientation of the end-effector, the derived inverse kinematics will provide an accurate solution. In other words, there exists no singular problem for the 5-DOF manipulator, which has wide application areas such as welding, spraying, and painting. Experiment results verify the effectiveness of the methods developed in this paper.     

Dynamics analysis of the Star parallel manipulator

Matrix relations in kinematics and dynamics of the Star parallel manipulator are established in this paper. The prototype of the manipulator is a three-degree-of-freedom mechanism, which consists of a system of parallel kinematical chains connecting to a moving platform. Knowing the translation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each robot’s link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Recursive formulae offer expressions and graphs for the power requirement comparison of each of three actuators in two computational complexities: complete dynamic model and simplified dynamic model.     

Estimation model for kinematic calibration of manipulators with a parallel structure

This article provides an estimation model for calibrating the kinematics of manipulators with a parallel geometrical structure. Parameter estimation for serial link manipulators is well developed, but fail for most structures with parallel actuators, because the forward kinematics is usually not analytically available for these. We extend parameter estimation to such parallel structures by developing an estimation method where errors in kinematical parameters are linearly related to errors in the tool pose, expressed through the inverse kinematics, which is usually well known. The method is based on the work done to calibrate the MultiCraft robot. This robot has five linear actuators built in parallel around a passive serial arm, thus making up a two-layered parallel-serial manipulator, and the unique MultiCraft construction is reviewed. Due to the passive serial arm, for this robot conventional serial calibration must be combined with estimation of the parameters in the parallel actuator structure. The developed kinematic calibration method is verified through simulations with realistic data and real robot kinematics, taking the MultiCraft manipulator as the case. © 1994 John Wiley & Sons, Inc.