Closed-form Kinematic Solution Research Articles

Kinematic modeling and dexterity evaluation of a PS-RRS-2RUS parallel manipulator used for controllable pitch propeller

ABSTRACTThis article investigates the kinematic modeling and dexterity evaluation of a PS-RRS-2RUS parallel manipulator. The design concept and mobility analysis of the manipulator are first addressed utilizing the screw theory. Second, the decoupled and closed-form kinematic solutions with multiple configurations are solved through vector method. Then, the analytical expressions for the velocity relationships are derived into a closed-form Jacobian matrix, which is then used to distinguish the singular postures. Finally, the workspace with fixed orientation is calculated and its dexterity is evaluated. The numerical simulations and validation are conducted in a case study.

Efficient Closed-Form Solution of the Kinematics of a Tunnel Digging Machine

In this work, the kinematics of a large size tunnel digging machine is investigated. The closed-loop mechanism is made by 13 links and 13 class 1 couplings, seven of which are actuated. This kind of machines are commonly used to perform ground drilling for the placement of reinforcement elements during the construction of tunnels. The direct kinematic solution is obtained using three methods: the first two are based on the numerical solution of the closure equation written using the Denavit–Hartenberg convention, while the third is based on the definition and solution in closed form of an equivalent spherical mechanism. The procedures have been tested and implemented with reference to a real commercial tunnel digging machine. The use of the proposed method for the closed-form solution of direct kinematics allows to obtain a major reduction of the computation time in comparison with the standard numerical solution of the closure equation.

Indirect disturbance compensation control of a planar parallel (2-PRP and 1-PPR) robotic manipulator

Abstract This study addresses the dynamic modelling and indirect disturbance compensation control of planar parallel robotic motion platform with three degrees of freedom (3-DOF) in the presence of parameter uncertainties and external disturbances. The proposed planar parallel motion platform is a singularity free manipulator and has three manipulator legs located on the same plane linked with a moving platform. Of the three aforementioned manipulator legs, two legs have a prismatic–revolute–prismatic (PRP) joint configuration each with only one prismatic joint deliberated to be active, and the other leg consists of prismatic–revolute–prismatic (PPR) joint configuration with one active prismatic joint. The closed form kinematic solution (both forward and reverse kinematics) for the platform has been obtained in completion. In addition, the dynamic model for the platform has been communicated using the energy based Euler–Lagrangian formulation method. The proposed controller is based on a computer torque control with disturbance compensation integrated with it. Disturbance vectors comprising disturbances due to parameter variations, payload variations, frictional effects and other additional effects have been estimated using an extended Kalman filter (EKF). The EKF proposed for this specific platform uses only position and orientation measurements for estimation and noise mitigation. Simulations with a characteristic trajectory are presented and the results have been paralleled with traditional controllers such as the proportional integral derivative (PID) controller and computed torque controller (CTC). The results demonstrate satisfactory tracking performance for the proposed controller in the presence of parameter uncertainties and external disturbances.

Kinematic Analysis of a Four Degreed-of-Freedoms Hybrid Machine Tool

On one hand, parallel machine tool enjoys many advantages over conventional serial counterpart, on the other hand, it also suffers from the disadvantages of coupled position and orientation, difficulty in kinematic modeling, strict requirements for components and difficulty in manufacturing of the spherical joint adopted in some limbs. Hybrid mechanism, however, will serve the turn in some cases. By using a three degree-of-freedoms parallel mechanism and a slide worktable which will fulfill one movement, a novel four degree-of-freedoms hybrid machine tool is put forward. The kinematic solutions are analyzed and closed-form kinematic solutions are given. The methods and theories adopted here can be used for design of other types of hybrid machine tools.

Kinematic Modeling of a Serial–Parallel Forging Manipulator with Application to Heavy-Duty Manipulations#

Heavy-duty forging manipulators are essential handling equipments for integrated open-die forging plants. This article presents a forging manipulator with serial–parallel hybrid mechanism and develops its closed-form kinematic solutions (inverse and direct) based on the detailed geometric description of the mechanism. The kinematic Jacobian matrix is also derived analytically. Case studies for kinematical simulation, workspace, and kinetostatic analysis are conducted throughout the developing process. The closed-form kinematic solution provides the foundation of simulation and control design, and the results of case studies demonstrate the special features of the proposed mechanism in load capacity and compliant manipulation ability for heavy tasks in automatic open-die forging processes.

Kinematic analysis of a hybrid serial-parallel manipulator

The kinematic analysis of a new type hybrid serial-parallel manipulator is presented. This manipulator is based on two kinds of 3-UPU parallel mechanisms (PM). Each 3-UPU possesses one platform, one base and three limbs, and hence has 3 degrees of freedom (DOF). Each limb comprises of universal (U), prismatic (P), and universal (U) joints in series. Therefore the hybrid manipulator has totally 6 degrees of freedom and has also an elegant structure. The moving platform (mid platform) of the first PM moves with pure translation with respect to the fixed base and the moving platform (end platform) in the second PM only changes its orientation with respect to the mid platform. In this paper, closed-form kinematic solutions are obtained for this type of mechanism and related theoretical results have been verified numerically.

Closed-form kinematic solution of a non-parallel cable reeving crane system

This paper presents the closed-form kinematic solutions, position and velocity of a non-parallel cable reeving crane system. These solutions are necessary in order to control a container crane that is widely used in cargo terminals. One PSD (position sensitive device) sensor and two IR (infrared) emissive beacons are used to find the angular position and angular velocity information of two reference points of a moving spreader. The sensor and beacons are mounted on trolley and reference points of spreader respectively. By using this information, the exact position and velocity of the spreader are determined analytically. These results can be used in the anti-sway and anti-skew control of a container crane.

Identification of Position-Independent Robot Parameter Errors Using Special Jacobian Matrices

Common production manipulators are designed to be controlled through the use of a closed-form kinematic solution algorithm. This closed-form solution uses manufacturer-specified nomi nal parameter values to model the given manipulator. These position-independent parameters, link lengths, twists, and off sets are geometrical and do not change as the manipulator is driven. However, manufacturing tolerances or usage may cause the actual parameters to deviate from the nominal robot para meters. In some cases, this deviation may be large and thus may cause the closed-form inversion to yield inaccurate joint value results.To assure proper end-effector positioning, it is important to identify these position-independent error values. The identifi cation algorithm to be presented uses the Denavit-Hartenberg (D-H) parameter notation to model any given M-jointed manip ulator. For the given model, a set of special Jacobian matrices are formulated with respect to the four D-H parameters (Jθ, Js, Jα, and Ja). This set of four special Jacobian matrices is used to determine a set of D-H error parameter values, which will allow one to estimate the actual D-H parameter values.The iterative regression algorithm for parameter identifi cation uses the end-effector information at several arbitrary manipulator positions, as well as nominal parameter and joint variable information to compute the parameter error values. The use of the special Jacobian matrices allows for easy de termination of mathematical singularity conditions. In addition, statistical methods are employed to provide numerical uni formity between examples and aid in the evaluation process. Through several examples, it will be shown that the use of this parameter identification algorithm produces accurate results. This article will discuss the possibilities of deterministic as well as probabilistic parameter errors. Through the use of this parameter identification algorithm, one is able to identify the D-H parameter error values that will otherwise cause a loss in end-effector accuracy.