Optimal dynamic trajectory planning for linearly actuated platform type parallel manipulators having task space redundant degree of freedom

2007 ◽  
Vol 42 (6) ◽  
pp. 727-750 ◽  
Author(s):  
Ka-Tjun Oen ◽  
Li-Chun T. Wang
Author(s):  
Mahir Hassan ◽  
Amir Khajepour

This paper presents a kinetostatic analysis of a class of hybrid cable-driven parallel manipulators consisting of cables and a rigid-link serial leg for lower-degree-of-freedom tasks. The serial leg provides the task constraints and the cables provide the required actuation to move the platform in the task space. Having a rigid-link serial leg providing the required constraints for the moving platform in lower-degree-of-freedom applications reduces the number of cables required to support the moving platform in the task space. As a result, the manipulator can be designed with fewer cables and actuators. In order for the manipulator to balance arbitrary applied wrenches, redundant actuation is required. This redundant actuation can be obtained from a redundant actuator mounted on one (or more) serial-leg joint(s). Conditions for analyzing the capability of the redundant actuation to generate cable tension are explained in the paper. A discussion is also given on the optimization of the cable layout and the redundant actuator forces to minimize the tension generated in the cables.


1998 ◽  
Vol 123 (1) ◽  
pp. 80-89 ◽  
Author(s):  
Ashitava Ghosal ◽  
Bahram Ravani

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, the possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.


Author(s):  
Zhihong Zou ◽  
Jin Chen ◽  
Xiaoping Pang

In this paper, a task space-based methodology for dynamic trajectory planning for digging process of a hydraulic excavator is presented, with the integration of soil–bucket interaction. An extended soil–bucket interaction model, which adds the resistive moment compared to the previous models, is provided in this research. This improved model is validated by comparing with the measurement data taken from field experiments before integrating it into a dynamic model of an excavator. Further, Newton–Euler method is used for the derivation of the dynamics of each link of the excavator to determine the joint forces, which can cause the machine damage. The position and orientation trajectories of the bucket in the task space are parameterized by using the B-splines, so as to achieve the task-oriented operations and ensure the operation flexibility. The joint space motion characteristics are obtained by solving the inverse kinematics of the working mechanism of an excavator. Moreover, to avoid the operation uncertainty for a given bucket tip position trajectory and reduce the computational effort, the self-motion parameters are introduced when solving the inverse kinematics of the redundant working mechanism. All these self-motion parameters are taken as a set of design variables in the trajectory optimization problem. Also, the limits on the hydraulic driving forces, joint angles, angular velocities and accelerations, as well as bucket capacity are considered as the optimization constraints for the digging process. Finally, optimization examples of two typical digging categories (i.e. level digging work and slope digging work) are given to demonstrate and verify the capabilities of the new methodology proposed in this research. The results show that the proposed method can effectively generate the optimal trajectories satisfying the following criteria: time efficiency, energy efficiency, and least machine damage. This work lays a solid foundation for motion planning and autonomous control of an excavator.


Author(s):  
Mengxia Li ◽  
Junmin Mou ◽  
Yixiong He ◽  
Xiaohan Zhang ◽  
Qinqiong Xie ◽  
...  

2005 ◽  
Vol 128 (1) ◽  
pp. 303-310 ◽  
Author(s):  
Saeed Behzadipour ◽  
Amir Khajepour

The stiffness of cable-based robots is studied in this paper. Since antagonistic forces are essential for the operation of cable-based manipulators, their effects on the stiffness should be considered in the design, control, and trajectory planning of these manipulators. This paper studies this issue and derives the conditions under which a cable-based manipulator may become unstable because of the antagonistic forces. For this purpose, a new approach is introduced to calculate the total stiffness matrix. This approach shows that, for a cable-based manipulator with all cables in tension, the root of instability is a rotational stiffness caused by the internal cable forces. A set of sufficient conditions are derived to ensure the manipulator is stabilizable meaning that it never becomes unstable upon increasing the antagonistic forces. Stabilizability of a planar cable-based manipulator is studied as an example to illustrate this approach.


Robotica ◽  
2008 ◽  
Vol 26 (6) ◽  
pp. 791-802 ◽  
Author(s):  
Flavio Firmani ◽  
Alp Zibil ◽  
Scott B. Nokleby ◽  
Ron P. Podhorodeski

SUMMARYThis paper is organized in two parts. In Part I, the wrench polytope concept is presented and wrench performance indices are introduced for planar parallel manipulators (PPMs). In Part II, the concept of wrench capabilities is extended to redundant manipulators and the wrench workspace of different PPMs is analyzed. The end-effector of a PPM is subject to the interaction of forces and moments. Wrench capabilities represent the maximum forces and moments that can be applied or sustained by the manipulator. The wrench capabilities of PPMs are determined by a linear mapping of the actuator output capabilities from the joint space to the task space. The analysis is based upon properly adjusting the actuator outputs to their extreme capabilities. The linear mapping results in a wrench polytope. It is shown that for non-redundant PPMs, one actuator output capability constrains the maximum wrench that can be applied (or sustained) with a plane in the wrench space yielding a facet of the polytope. Herein, the determination of wrench performance indices is presented without the expensive task of generating polytopes. Six study cases are presented and performance indices are derived for each study case.


Author(s):  
C. Gosselin

Abstract This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-parallel manipulator.


Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.


Sign in / Sign up

Export Citation Format

Share Document