scholarly journals Trajectory Planning for Constrained Parallel Manipulators

2003 ◽  
Vol 125 (4) ◽  
pp. 709-716 ◽  
Author(s):  
Hai-Jun Su ◽  
Peter Dietmaier ◽  
J. Michael McCarthy
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Numerical Approach ◽  
Parallel Mechanisms ◽  
Dual Quaternion ◽  
End Effector ◽  
System Trajectory ◽  
Articulated Systems ◽  
Serial Chains

This paper presents an algorithm for generating trajectories for multi-degree of freedom spatial linkages, termed constrained parallel manipulators. These articulated systems are formed by supporting a workpiece, or end-effector, with a set of serial chains, each of which imposes a constraint on the end-effector. Our goal is to plan trajectories for systems that have workspaces ranging from two through five degrees-of-freedom. This is done by specifying a goal trajectory and finding the system trajectory that comes closest to it using a dual quaternion metric. We enumerate these parallel mechanisms and formulate a general numerical approach for their analysis and trajectory planning. Examples are provided to illustrate the results.

Wrench-Closure Workspace Generation for Cable Driven Parallel Manipulators Using a Hybrid Analytical-Numerical Approach

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Darwin Lau ◽  
Denny Oetomo ◽  
Saman K. Halgamuge
Keyword(s):  
Degrees Of Freedom ◽  
Hybrid Approach ◽  
Parallel Manipulators ◽  
Numerical Approach ◽  
Parallel Mechanisms ◽  
Task Space ◽  
Numerical Techniques ◽  
End Effector ◽  
Computational Costs ◽  
Univariate Polynomial

In this paper, a technique to generate the wrench-closure workspace for general case completely restrained cable driven parallel mechanisms is proposed. Existing methods can be classified as either numerically or analytically based approaches. Numerical techniques exhaustively sample the task space, which can be inaccurate due to discretisation and is computationally expensive. In comparison, analytical formulations have higher accuracy, but often provides only qualitative workspace information. The proposed hybrid approach combines the high accuracy of the analytical approach and the algorithmic versatility of the numerical approach. Additionally, this is achieved with significantly lower computational costs compared to numerical methods. It is shown that the wrench-closure workspace can be reduced to a set of univariate polynomial inequalities with respect to a single variable of the end-effector motion. In this form, the workspace can then be efficiently determined and quantitatively evaluated. The proposed technique is described for a 3 degrees of freedom (3-DOF) and a 6-DOF cable driven parallel manipulator. A detailed example in workspace determination using the proposed approach and comparison against the conventional numerical approach is presented.

A Statically Balanced Gough/Stewart-Type Platform: Conception, Design, and Simulation

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Marco Carricato ◽  
Clément Gosselin
Keyword(s):  
Sufficient Conditions ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Theoretical Point ◽  
Constant Force ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Neutral Equilibrium ◽  
The Difference ◽  
Elastic Elements

Gravity compensation of spatial parallel manipulators is a relatively recent topic of investigation. Perfect balancing has been accomplished, so far, only for parallel mechanisms in which the weight of the moving platform is sustained by legs comprising purely rotational joints. Indeed, balancing of parallel mechanisms with translational actuators, which are among the most common ones, has been traditionally thought possible only by resorting to additional legs containing no prismatic joints between the base and the end-effector. This paper presents the conceptual and mechanical designs of a balanced Gough/Stewart-type manipulator, in which the weight of the platform is entirely sustained by the legs comprising the extensible jacks. By the integrated action of both elastic elements and counterweights, each leg is statically balanced and it generates, at its tip, a constant force contributing to maintaining the end-effector in equilibrium in any admissible configuration. If no elastic elements are used, the resulting manipulator is balanced with respect to the shaking force too. The performance of a study prototype is simulated via a model in both static and dynamic conditions, in order to prove the feasibility of the proposed design. The effects of imperfect balancing, due to the difference between the payload inertial characteristics and the theoretical/nominal ones, are investigated. Under a theoretical point of view, formal and novel derivations are provided of the necessary and sufficient conditions allowing (i) a body arbitrarily rotating in space to rest in neutral equilibrium under the action of general constant-force generators, (ii) a body pivoting about a universal joint and acted upon by a number of zero-free-length springs to exhibit constant potential energy, and (iii) a leg of a Gough/Stewart-type manipulator to operate as a constant-force generator.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator

2003 ◽  
Vol 125 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Han Sung Kim ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Solution Methods ◽  
Moving Platform ◽  
At Will

This paper presents the design of spatial 3-RPS parallel manipulators from dimensional synthesis point of view. Since a spatial 3-RPS manipulator has only 3 degrees of freedom, its end effector cannot be positioned arbitrarily in space. It is shown that at most six positions and orientations of the moving platform can be prescribed at will and, given six prescribed positions, there are at most ten RPS chains that can be used to construct up to 120 manipulators. Further, solution methods for fewer than six prescribed positions are also described.

An algorithm for smooth trajectory planning optimization of isotropic translational parallel manipulators

2015 ◽  
Vol 230 (12) ◽  
pp. 1987-2002 ◽  
Author(s):  
Mahmood Reza Azizi ◽  
Rahmatolah Khani
Keyword(s):  
Trajectory Planning ◽  
Parallel Manipulators ◽  
Geometric Constraints ◽  
Nsga Ii ◽  
End Effector ◽  
B Splines ◽  
Planning Optimization ◽  
Need To Evaluate ◽  
Significant Performance ◽  
Fifth Order

This paper presents a new algorithm for smooth trajectory planning optimization of isotropic translational parallel manipulators (ITPM) that their Jacobian matrices are constant and diagonal over the whole robot workspace. The basic motivation of this work is to formulate the robot kinematic and geometric constraints in terms of optimization variables to reduce the mathematical complexity and running time of the resulting algorithm which are important issues in trajectory planning optimization. To achieve this aim, the end-effector trajectory of ITPMs in Cartesian space is defined using fifth-order B-Splines, and as a main contribution, all of the actuators limitations and robot constraints are formulated in terms of B-Spline parameters with no need of any information about the workspace geometry. Then the total required energy, total time of motion, and maximum absolute value of actuators’ jerk are defined as objective functions and non-dominated sorting genetic algorithm-II (NSGA-II) is used to solve the resulting nonlinear constrained multi-objective optimization problem. Finally, the proposed algorithm is implemented in MATLAB software for Cartesian parallel manipulator (CPM) as a case study, and the results are demonstrated and discussed. The obtained results show the significant performance of the proposed algorithm with no need to evaluate the robot’s constraints and boundaries of its workspace in each point of the end-effector trajectory.

Optimal Continuous Path Planning for Seven-Degrees-of-Freedom Robots

1986 ◽  
Vol 108 (3) ◽  
pp. 213-218 ◽  
Author(s):  
B. Benhabib ◽  
A. A. Goldenberg ◽  
R. G. Fenton
Keyword(s):  
Path Planning ◽  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Polynomial Interpolation ◽  
Continuous Path ◽  
End Effector ◽  
Joint Level ◽  
Redundant Robots ◽  
Planning And Control ◽  
Optimization Search

The paper addresses the problem of end effector trajectory planning and control of seven degrees of freedom (DOF) kinematically redundant robots. An off-line optimal continuous path planning method is developed for on-line control at joint level. The specified end effector path is approximated by a set of location nodes selected on the desired path. The motion control of the robot is provided by cubic polynomial interpolation at joint level. The proposed approach to trajectory planning of kinematically redundant robots consists of obtaining an optimal set of nodes which guarantees minimum deviation from the desired Cartesian path. The redundant DOF of the robot is used as a constrained variable in the optimization search. The method is illustrated in an example.

A class of reconfigurable parallel mechanisms with five-bar metamorphic linkage

2016 ◽  
Vol 231 (11) ◽  
pp. 2089-2099 ◽  
Author(s):  
Chunxu Tian ◽  
Yuefa Fang ◽  
Sheng Guo ◽  
Haibo Qu
Keyword(s):  
Potential Application ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Constraint Force ◽  
Motion Modes ◽  
Moving Platform ◽  
Five Phases ◽  
Serial Chains

This paper presents a planar five-bar metamorphic linkage which has five phases resulting from locking of motors. Reconfigurable limbs are constructed by integrating the five-bar metamorphic linage as sub-chains. The branch transition of metamorphic linkage is analyzed. By adding appropriate joints to the planer five-bar metamorphic linkage, reconfigurable limbs whose constraint can switch among no constraint, a constrained force and a constrained couple are obtained. Serial limb structures that can provide a constraint force and a constraint couple are synthesized based on screw theory. Reconfigurable limbs that have five configurations associated with the five phases of the five-bar metamorphic linkage are assembled with 4-DOF (degrees-of-freedom) serial chains. A class of reconfigurable parallel mechanisms is derived by connecting the moving platform to the base with three identical kinematic limbs. These parallel mechanisms can perform various output motion modes such as 3T, 3R, 2T1R, 1T2R, 3T1R, 2T2R, 1T3R, 2T3R, 3T2R and 3T3R. Finally, the potential application of the proposed mechanisms is analyzed and conclusions are drawn.

Dynamic Trajectory Planning for a Three Degrees-of-Freedom Cable-Driven Parallel Robot Using Quintic B-Splines

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Sen Qian ◽  
Kunlong Bao ◽  
Bin Zi ◽  
W. D. Zhu
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Planning Method ◽  
End Effector ◽  
B Spline ◽  
B Splines ◽  
Pick And Place ◽  
Two Factors ◽  
Three Degrees Of Freedom

Abstract This paper presents a new trajectory planning method based on the improved quintic B-splines curves for a three degrees-of-freedom (3-DOF) cable-driven parallel robot (CDPR). First, the conditions of positive cables’ tension are expressed in terms of the position and acceleration constraints of the end-effector. Then, an improved B-spline curve is introduced, which is employed for generating a pick-and-place path by interpolating a set of given via-points. Meanwhile, by expressing the position and acceleration of the end-effector in terms of the first and second derivatives of the improved B-spline, the cable tension constraints are described in the form of B-spline parameters. According to the properties of the defined pick-and-place path, the proposed motion profile is dominated by two factors: the time taken for the end-effector to pass through all the via-points and the ratio between the nodes of B-spline. The two factors are determined through multi-objective optimization based on the efficiency coefficient method. Finally, experimental results on a 3-DOF CDPR show that the improved B-spline exhibits overall superior behavior in terms of velocity, acceleration, and cables force compared with the traditional B-spline. The validity of the proposed trajectory planning method is proved through the experiments.

Structure Synthesis of Parallel Manipulators With Fully Decoupled Projective Motion and Any Degrees of Freedom

2020 ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Special Class ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
End Effector ◽  
Structure Synthesis ◽  
Decoupled Motion ◽  
Synthesis Procedure ◽  
Motion Constraint

Abstract This paper presents the structure synthesis of a special class of parallel manipulators with motion decoupleability. The manipulator is synthesized by grouping a motion constraint leg and a set of constraint-free legs. The desired motion, i.e., the output degrees of freedom (DOFs), of the end-effector is expressed by a projective angle representation. It was found that the fully decoupled design for parallel manipulators with any DOFs is achievable when the output motion is described by the projective angles. A synthesis procedure is proposed based on the reasoning of the screw systems and reciprocal screws of the decoupled motion. Several design examples of fully decoupled 2-, 3-, 4-, 5-, and 6-DOF parallel manipulators are provided.

DeltaBot: A New Cable-Based Ultra High Speed Robot

2003 ◽  
Author(s):  
Saeed Behzadipour ◽  
Robert Dekker ◽  
Amir Khajepour ◽  
Edmon Chan
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Manufacturing Industry ◽  
Design Procedure ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Manufacturing Cost ◽  
End Effector ◽  
Serial Manipulators

The growing needs for high speed positioning devices in the automated manufacturing industry have been challenged by robotic science for more than two decades. Parallel manipulators have been widely used for this purpose due to their advantage of lower moving inertia over the conventional serial manipulators. Cable actuated parallel robots were introduced in 1980’s to reduce the moving inertia even further. In this work, a new cable-based parallel robot is introduced. For this robot, the cables are used not only to actuate the end-effector but also to apply the necessary kinematic constraints to provide three pure translational degrees of freedom. In order to maintain tension in the cables, a passive air cylinder is used to push the end-effector against the stationary platform. In addition to low moving inertia, the new design benefits from simplicity and low manufacturing cost by eliminating joints from the robot’s mechanism. The design procedure and the results of experiments will be discussed in the following.

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