Rotatability of the Floating Link on Multi-Loop Planar Linkages

2020 ◽  
Vol 12 (6) ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Rotation Angle ◽  
Parallel Manipulators ◽  
Orientation Error ◽  
Joint Rotation ◽  
Position Uncertainty ◽  
End Effector ◽  
Uncertainty Model ◽  
Branch Formation ◽  
Joint Clearances ◽  
Planar Linkages

Abstract This paper proposes a method to deal with the orientation uncertainty problem affected by joint clearances. To solve this problem, it is necessary to establish the theory of mobility of the floating link of multi-loop linkages. Since the theory of the mobility of floating link is yet complete, this paper provides a simple treatment to determine the rotatability between any two links, adjoined or not, in planar multi-loop linkages. The rotation angle of the floating link with respect to the reference link is defined so that there is no ambiguity in analyzing the rotation range of the floating link. Based on the joint rotation space (JRS) method, one may identify not only the branch formation but also the rotatability between any two links on each of the branches. It is a visualized method that reveals the rotation characteristic of multi-loop linkages. This paper demonstrates the rotation range of the floating link with respect to the reference link on six-bar Stephenson linkages, 2-degree-of-freedom (DOF). 7-bar linkages, and 3-DOF. Eight-bar parallel manipulators. This might be the first paper to deal with the rotatability of 3-DOF planar multi-loop linkages. This paper uses the method to predict the clearance-induced angle uncertainty of the 8-bar parallel manipulators, which determines the worst orientation error of the end-effector and fills up the void of the joint clearance uncertainty model proposed by Ting et al. (2017, “Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators,” J. Mech. Rob., 9, p. 061001).

Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators

2017 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu
Keyword(s):  
Kinematic Model ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Position Uncertainty ◽  
Joint Clearances ◽  
Planar Linkages ◽  
Oscillation Characteristics ◽  
Linkage Model ◽  
Input Error

The paper presents a simple and effective kinematic model and methodology, based on Ting’s N-bar rotatability laws [2629], to assess the extent of the position uncertainty caused by joint clearances for any linkage and manipulators connected with revolute or prismatic pairs. The model is derived and explained with geometric rigor based on Ting’s rotatability laws. The significant contribution includes (1) the clearance link model for P-joint that catches the translation and oscillation characteristics of the slider within the clearance and separates the geometric effect of clearance from the input error, (2) a simple uncertainty linkage model that features a deterministic instantaneous structure mounted on non-deterministic flexible legs, (3) the generality of the method, which is effective for multiloop linkages and parallel manipulators. The discussion is carried out through symmetrically constructed planar eight-bar parallel robots. It is found that the uncertainty region of a three-leg parallel robot is enclosed by a hexagon, while that of its serial counterpart is enclosed by a circle inscribed by the hexagon. A numerical example is also presented. The finding and proof, though only based on three-leg planar 8-bar parallel robots, may have a wider implication suggesting that based on kinematics, parallel robots tends to inherit more position uncertainty than their serial counterparts. The use of more loops in parallel robots cannot fully offset the adverse effect on position uncertainty caused by the use of more joints.

Application of Workspace Generation Techniques to Determine the Unconstrained Motion of Parallel Manipulators

2004 ◽  
Vol 126 (2) ◽  
pp. 283-290 ◽  
Author(s):  
Philip Voglewede ◽  
Imme Ebert-Uphoff
Keyword(s):  
Large Class ◽  
General Framework ◽  
Parallel Manipulators ◽  
End Effector ◽  
Singular Configurations ◽  
Joint Clearances ◽  
Generation Problem ◽  
Unconstrained Motion

Due to clearances in their passive joints, parallel manipulators always exhibit some unconstrained motion at the end effector. The amount of unconstrained motion depends on the pose of the manipulator and can increase significantly at or near singular configurations. This paper shows precisely how much unconstrained end effector motion exists at the end effector for a large class of parallel manipulators, namely those with passive revolute and/or spherical joints, if all the joint clearances are known. This includes the planar 3R_RR, and, in approximation the Gough-Stewart and the Hexa manipulators. For the analysis, the passive joints are assumed to be revolute or spherical because these are the simplest cases. However, the general framework also applies to other joint types, although leading to more complex calculations. For most manipulators, determining the amount of end effector motion can be transformed to a workspace generation problem. Therefore, general workspace generation techniques can be utilized.

Singularity and Sub-Branch Identification of Two-DOF Seven-Bar Parallel Manipulators

2009 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Changyu Xue ◽  
Kenneth R. Currie
Keyword(s):  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Simple Explanation ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Computer Aided ◽  
Center Position ◽  
Planar Linkages ◽  
General Method ◽  
Unified Method

Mobility analysis of multi-DOF multiloop planar linkages is much more complicated than the single-DOF planar linkages and has been little explored. This paper offers a unified method to treat the singularity (dead center position) and sub-branch identification of the planar two-DOF seven-bar linkages regardless of the choice of the inputs or fixed links. This method can be extended for the singularity analysis of other multi-DOF multiloop linkages. Based on the concept of joint rotation space and N-bar rotatability laws, this paper presents a general method for the sub-branch identification of the seven-bar linkages. It offers simple explanation and geometric insights for the formation of branch, singularity and sub-branch of the two-DOF seven-bar linkages. The presented algorithm for sub-branch identification is suitable for automated computer-aided mobility identification. Examples are employed to demonstrate the proposed method.

scholarly journals The Kinematic Sensitivity of Robotic Manipulators to Joint Clearances

2010 ◽  
Author(s):  
Nicolas Binaud ◽  
Philippe Cardou ◽  
Ste´phane Caro ◽  
Philippe Wenger
Keyword(s):  
Reference Point ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Error Prediction ◽  
Orientation Error ◽  
Moving Platform ◽  
Joint Clearances ◽  
Kinematic Sensitivity ◽  
Quadratically Constrained ◽  
Clearance Model

The paper deals with the kinematic sensitivity of robotic manipulators to joint clearances. First, an error prediction model applicable to both serial and parallel manipulators is developed. A clearance model associated with axisymmetrical joints, which are widely used in robotic manipulators, is also proposed. Then, two nonconvex quadratically constrained quadratic programs (QCQPs) are formulated in order to find the maximum reference-point position error and the maximum orientation error of the moving-platform for given joint clearances. Finally, the contributions of the paper are highlighted by means of two illustrative examples.

Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu ◽  
Jun Wang
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Target Position ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Joint Clearance ◽  
Position Uncertainty ◽  
Kinematic Effect ◽  
Joint Clearances

The paper presents a simple and effective kinematic model and methodology to assess and evaluate the extent of the position uncertainty caused by joint clearances for multiple-loop linkage and manipulators connected with revolute or prismatic pairs. The model is derived and explained with geometric rigor based on Ting's rotatability laws. The significant contributions include (1) the clearance link model for a P-joint that catches the translation and oscillation characteristics of the slider within the clearance and separates the geometric effect of clearances from the input error, (2) the generality of the method, which is effective for multiloop linkages and parallel manipulators, and (3) settling the dispute on the position uncertainty effect to parallel and serial robots due to joint clearance. The discussion is illustrated and carried out through symmetrically configured planar 8 bar parallel robots. It is found that at a target position, the uncertainty region of a three degrees-of-freedom (DOF) three-leg parallel robot is enclosed by a hexagon with curve edges, while that of its serial counterpart is enclosed by a circle included in the hexagon. A numerical example is presented. The finding and proof, though only based on three-leg planar 8 bar parallel robots, may have a wider implication suggesting that based on the kinematic effect of joint clearance, parallel robots tends to inherit more position uncertainty than their serial counterparts. The use of more loops in not only parallel robots but also single-DOF linkages cannot fully offset the adverse effect on position uncertainty caused by the use of more joints.

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.

A New Measurement Device for Kinematic Calibration of Parallel Manipulators

2004 ◽  
Author(s):  
Abdul Rauf ◽  
Sung-Gaun Kim ◽  
Jeha Ryu
Keyword(s):  
Parallel Manipulators ◽  
Measurement Procedure ◽  
Initial Guess ◽  
Measurement Noise ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
End Effector ◽  
Experimental Procedure ◽  
New Device ◽  
Rotation Component

Kinematic calibration is a process that estimates the actual values of geometric parameters to minimize the error in absolute positioning. Measuring all the components of Cartesian posture assure identification of all parameters. However, measuring all components, particularly the orientation, can be difficult and expensive. On the other hand, with partial pose measurements, experimental procedure is simpler. However, all parameters may not be identifiable. This paper proposes a new device that can be used to identify all kinematic parameters with partial pose measurements. Study is performed for a 6 DOF (degree-of-freedom) fully parallel Hexa Slide manipulator. The device, however, is general and can be used for other parallel manipulators. The proposed device consists of a link with U joints on both sides and is equipped with a rotary sensor and a biaxial inclinometer. When attached between the base and the mobile platform, the device restricts the end-effector’s motion to 5 DOF and measures two position components and one rotation component of the end-effector. Numerical analyses of the identification Jacobian reveal that all parameters are identifiable. Computer simulations show that the identification is robust for the errors in the initial guess and the measurement noise. Intrinsic inaccuracies of the device can significantly deteriorate the calibration results. A measurement procedure is proposed and cost functions are discussed to prevent propagation of the inaccuracies to the calibration results.

Research on Measurement Modeling of Spherical Joint Rotation Angle Based on RBF–ELM Network

2021 ◽  
pp. 1-1
Author(s):  
Liangqiong Xia ◽  
Penghao Hu ◽  
Kunlong Ma ◽  
Long Yang
Keyword(s):  
Rotation Angle ◽  
Spherical Joint ◽  
Joint Rotation

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.

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