Increase of Singularity-Free Zones in the Workspace of Parallel Manipulators Using Mechanisms of Variable Structure

TLDR: In this article, the authors focused on the study of singularity of planar parallel manipulators taking into account the force transmission, i.e., the singularity zones in the workspace of the manipulator are defined not only by kinematic criterions from the theoretical perfect model, but also by the quality of force transmission.

About: This article is published in Mechanism and Machine Theory.The article was published on 2008-09-01 and is currently open access. It has received 62 citations till now. The article focuses on the topics: Parallel manipulator & Singularity.

Figures

Fig. 3. Leg with variable structure: a) input link iiCA ; b) input link ii DA .

Table 2 Maximum values of the pressure angles ( 45 )

Fig. 9. Planar parallel manipulator 3-RRR with legs of variable structure.

Table 1 Maximum values of the pressure angles ( 0 )

Fig. 8. Torques of the actuators.

Fig. 7. Torques of the actuators.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Increase of singularity-free zones in the workspace of parallel manipulators using mechanisms of variable structure" ?

This paper is focused on the study of singularity of planar parallel manipulators taking into account the force transmission, i. e. study of singularity of planar manipulator by introducing the force transmission factor. The suggested procedure to determination of the optimal structure of the planar parallel manipulator 3-RPR is illustrated by two numerical simulations. 

Q2. What is the obvious solution to the problem of singularity?

One of the most evident solutions of this problem is the introduction in the initial system of complementary actuators, which make it possible to eliminate the singular configurations of the parallel manipulator by means of optimal control of the motion [2, 3]. 

Q3. What is the definition of a singularity in kinematics?

The physical interpretation of a singularity in kinematics refers to those configurations in which the number of degrees of freedom of the mechanical structure changes instantaneously, either the manipulator gains some additional, uncontrollable degrees of freedom or loses some degrees of freedom. 

Q4. How many zones are visible in the workspace of the modified manipulator?

The authors can see that the workspace of the modified manipulator is only composed of singularity-free zones and the whole workspace of the manipulator is reachable (increase until 100%). 

Q5. How is the quality of motion in the three degrees of freedom manipulators evaluated?

O. Alba-Gomez, P. Wenger and A. Pamanes [22] have evaluated the quality of motion in the three degrees of freedom manipulators by means of a kinetostatic indicator, which is similar to the pressure angle. 

Q6. What is the torques of the parallel manipulator?

The authors can note that the torques haveadmissible values along the trajectory but there is a discontinuity in the point 2P caused by the structural change of the parallel mechanism. 

Q7. What is the definition of the kinematic angle of the moving platform?

But from the point of view of force transmission invalid configuration can appear even when the determinant consisting of the Plücker coordinates of the wrenches acting on the moving platform from the kinematic chains is not equal to zero. 

Q8. How can the authors obtain the leg’s mechanisms with different structural parameters?

In this way the authors can obtain the leg’s mechanisms with different structural parameters and carry out the given trajectory taking into account the limit value of the pressure angle.