**7. Manipulator for external conditions**

368 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

are parallel to the main central inertia axes of the platform. The proposed approach can be applicable for manipulators characterized by small displacements and high speeds. Moreover, this architecture causes partial kinematic decoupling because if the generalized coordinates corresponding to the opposite legs are equivalent then the moving platform

The parallel manipulators have singularity configurations in which there is an uncontrolled mobility because some of the wrenches acting on the output link are linearly dependent. The local criterion of singular configurations is the singular matrix of the screw coordinates of

has a perpendicular moment at about any points of the axis. All stalled actuators but one the

reciprocal to five-member group of the wrenches corresponding to stalled actuators. We can

acting on the output link of the such manipulators, determinant composed of the screw

The velocity of any point *Ai (i=1,…,6)* of the mobile platform can be found as a twist

<sup>0</sup> , 1,...,6 *A A i i V ri*

. arccos , 1,...,6 . *i i*

*i*

*A i*

*V F*

 

*V F*

*A i*

where *Fi* is the force vector on the actuator axis. For normal functions of the manipulator it is

, 1,...,6 *i KP*

The manipulator control system must be provided by algorithm testing the nearness to singular configurations based on the analysis of singular matrix (5) or on the pressure angle

manipulator has *DOF=1* and its output link can move along some twist = +

In general the six-member group of the unit wrenches of zero parameter *Ri(ri, ri*

 

*i*

 

*КР* is maximum pressure angle is defined by friction coefficient.

necessary that working space be limited by positions:

*\** is the preassigned minimal determinant value. The pressure angle of the linear

*\** (17)

0 (*2 = 0*)

(19)

(20)

*i* (21)

*o) (i=1,…,6)* is

*/2*, as a reciprocal twist to five-member group of screws

( , ) 0, 1,...,5 *mom R i <sup>i</sup>* (18)

*<sup>i</sup>* for the stalled actuator *i-th* of the parallel manipulators (Fig.1) can be

keeps constant orientation.

**6. Pressure angles** 

the wrenches, such as:

dependent sub-chain is equal to

moment relative to this point:

The pressure angle

determined as:

where 

determination.

where 

det(*E*) =

find this twist from the reciprocity condition:

coordinates of these wrenches as given in (5).

where *rAi* is radius-vectors of the points *Ai.*

In Fig. 4, (a, b) the six-DOFs parallel mechanisms and their sub-chain has a parallel connection of links and actuators are shown in (Glazunov, et al. 1999) which were invented by (Kraynev, & Glazunov, 1991). Such mechanisms may be utilized to manipulate the corrosive medium at all actuators that are located out of the working space. Existence of several sub-chains and many closed loops determine the essential complication of the mathematical description of these mechanisms. Screw calculus using screw groups is universal and effective for parallel mechanisms analysis. Here, *1* describes the fixed base, *2* describes the output link and *3* describes the actuators. Addition, *Ai* expresses the spherical joint center situated on the fixed base; *Bj* expresses the center of the spherical joints combined with translational; *Cj* expresses the output link spherical joint centers; *li, dj* expresses the generalized coordinates and *sj, fj* expresses the link lengths *(i=1,…,6; j=1,…, 3)*.

Fig. 4. The six-DOFs parallel mechanisms

In general, the wrench axis corresponding to *i-th* stalled actuator is located in the plane (*АiВjСj*), passes through center joint *Cj* and is directed perpendicular to its possible displacement. With the mechanisms as in (Fig. 3, a) the components of the wrench *Ri* can be find as:

$$r\_i = \frac{1}{p\_i \left\{ a\_i + \left[ \frac{s\_j}{f\_j} - \left( \frac{1}{f\_j} + \frac{1}{s\_j} \right) \frac{a\_i.b\_j}{d\_j} \right] b\_j \right\}}, \; r\_i^0 = \rho\_{\mathbb{C}\_j} \times r\_i \tag{22}$$

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where *pi* - vector defining the wrench axis, *ai* - vector from point *Ai* to point *Cj*, *bi* - vector from point *Dj* to point *Cj* and *Cj* - radius vector point *Cj*.

Besides, with the mechanism as in (Fig. 4, b) the wrench axis *(j=1, …,3)* coincides with actuator axis. The wrench of the *i-th* stalled actuator *(i=, …,3)* is given as

$$r\_i = \frac{1}{l\_i} \left| a\_i - \frac{\left(a\_i, b\_j\right) b\_j}{d\_j^2} \right|, \; ; \; r\_i^0 = \rho\_{C\_j} \times r\_i \tag{23}$$

The present approach may be applied for different types of mechanisms such as sub-chains with varied actuator connection using spherical pairs.

#### **8. Conclusion**

Thus in this paper various criteria of design and singularity analysis of parallel manipulators are presented. The constraint wrenches imposed to the platform by kinematic chains is proposed to rely on the screw theory by determinants of matrix consisting of the Plücker coordinates of the unit screws. Criteria for design and singularity analysis of parallel manipulators with linear actuators located on the base are presented. The kinematic criterion of singularity corresponds to linear dependence of wrenches supporting the mobile platform; the static criterion corresponds to the limitation of pressure angles. The dynamical decoupling allows increasing the accuracy, parametrical optimization allows designing the mechanisms with optimal working volume, dexterity and stiffness, determination of the twists inside singularity allows finding the differential conditions of singular loci. Furthermore, the use of screw groups in order to determination of the singular zones of the multi-DOFs parallel mechanisms that make form of continuous areas and manipulators for external conditions are expressed.

### **9. References**


displacement. With the mechanisms as in (Fig. 3, a) the components of the wrench *Ri* can be

. 1 1

where *pi* - vector defining the wrench axis, *ai* - vector from point *Ai* to point *Cj*, *bi* - vector

Besides, with the mechanism as in (Fig. 4, b) the wrench axis *(j=1, …,3)* coincides with

The present approach may be applied for different types of mechanisms such as sub-chains

Thus in this paper various criteria of design and singularity analysis of parallel manipulators are presented. The constraint wrenches imposed to the platform by kinematic chains is proposed to rely on the screw theory by determinants of matrix consisting of the Plücker coordinates of the unit screws. Criteria for design and singularity analysis of parallel manipulators with linear actuators located on the base are presented. The kinematic criterion of singularity corresponds to linear dependence of wrenches supporting the mobile platform; the static criterion corresponds to the limitation of pressure angles. The dynamical decoupling allows increasing the accuracy, parametrical optimization allows designing the mechanisms with optimal working volume, dexterity and stiffness, determination of the twists inside singularity allows finding the differential conditions of singular loci. Furthermore, the use of screw groups in order to determination of the singular zones of the multi-DOFs parallel mechanisms that make form of continuous areas and manipulators for

Angeles, J. (2004). The Qualitative Synthesis of Parallel Mechanisms, *In Journal of Mechanical* 

Arakelian, V.; Briot, S. & Glazunov, V. (2007). Improvement of functional performance of

Bonev, I.; Zlatanov, D. & Gosselin, C. (2003). Singularity analysis of 3-DOF planar parallel

spatial parallel mechanisms using mechanisms of variable structure, *In Proceedings of the 12th World Congress in Mechanism and Machine Science*, Besancon, France, 1:

mechanisms via screw theory, *In Transactions of the ASME, Journal of Mechanical* 

*j i j i i j j jj j*


 2 . <sup>1</sup> , *ij j*

*ab b*

*i j*

*l d* 

*s a b p a b f fs d* 

 <sup>1</sup> ,

; <sup>0</sup>

*<sup>j</sup> i Ci r r* 

; <sup>0</sup>

*<sup>j</sup> i Ci r r* 

(22)

(23)

find as:

*i*

actuator axis. The wrench of the *i-th* stalled actuator *(i=, …,3)* is given as

*i i*

*r a*

with varied actuator connection using spherical pairs.

*r*

from point *Dj* to point *Cj* and *Cj*

external conditions are expressed.

*Design*, 126: 617-624.

*Design*, 125: 573-581.

159-164.

**8. Conclusion** 

**9. References** 


**19** 

Özer Çiftçioğlu and Sevil Sariyildiz

*Delft University of Technology, Faculty of Architecture, Delft* 

*The Netherlands* 

**Data Sensor Fusion for Autonomous Robotics** 

Multi-sensory information is a generic concept since such information is of concern in all robotic systems where information processing is central. In such systems for the enhancement of the accurate action information redundant sensors are necessary where not only the number of the sensors but also the resolutional information of the sensors can vary due to information with different sampling time from the sensors. The sampling can be regular with a constant sampling rate as well as irregular. Different sensors can have different merits depending on their individual operating conditions and such diverse information can be a valuable gain for accurate as well as reliable autonomous robot manipulation via its dynamics and kinematics. The challenge in this case is the unification of the common information from various sensors in such a way that the resultant information presents enhanced information for desired action. One might note that, such information unification is a challenge in the sense that the common information is in general in different format and different size with different merits. The different qualities may involve different accuracy of sensors due to various random measurement errors. Autonomous robotics constitutes an important branch of robotics and the autonomous robotics research is widely reported in literature, e.g. (Oriolio, Ulivi et al. 1998; Beetz, Arbuckle et al. 2001; Wang and Liu 2004). In this branch of robotics continuous information from the environment is obtained by sensors and real-time processed. The accurate and reliable information driving the robot is essential for a safe navigation the trajectory of which is in general not prescribed in advance. The reliability of this information is to achieve by means of both physical and analytical redundancy of the sensors. The accuracy is obtained by coordinating the sensory information from the redundant sensors in a multisensor system. This coordination is carried out by combining information from different sensors for an ultimate measurement outcome and this is generally termed as sensor fusion. Since data is the basic elements of the information, sometimes to emphasize this point the fusion process is articulated with data as *data fusion* where the *sensor fusion* is thought to be as a

"Data fusion is the process by which data from a multitude of sensors is used to yield an optimal estimate of a specified state vector pertaining to the observed system."

"Data fusion deals with the synergistic combination of information made available by various knowledge sources such as sensors, in order to provide a better understanding

**1. Introduction** 

synonym. Some examples are as follows.

(Richardson and Marsh 1988)

of a given scene." (Abidi and Gonzales 1992)

