optimal grasp of vacuum grippers with multiple suction cups

Mechanism

Mechanism and Machine Theory 42 (2007) 18–33

www.elsevier.com/locate/mechmt

andMachine Theory

Optimal grasp of vacuum grippers with multiple suction cups

Giacomo Mantriota *

Dipartimento di Ingegneria dell’Ambiente e per lo Sviluppo Sostenibile, Politecnico di Bari, Viale del Turismo, 8; 74100 Taranto, Italy

Received 22 February 2005; received in revised form 16 February 2006; accepted 28 February 2006Available online 27 April 2006

Abstract

Vacuum grippers allow the grasping and movement of objects, often of large dimension, with remarkable simplicity anddelicacy.

In this work, a mathematical model is proposed for the grasp of vacuum grippers with multiple suction cups. The modelallows us to determine the minimum value of the vacuum force and the friction coefficient able to guarantee the graspingand movement of the object by means of a gripper with multiple suction cups without separating or skidding. A criterion isalso proposed to determine the best position of the vacuum gripper with the objective of minimizing the vacuum force.Finally, an example related to the motion of an irregular object is described.� 2006 Elsevier Ltd. All rights reserved.

1. Introduction

Vacuum grippers are largely diffused for moving objects of various natures (glass, marble, sacks, etc.).Single or multiple suction cups of different shapes and sizes are used for grasping objects. Used extensivelythroughout the packaging industry, vacuum suction can be found in most other fields of robotics as well[1–8]. In addition to the advantage of producing an attraction force, vacuum grippers permit a soft graspand are able to take hold of large and heavy objects.

Recent applications of vacuum suctions are related to wall surface mobile robots with vacuum gripper feet[9–13].

In Mangialardi et al. [14] and Mantriota [15], a criterion has been proposed which determines the mostfavorable grip points with a view to ensure grasp stability while minimizing the grasp forces or the frictioncoefficient required to balance any external force acting on the object.

Confronting the numerous applications of vacuum suctions, there have been very few studies regarding suc-tion cup models aimed at determining load capacities while the objects are in movement. The safety measureof suction cups is important for the payload capacity. There are two dangerous circumstances that couldoccur: one is the object slipping and the other is the object falling. A theoretical analysis of the loading

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G. Mantriota / Mechanism and Machine Theory 42 (2007) 18–33 19

capacity has been performed by Zhu et al. [16] to obtain conditions that prevent slipping and falling. Thesimple model is related to the multi-vacuum system used in a tracked climbing robot.

The model and the kineostatic analysis of the climbing robot were proposed by Bahr et al. [9].During the motion of an object, often a torsion torque is present on the suction cup in which the equilib-

rium is allowed by the adhesion force between the suction cup and object.The vacuum grippers with multiple suction cups have the advantage of being highly capable of balancing

torques. Such devices are used therefore, for the motion of objects of large dimensions.Today the limited use of vacuum grippers is due to the difficulty of being able to estimate their perfor-

mances well while the objects are in motion. The main complexity is caused by the simultaneous presenceof tangential forces and torsional torques, which can produce skidding.

Consequently, vacuum grippers are generally used for the motion of regular shaped objects (plates, paral-lelepipedons, etc.). Furthermore, since mathematical models for systems of multiple suction cups do not exist,for fear of the separating or skidding of the object, vacuum grippers are often under utilized.

In Mantriota [17] a mathematical model has been proposed for determining the normal and tangentialcontact pressures between a single suction cup and the object. The main purpose of the model is to determinethe minimum vacuum level to guarantee the grasp without detachment of the object and the minimum value ofthe adhesion coefficient in order to avoid the object from skidding.

In this work, a model is suggested to determine the minimum value of the vacuum force and the adhesioncoefficient able to guarantee the grasp and movement of the object by means of grippers with multiple suctioncups without detachment or skid effects.

Additionally, a criterion for determining the optimal position of the vacuum gripper is proposed with theobjective of minimizing the needed vacuum force to guarantee a grasp.

2. Minimum vacuum force for the grasp and motion

Two or more suction cups bound to a single rigid frame are utilized when moving large sized objects suchas plates of glass or marble. A solution such as this allows us to increase the system’s capability to balancebending and torsional torques created by the grasped object.

An example of a multiple suction cups apparatus is stated in Fig. 1.The model of a single suction cup has been examined in Mantriota [17].Particularly, the suction cup produces a force on the object due to the vacuum level created in the suction

cup and a contact pressure along the edge.The forces created by the suction cup on the object are referable to (Fig. 2):

Force due to the vacuum level generated inside the suction cup (FV).Pressure ‘‘p’’ along the edge of the suction cup in normal direction.Pressure along the edge of the suction cup in tangential direction because of friction.

In Mantriota [17] the normal and tangential distribution is considered for the contact pressures thatgenerate the three components of the force and the resultant torque.

In the case of multiple suction cups, the dimension of the suction cup is much smaller than the distancebetween the them, therefore, the resultant torques generated by the unequal normal and tangential contactpressures are negligible.

Consequently, in this paper, a simplified model of the multiple suction cups system is considered in whicheach suction cup is able to create only the three components of the resultant force, while the torques producedby an unequal distribution of the contact pressures are neglected.

Four suction cups connected together by a single rigid system are considered and shown in Fig. 3. Hypo-thesizing equal rigidity along axle ‘‘Z’’ for the four suction cups, the normal forces ðF N1; F N2; F N3; F N4Þgenerated by the suction cups must verify the following relationship:

F N1 þ F N3 ¼ F N2 þ F N4 ð1Þ
The tangential forces of adhesion lie in the contact plane with the object (Fig. 3).

hp

Highlight

Fig. 1. Vacuum grippers with multiple suction cups.

Fig. 2. Forces created by the suction cup on the object.

20 G. Mantriota / Mechanism and Machine Theory 42 (2007) 18–33

Neglecting the inertia forces, the equations of equilibrium become

F ðeÞZ þ 4F V �X4

i¼1

F Ni ¼ 0 ð2Þ

F ðeÞX þX4

i¼1

F Txi ¼ 0 ð3Þ

F ðeÞY þX4

i¼1

F Tyi¼ 0 ð4Þ

T ðeÞX � b F N4 � F N2ð Þ ¼ 0 ð5ÞT ðeÞY � a F N3 � F N1ð Þ ¼ 0 ð6ÞT ðeÞZ � F Tx4

� F Tx2ð Þb� F Ty3

� F Ty1

� �a ¼ 0 ð7Þ

Fig. 3. Forces created by the vacuum grippers with multiple suction cups.


Having pointed out with ‘‘a’’ and ‘‘b’’ the distance between the suction cups (Fig. 3) and with F ðeÞX ; FðeÞY ; F

ðeÞZ and

T ðeÞX ; T ðeÞY ; TðeÞZ , the components respectively of the external force and torque on the vacuum gripper respect to

(V,X,Y,Z).In this work, the hypothesis of the rigid body of the object to be moved and of the whole support device for

the suction cups is considered, while only the edge of the suction cups is considered yielding.The two limited conditions for the tangential forces occur when a tangential external force is applied on the

suction cup in ‘‘V’’ or when only a torsional torque is present ðT ðeÞz Þ.Hypothesizing a normal contact force that is equal for the four suction cups, when only a tangential force

(F(e)) is applied in the center of the suction cup in order to guarantee the stability of the grasped object, theadhesion forces will presumably be parallel to the direction of the F(e) (Fig. 4a).

(a) (b)

Fig. 4. Static-friction forces: (a) the external force F (e) is only a tangenzial force; (b) the external force is only torsional torque T (e).


When only a torsional torque ðT ðeÞz Þ is present on the suction cup, the suction cup has the tendency to rotatearound its center and the forces of static friction can be hypothesized perpendicular to the straight line thatconnects the point of contact with the center of the suction cup (Fig. 4b).

In a generic load condition of the vacuum gripper, the elementary displacements of relative motion of thesuction cup compared to the object are characterized as having a plane motion. If there were a skid effectbetween the suction cup and object, the direction of the tangential forces would be a function of the instan-taneous axis of rotation of the vacuum gripper’s compared to the object. Particularly, (Fig. 5) the directionwould be perpendicular to the straight line that connects the suction cup with the instantaneous axis of rota-tion (K). In case of adhesion, the existence of a point could be imagined around which there is a ‘‘rotationtendency’’ of the grasp device with a consequent direction of the tangential force similar to the case of skid-ding. This consideration becomes truer as it becomes closer to the conditions of incipient skidding.

(V,X,Y,Z) is considered a reference system with the origin of coordinates in the center of the vacuum grip-per (Fig. 3). Pointing out with K(xk,yk) the point around which the suction cup has the tendency to rotate,tangential forces are generated for the four suction cups and are reported in Fig. 5.

In absence of the skid effect, the components of the tangential force for every suction cup must verify thefollowing relationship:

F 2Txiþ F 2

Tyi6 f 2

sf F2Ni; i ¼ 1; . . . ; 4 ð8Þ

where fsf is the static-friction coefficient.Moreover, always using K to indicate the point around which there is the tendency of rotation, the com-

ponents of the tangential force will verify the followings relationships:

F Tyi

F Txi

¼ � ðxi � xKÞðyi � yKÞ

; i ¼ 1; . . . ; 4 ð9Þ

where xi,yi are the coordinates of the center of a generic suction cup.In case of incipient skidding of the suction cup (condition limit), the relationship (8) is verified with the

equal sign:

F 2Txiþ F 2

Tyi¼ f 2

sfF2Ni ð10Þ

It cannot be assumed that the relationship between the static-friction tangential force ðF TiÞ and the normalforce ðF NiÞ is the same for the four suction cups under conditions different from that of incipient skid.Nevertheless, such a hypothesis will be more accurate as the conditions of operation become close to the skideffect. The conditions of incipient skid are in fact those researched in this work, considering that the mainobjective is to determine the minimum value of the static-friction coefficient and of the vacuum force able

Fig. 5. Direction of the tangential forces.


to guarantee the absence of skid. In sofar in this work, the ratio ‘‘f’’ between tangential and normal compo-nent of the contact forces is considered the same for the four suction cups.

In this hypothesis, the model of the device with four suction cups consists of the following equations:


i¼1

F Ni ¼ 0 ð11Þ

F ðeÞX þX4

i¼1

F Txi ¼ 0 ð12Þ

F ðeÞY þX4

i¼1

F Tyi¼ 0 ð13Þ

T ðeÞX � b F N4 � F N2ð Þ ¼ 0 ð14ÞT ðeÞY � a F N3 � F N1ð Þ ¼ 0 ð15ÞT ðeÞZ � F Tx4


� F Ty1

� �a ¼ 0 ð16Þ

F N1 þ F N3 ¼ F N2 þ F N4 ð17ÞF Tyi

F Txi


; i ¼ 1; . . . ; 4 ð18Þ

F 2Txiþ F 2

Tyi¼ f 2F 2

Ni; i ¼ 1; . . . ; 4 ð19Þ

The system consists of 15 equations (Eqs. (11)–(19)) containing the followings 16 unknowns:

F Ni; F Txi ; F Tyi; i ¼ 1; . . . ; 4 ð20Þ

f ; F V; xk; yk ð21Þ

The equation system obviously permits infinite solutions. If the value of the vacuum force FV were known, theequation system could be solved and the value of each unknown could be found. Obviously if the parameter f

results bigger than fsf, it would produce skid whereas if one of the F Ni is negative, the grasp of the object wouldnot be guaranteed because of the suction cup detachment.

To the extent that the following constraints must be added to the previous equations:

F Ni P 0; i ¼ 1; . . . ; 4 ð22Þf 6 fST ð23Þ

If the value of the static-friction coefficient (fsf) is fixed, in order to determine the minimum value of the vac-uum level with the purpose of guaranteeing a stable grasp, it is enough to consider the FV (force produced bythe vacuum level in each suction cup) as an objective function to be minimized.

The minimum value of the vacuum force to guarantee the absence of detachment and skid is determinedresolving the following optimization problem with non-linear constraints:

Objective function: MinFV

subjected to the following constraints:


i¼1

F Ni ¼ 0 ð24Þ

F ðeÞX þX4

i¼1

F Txi ¼ 0 ð25Þ

F ðeÞY þX4

i¼1

F Tyi¼ 0 ð26Þ

T ðeÞX � b F N4 � F N2ð Þ ¼ 0 ð27Þ

Fig.


T ðeÞY � a F N3 � F N1ð Þ ¼ 0 ð28ÞT ðeÞZ � F Tx4


� F Ty1

� �a ¼ 0 ð29Þ


F Txi


; i ¼ 1; . . . ; 4 ð31Þ

F 2Txiþ F 2

Tyi¼ f 2F 2

Ni; i ¼ 1; . . . ; 4 ð32ÞF Ni P 0; i ¼ 1; . . . ; 4 ð33Þf 6 fST ð34Þ

The problem variables are

F Ni; F Txi ; F Tyi; i ¼ 1; . . . ; 4 ð35Þ


Obviously, the optimization problem can easily be modified for vacuum grippers constituted by more thanfour suction cups or with different positions of the suction cups.

3. Optimal position of the vacuum gripper with multiple suction cups

The positioning of the grasp device has fundamental importance in guaranteeing the stability of the grasp.In fact, the torques applied by the object on the suction cups depend on the position of the cups themselves.Considering the same performances of the vacuum gripper, depending on the grasp position, it is possible tohave skidding or detachment of the suction cups. It is therefore important to determine the optimal grasp posi-tion of the object.

The mathematical model of the multiple suction cups system could also be used for the evaluation of theoptimum position of the grasp device.

Considering a coordinate reference system (Fig. 6) related to the object (origin ‘‘O’’) and another onerelated to the vacuum gripper (origin ‘‘V’’) with parallel and concord axis, the external forces on the objectcan be reduced to the point ‘‘V’’ keeping in mind the position of the suction. Using xV and yV to specificallypoint out the position of the center of the suction cup, the external torques in comparison to ‘‘V’’ are

T ðV ÞZ ¼ T ðOÞZ þ F ðeÞX yV � F ðeÞY xV ð37ÞT ðV ÞX ¼ T ðOÞX � F ðeÞZ yV ð38ÞT ðV ÞY ¼ T ðOÞY þ F ðeÞZ xV ð39Þ

where T ðOÞX ; T ðOÞY ; T ðOÞZ are the torques in comparison to (O,X,Y,Z).

6. Coordinate reference systems related to the object (origin ‘‘O’’) and another one related to the vacuum gripper (origin ‘‘V’’).


The location of point V(xV,yV) on one surface of the object may be expressed by means of a convex com-bination of the vertices [14] composing that surface (assuming that the surface is represented by a convex poly-gon). In other words, with ‘‘n’’ indicating the number of vertices (xPi,yPi), of the surface, the coordinates ofpoint V(xV,yV) may be expressed by

xV ¼Xn

i¼1

kixPi ð40Þ

yV ¼Xn

i¼1

kiyPi ð41Þ

with

0 6 ki 6 1 ð42ÞXn

i¼1

ki ¼ 1 ð43Þ

Adding the term ki to the variables that specify the coordinates of the center of the suction cup, it is now pos-sible to determine the best possible position of the vacuum gripper with the objective of minimizing the vac-uum force. The optimization problem becomes




i¼1

F Ni ¼ 0 ð44Þ

F ðeÞX þX4

i¼1

F Txi ¼ 0 ð45Þ

F ðeÞY þX4

i¼1

F Tyi¼ 0 ð46Þ

T ðOÞX � F ðeÞZ yV � b F N4 � F N2ð Þ ¼ 0 ð47Þ

T ðOÞY þ F ðeÞZ xV � a F N3 � F N1ð Þ ¼ 0 ð48Þ

T ðOÞZ þ F ðeÞX yV � F ðeÞY xV � F Tx4� F Tx2

ð Þb� F Ty3� F Ty1

� �a ¼ 0 ð49Þ


F Txi


; i ¼ 1; . . . ; 4 ð51Þ

F 2Txiþ F 2

Tyi¼ f 2F 2


xV ¼Xn

i¼1

kixPi ð55Þ

yV ¼Xn

i¼1

kiyPi ð56Þ

0 6 ki 6 1; i ¼ 1; . . . ; n ð57ÞXn

i¼1

ki ¼ 1 ð58Þ


In this case the variables are

F Ni; F Txi ; F Tyi; ki ð59Þ

f ; F V; xk; yk; xV; yV ð60Þ
In which xV,yV are the coordinates of the vacuum gripper center in comparison to the coordinate referencesystem integrant to the object (O,X,Y,Z).
The solution of the problem allows us to carry out the optimal position (xV,yV) of the vacuum gripper incorrespondence with the minimum vacuum force value necessary to prevent the detachment and skid of theobject being grasped.

4. Example

In this example, the lifting and rotating of a homogeneous object (Mg = 500 N) of Fig. 7 through a vacuumgripper is assumed, made up of four suction cups, placed in correspondence with the origin of the reference(O,X,Y,Z) of the object. The center of gravity of the object has coordinated xG = 243 mm; yG = 0;zG = � 636 mm. Assuming that the object has a rotation of 90� (Fig. 8).

The objective is to determine the minimum value of the vacuum force needed to allow lifting and the sub-sequent 90� rotation of the object.

While the object is in motion, taking the reference system O,X,Y,Z into consideration, the object appliesthe following forces and torques on the suction cup:

F ðeÞX ¼ 0 ð61ÞF ðeÞY ¼ �Mg sin b ð62ÞF ðeÞZ ¼ �Mg cos b ð63ÞT ðeÞX ¼ �MgzG sin b ð64ÞT ðeÞY ¼ MgxG cos b ð65ÞT ðeÞZ ¼ �MgxG sin b ð66Þ

Fig. 7. Object and vacuum gripper.

Fig. 8. Motion of the object.


Changing the angle of rotation b, it is possible to determine the minimum value of the vacuum force throughthe following optimization problem:



�Mg cosðbÞ þ 4F V �X4

i¼1

F Ni ¼ 0 ð67Þ

X4

i¼1

F Txi ¼ 0 ð68Þ

�Mg sin bþX4

i¼1

F Tyi¼ 0 ð69Þ

�MgzG sin b� a F N4 � F N2ð Þ ¼ 0 ð70ÞMgxG cos b� a F N3 � F N1ð Þ ¼ 0 ð71Þ�MgxG sin b� a F Tx4

� F Tx2þ F Ty3

� F Ty1

� �¼ 0 ð72Þ


F Txi


; i ¼ 1; . . . ; 4 ð74Þ

F 2Txiþ F 2

Tyi¼ f 2F 2


The variables are

F Ni; F Txi ; F Tyi; i ¼ 1; . . . ; 4 ð78Þ


A commercial software, MATLAB, was run to solve the examples reported in this paper.


In Fig. 9 for three different values of the static-friction coefficient (0.25; 0.3; 0.4), the minimum value of thetotal vacuum force (4FV) in function of the angle b is reported. It is seen that up to around b = 20� the vacuumforce is independent from the static-friction coefficient, therefore for angles b included between 0 and 20� themost restrictive condition is that related to the detachment of the suction cups and not the skid. For values ofb included between 20� and 60� the minimum vacuum force is independent from the static friction coefficientfST if this last one is more than 0.3. In other words, the most critical condition is the skid if fST is less than 0.3.The maximum value results to be equal to 3270, 2735 and 2545 [N] respectively for fST = 0.25, 0.3, 0.4.

Considering a total vacuum force (4 * FV) equal to 2800 [N] and the angle b variation, the minimum valueof the static-friction coefficient (Fig. 10) and the normal contact forces was calculated (Fig. 11). We can seethat fST Min increases with the growth of the angle of rotation b. Particularly when b = 0, because torsionaltorques or tangential forces are not present, static-friction forces are not necessary (fST = 0). Whereas whenb = 90� the values of F ðeÞY and T ðeÞZ are the maximum and therefore also the requested value of fST is the max-imum to avoid skidding (0.296).

In Fig. 11 it is possible to note that the normal forces of the four suction cups are all positive, this meansthat the absence of detachment of the suction cups is guaranteed. Considering that the F4 is the smallest forceand is close to zero for b = 80�, suction cup number 4 is the one in condition of incipient detachment.

Finally, the most favorable position of the vacuum gripper was sought with the objective of reducing thenecessary vacuum force for the motion. The optimization was performed considering a more serious load con-dition (b = 90�).

The polygon inside which the center of the vacuum gripper can be positioned is a square with sides of0.30 m having the center in ‘‘O’’ (Fig. 7). Therefore, the optimization problem was solved (Eqs. (44)–(58))in which the coordinates xpi

; ypiare those of the square vertexes with sides of 0.3 m.

For fST = 0.25 and 0.3 the obtained result was xV = 0.15 m, while yV is indifferent for the optimization. Infact, for b = 90�, the maximum value of (0.15 m) reduces the torsional torque on the vacuum gripper, while thevalue of yV is indifferent because it does not influence any component of the external forces.

To evaluate the influence of yV, the optimum position was researched for values of b smaller of 90�. There-fore, an optimum for b = 80� with xV = 0.15 m and yV = 0.15 m was obtained.

Finally, the value of the minimum vacuum force was calculated considering the optimum positionxV = 0.15 m and yV = 0.15 m. In Fig. 12 the comparison between the minimum vacuum force for the optimumposition and the position in which the vacuum gripper is located in the center of the support surface (O = V) is

0

500

1000

1500

2000

2500

3000

3500

0 10 20 30 40 50 60 70 80 90

Fvm

in[N

]

fsf=0.25fsf=0.3

fsf=0.4

β[°]

Fig. 9. Minimum value of the vacuum force in function of the angle b.

0

200

400

600

800

1000

1200

1400

0 10 20 30 40 50 60 70 80 90

β[°]

F1

F2

F3

F4

F [N]

Fig. 11. Normal contact forces in function of the angle b.

0

0.05

0.1

0.15

0.2

0.25

0.3

β[°]

fMin

0 10 20 30 40 50 60 70 80 90

Fig. 10. Minimum value of the static-friction coefficient in function of the angle b.


reported. For fST = 0.25 (Fig. 12) a notable reduction (22%) of the vacuum force for high values of b can beseen, passing from a maximum value of 3270–2545 [N] (b = 90�). The reduction of the vacuum force is,instead, less notable when fST = 0.3 (Fig. 13), passing from 2735 to 2545 N.

For fST = 0.4 and b = 90� the position of the vacuum gripper is indifferent when the minimization of thevacuum force is considered. In fact, in this case the most serious stress is due to the torques (TX, TY), whichhas the tendency to produce the detachment of suction cup number 4. Always for fST = 0.4, with the decreaseof angle b the optimum position was researched, reaching the position xV = 0.15 m, yV = 0.15 m for b = 60�.

0

500

1000

1500

2000

2500

3000

β[°]

Fv m

in [N

]

with optimization (xV=0.15; yV=0.15)

fsf=0.3

without optimization

0 10 20 30 40 50 60 70 80 90 100

Fig. 13. Minimum vacuum force for the optimum position and the position in which the vacuum gripper is located in the center of thesupport surface (fsf = 0.3).

0

500

1000

1500

2000

2500

3000

3500

β[°]

Fv m

in [N

]


fsf=0.25

without optimization

0 10 20 30 40 50 60 70 80 90 100



In Fig. 14 the comparison of the vacuum force for the position xV = 0.15 m, yV = 0.15 m and that in which thevacuum gripper is centered on the surface, was reported. We can see that a consistent reduction of the vacuumforce occurs for low values of b, such advantage disappears when b = 90�.

From this example, the important role of the static-friction coefficient that influences the more unfavorablecondition (suction cup detachment or skid) and the optimal position of the vacuum gripper is demonstrated.

0

500

1000

1500

2000

2500

3000

β[°]

Fv m

in [N

]without optimization


fsf=0.4

0 10 20 30 40 50 60 70 80 90



A comparison was finally performed between two configurations of the vacuum gripper modifying the posi-tion of the suction cups (Fig. 15). Considering a vacuum total force (4 * FV) equal to 2800 [N] in Fig. 16 theminimum value of the static-friction coefficient is compared for the two configurations. It is possible to noticethat setting the suction cups on the edges of the square, the needed friction coefficient to avoid the skid isalways smaller in comparison to the other configuration. The maximum value reduces from 0.295 to 0.250.Considering instead an static-friction coefficient equal to 0.3, in Fig. 17 the minimum vacuum total force is

(a)

(b)

Fig. 15. Two configurations of the vacuum gripper.

0

0.05

0.1

0.15

0.2

0.25

0.3

β[°]

f

0 10 20 30 40 50 60 70 80 90

Fig. 16. Minimum value of the static-friction coefficient for the two configurations.

0

500

1000

1500

2000

2500

3000

Fv m

in [N

]

fsf=0.3

β[°]

0 10 20 30 40 50 60 70 80 90

Fig. 17. Minimum vacuum total force for the two configurations.


reported (4 * FV). Also in this case, the disposition of the suction cups to the vertexes of the square reduces themaximum value from 2735 to 2560 N.

5. Conclusions

The vacuums grippers with multiple suction cups have a great ability to balance torques and therefore areused for moving large objects.


In this paper a model was proposed to determine the minimum value of the vacuum force and the frictioncoefficient necessary to guarantee the grasp and movement of objects through grippers with multiple suctioncups without detachment or skid.

Furthermore, utilizing an optimization problem with non-linear constraints, a criterion for determining theoptimum position of the vacuum gripper with the objective of the minimization of the vacuum force necessaryfor grasping, was proposed.

An example of an object in motion was demonstrated using a vacuum gripper with four suction cups. Theminimum values of the friction coefficient and the vacuum force to guarantee motion and the advantages thatshould derive from an optimal positioning of the vacuum gripper were reported. Lastly, the performances oftwo different vacuum grippers with different placements of the suction cups were compared.

The model proposed in this research is easily applicable to vacuum grippers made up of a large number ofsuction cups or with different placements of suction cups.

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j.mechmachtheory.2006.03.003.

http://dx.doi.org/10.1016/j.mechmachtheory.2006.03.003

http://dx.doi.org/10.1016/j.mechmachtheory.2006.03.003

optimal grasp of vacuum grippers with multiple suction cups

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optimal grip points

tracked climbing robot

mantriota mechanism

multiple suction cups

total vacuum force

min fv subjected

n2 0e ty

single suction cup