Keywords

1 Introduction—Challenges for Universal Handling

The automation of handling processes is one of the key features and challenges for modern production and assembly. In large-scale automation processes with many identical objects, handling tools are adapted or specified for individual components. As an example, this can be done by choosing a suitable vacuum gripper size for the accessible object surface or adapting gripper fingers of mechanical grippers to the object contours [1]. For industrial applications with shortening development cycles of new product variants and sometimes even overlapping transitions between product generations, solutions for a multifunctional, flexible handling or gripping of different components are required [2]. According to Hesse [3], three different types of flexibility for automated hand-ling processes can be defined:

  • Functional flexibility

    Integration of multiple handling operations, such as draping with handling

  • Disturbance flexibility

    Automatic correction functionality in case of malfunction or misorientation

  • Object flexibility

    Handling large spectrums of parts with the same gripper

Especially for smaller batches of varying or even individualized products, the necessary versatility and range of grippable objects can be achieved with universal grippers, which enable adaptable and flexible automation of these handling processes. In order to assess the suitability of a universal gripper for a spectrum of grippable objects, the respective effective gripping force and success frequency has to be examined in order to validate a grippers applicability [4]. The main focus of this publication is the development of such an assessment for a universal gripper created at the Technische Universität Braunschweig [5] and to enable an analytical model to predict the respective gripping forces for different types of object contours.

2 State of the Art

The current state of the art describes multiple solutions for flexible gripping of different kinds of objects. One possibility for universal gripping is the combination of multiple different grippers into one multi-effector system, which is able to choose a suitable gripper from a selection of pre-installed specialized grippers. This can lead to high weights as well as somewhat bulky effector setups, but allows effective handling of multiple pre-selected types of objects (Fig. 1a). Another possible solution are effector changing systems. The applications are similar to multi-effector systems, as the spectrum of objects also has to be exactly determined beforehand, as a suitable gripper has to be available for the required tasks (Fig. 1b).

Fig. 1
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Solutions for gripping different objects [6,7,8,9]

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Actually adaptable grippers (Fig. 1c) suitable for multiple shapes and object types can often be assigned to the field of soft robotics. Typical examples are usages of adaptable surfaces, such as FinRays [9,10,11], often in combination with other gripping principles such as mechanical and electrostatic mechanisms [12].

One of these soft robotic applications, that has been gaining traction in the past few years, are robotic grippers based on the jamming of granular materials [13, 14]. These grippers use airtight cushions filled with different granular materials. When a vacuum is applied to these cushions, the granular material compacts, jams and enables a gripping force to be exerted on different kinds of objects through friction and interlocking with the respective surfaces. For these grippers, influences such as the stiffness of cushion membrane material, the granulate material, the object enclosure and the conditions of the granulate material have been examined [15,16,17,18].

Previous Works

Based on a combination of the granulate grippers with a vacuum gripper, an innovative handling principle for form-flexible handling was developed at Technische Universität Braunschweig. The key difference to standard granulate grippers is a porous area in the gripping cushion, which allows an additional vacuum force to build up (Fig. 2).

Fig. 2
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Innovative vacuum-based granulate gripper a Example for this gripper [19], b Schematic and structure of the gripper

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Previous research has shown that this combination of gripping principles can achieve a high adaptability for gripping mechanisms and therefore a capability for handling large varieties of objects [20,21,22]. This previous research also examined influences of the airflow rate and vacuum on the state of the granulate material, with a certain solidity of the granulate being reached for the best vacuum seal and thus the highest vacuum. In this state the gripper combines the two gripping principles most effectively and the highest gripping forces are reached [5]. The key advantage compared to previous research on granulate grippers is the combination of the ability to grip flat objects [14] with the large increase in adaptability achieved with the granulate gripping principles.

3 Analytical Model Frameworks for Gripping Forces

The resulting gripping force is influenced by different factors, which are described in Fig. 3. The influences are divided into three categories, originating from the applied gripper, the grasped object as well as the influences of the gripping strategy.

Fig. 3
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Influencing factors for the achievable gripping strength with the examined vacuum-based granulate gripper [5, 22, 23]

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Under optimum conditions for all of these influencing factors, the porous area in the gripper cushion is fully sealed with the grasped object and a maximum vacuum gripping force can be applied. The theoretical maximum of this vacuum-based gripping force is calculated with the following formula:

$$F=\Delta p \cdot A$$
(1)

The gripping force F results from the applied vacuum Δp and the covered surface area A of the grasped object. For this research, the influences of the grasped objects are the main focus.

Experimental Setup

In alignment with preliminary experiments, a cylindrical gripper with a diameter of 150 mm and a height of 60 mm was chosen (see Fig. 2). The membrane consists of 1.25 mm Polyurethane, the porous area with a size of ~4500 mm2 extends to a maximum diameter of 95 mm and is arranged symmetrically around the center axis. As granulate material, ~ 4100 ABS (Acrylonitrile–Butadiene–Styrene) beads with a diameter of 6 mm were used, filling 66% of the maximum cushion volume. The gripper is mounted to a K6D40 force sensor with a maximum force in Z-direction of 500 N, a Kuka LBR iiwa 14 R820 and coupled with an adjustable vacuum pump Variair Unit SV 201/2. The maximum compressor power of 4 kW results in a maximum pressure difference of up to 0.42 bar. The pressure difference is measured by a VS VP8 SA M8-4 with a range of −1 to +8 bar mounted close to a valve between the vacuum pump and the gripper.

As the gripper shows similarities to approaches with standard vacuum grippers, a similar gripping and motion sequence is applied in this research and the measured forces and pressure differences are shown in Fig. 4. After positioning the gripper directly above the clamped test object, the gripper is moved perpendicularly to the object surface until a previously defined initial contact force is reached. No manual positioning or external influencing of the gripper is applied, even though this manual intervention has achieved a form fit for standard granulate grippers in the past [14]. With the gripper being positioned directly on the test object, a valve to the air compressor is opened and a vacuum is generated in the gripper. After a delay of 2.5 s, the maximum vacuum with the applied compressor power is reached and the gripper is pulled vertically upwards at a defined pull-off-speed. The maximum force at which the gripper detaches from the objects surface is used in the next chapters for the analysis of influencing parameters.

Fig. 4
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Experimental procedure for an initial contact force of 80 N and 50% compressor power

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Experimental analysis of influencing parameters

The main goal is to model the influences of different objects and geometries on the possible gripping forces using the specified gripper. For an optimal setup of objects, the influence of the object material, surface roughness and air permeability as well as the initial contact force has to be quantified. For this, the type of material as well as the surface roughness and the initial contact force was examined (see Fig. 5). Five different convex cylinders with a diameter of 242 mm made from realistic materials such as aluminum as a representation for milled parts, polyurethane and paper for parcels and packaging and PLA (polyactic acid) for synthetic components were used. Fifty experiments with a rising contact force between 20 and 280 N and a constant compressor power of 50% were carried out on the curved surface of the convex cylindrical surfaces.

Fig. 5
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Resulting maximum gripping forces for convex cylinders with a diameter of 242 mm with different surfaces, materials and initial contact forces. The mean and variance values in the marked area between 50 and 200 N are shown in the table

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Resulting from these experiments, initial contact forces between 50 and 200 N prove to be most applicable, as the maximum gripping force falls off for initial contact forces below 50 N and scatters broadly over 200 N. In this range for initial contact forces, the mean and variance values of the different objects are quite comparable with the highest deviation between the mean values being under 5%. As a result of these experiments, the objects used for the further research were manufactured additively with the settings achieving the surface quality of the “smooth PLA” (Fig. 5), as this enables a time-efficient and precise design for complex geometries.

As a secondary examination, the air permeability of the objects as well as the influence of the compressor power and resulting pressure difference is analyzed (Fig. 6). For this, air permeable rotationally symmetrically perforated flat surfaces with a gripping area of 60, 80 and 90% were prepared and compared to a 100% airtight surface, a constant initial contact force of 50 N was used. Due to air flow effects of different sized porous openings, not all air permeable surfaces will show the exact same resulting gripping forces. Therefore, these experiments serve as a reference for the assessment of the influence of air permeability.

Fig. 6
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Four steps of equally distributed relative coverage of the porous areas by flat surfaces. a Relative compressor power over pressure difference. b Maximum achievable gripping force over pressure difference

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As seen in Fig. 6, compressor power under 40% results in a low pressure difference for all test objects. For higher levels of compressor power, the air permeability of 60 and 80% fail to achieve a pressure difference of over 0.1 bar, the maximum gripping forces are below 25 N. As the experiments for over 90% are able to achieve a higher pressure of over 0.1 bar as well as a gripping force of over 50 N, this range of porosity is defined as a minimum requirement for the grippability of objects. For the highest achieved pressure differences, a comparably large spread for the datapoints is observed. This is presumed to be a result of a squeeze-out-effect pushing the granular material through the outer membrane, creating a structured surface with reduced contact to the surface.

After analyzing the influence of material and air permeability, a multitude of objects made from “smooth PLA” are used in order to examine the influences of different geometries. The surfaces of these example geometries are airtight, experiments resulting in gripping forces below 50 N are considered failures and can be classified as the gripper not being able to achieve a seal with the surface with an air permeability of over 90%. An exemplary extract for flat surfaces, convex edges and concave cylinders is shown in Fig. 7. Visible is a seemingly linear correlation of the maximum gripping forces with the pressure difference as well as a clear difference in the slopes for the different objects, resulting in different maximum gripping forces for high pressure differences.

Fig. 7
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Maximum gripping force over pressure difference for three example objects

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Empirically adapted analytical model

Using the linear dependence of resulting vacuum forces on the pressure difference shown in formula 1 as well as the surface of the porous area of the gripper cushion of Apor = 4500 mm2, a theoretical achievable maximum vacuum gripping force of 189 N at a maximum pressure difference Δpmax of 0.42 bar is calculated. However, experiments have shown a larger mean gripping force of 250 N for an airtight flat surface with this pressure difference. Influences from the granulate gripping principles are not applicable, as previous research has shown no effect on flat surfaces for purely granulate grippers. As another influencing factor, the pressure difference at the porous surface will most likely differ somewhat, as the vacuum sensor cannot be feasibly located there. However, the used vacuum pump is not able to create a pressure difference of over 0.42 bar and the sensor is able to measure this maximum value, so this difference in force is most likely not only a result of a deviation from the measured pressure difference. Therefore, this discrepancy between the theoretical and measured gripping forces is empirically approximated by a larger surface area being under the effect of the pressure difference than the actual porous area of the gripper (see Fig. 8).

Fig. 8
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Approximation for the empirical area. a Model for only Apor being in effect. b Model for effective area

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A theoretical effective surface area of ~6000 mm2 can be calculated with formula 1, which translates to an effective circular area with a diameter of 87 mm. The theoretical maximum gripping force Ftmax for a greatest possible affected area Atmax (~17,668 mm2) with the maximum diameter of the gripper of 150 mm and Δpmax is 742 N. For more complex objects and geometries, the gripping forces resulting from the granulate gripping principles such as friction have to be considered. However, specific forces resulting purely from the granulate gripping principle cannot be distinguished, as the vacuum gripping force cannot be avoided. Therefore, a combined correction parameter Ccombined for the influence of the object geometry on granulate as well as vacuum-based gripping forces is introduced in formula 2. This correction parameter is defined as a value between 0 and 1 (see formula 3).

$$F= C_{combined} \cdot \Delta p \cdot A_{tmax}$$
(2)
$$C_{combined}=\frac{S_{object}} {S_{max}}$$
(3)

Sobject is calculated as the slope of the linear approximation (Fi/Δpi, see Fig. 7) of the achievable gripping forces over the pressure difference. Smax is the theoretical maximum achievable slope calculated with Ftmax. As an example, this results in a Ccombined of 0.330 for the airtight flat surface previously examined.

In an ideal setup of an airtight flat surface, Ccombined represents a factor for the effective pressure difference as well as the effective area, since this setup is only affected by the vacuum gripping principles. For 3D-objects, Ccombined represents the influences of the granular as well as vacuum gripping principles. For more complex objects, some parts of the porous area will not be perpendicular to the gripping trajectory, which reduces the effective gripping area. However, no direct correlation between the perpendicular area and Ccombined is observed, as the minimum requirements for shapes are not identical for convex and concave surfaces. Therefore, formula 3 continues to use Atmax. An overview for the resulting values for Ccombined approximated over 30 experiments with a linear distribution of compressor power between 33 and 100%, an initial contact force of 80 N for different object shapes, which should enable a broad overview for most common geometries as well as specific requirements for a grippability is shown in Table 1. The requirements all result in a sealing of the gripper with the surface of over 90% (see Fig. 6) and thus a gripping force of over 50 N. The grippability of concave cylinders, spheres and cones is mostly influenced by the size of the objects opening for the base frame of gripper to fit, so this is not shown further. The correction parameters shown in Table 1 prove a variety of gripping strengths for different objects with a regression quality of over 0.9, which is evidence for a good approximation.

Table 1 Correction parameters for different objects with the respective regression quality
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Influence of Scale and Diameter

Remarkable is a somewhat low influence of the scale of the object. Starting at the specified minimum requirement shown in the last column, the correction parameter rises somewhat insignificantly until a sufficient similarity to a flat surface is reached (see Fig. 9). A cylinder diameter of 200 mm, more than double the initial value of 90 mm has a slightly higher slope and thus a slightly increased Ccombined. However, up to a diameter of 160 mm almost no difference is visible. A merged calculation of Ccombined for the five shown convex cylinders results in a value of 0.311 with an R2 of 0.907, which differs less than 5% from the calculated Ccombined for a diameter of 90 mm.

Fig. 9
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Gripping forces over pressure difference for different diameters of convex cylinders

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4 Conclusion and Outlook

The main goal of this research was to show a dependence of gripping forces on object geometries and to formulate an analytical model for calculating the maximum possible forces for these geometries. This is done to gain an understanding of the applicability of this flexible gripping solution. These goals were achieved and a linear approximation showed high regression quality for a spectrum of different objects. Minimum requirements for the usage of this model are the defined geometric characteristics, which result in a sealing of the gripper with the surface of the object of more than 90%. This enables further applications in combination with approximations of objects with similar shapes and geometric features. This could be done by comparing objects to previously tested data sets and interpolating Ccombined or through a utilization of machine learning with a 3D-camera. This would enable applications for a gripping force prediction for unknown objects on the basis of this research. Further expansion of the formula is possible for variations in the gripper configuration, previous research has shown some influences of parameters such as granulate size, material of the membrane etc., which will be examined in further research. Additionally, the current approach is limited to a basic vertical gripping strategy, other, more complex trajectories might result in a better sealing of the gripper cushion with the object surface and thus a higher possible gripping force.