A Variable Stiffness Gripper with Reconfigurable Finger Joint for Versatile Manipulations

Abstract

A reconfigurable dexterous gripper is designed which can switch states, including rigidity and flexibility, for different application scenarios. Moreover, the stiffness of the fingers in the flexible state can also be tuned for different objects. Three fingers are connected to the revolute joints of the palm, and each finger has a reshape mechanism with a slider moving up and down to lock or release the fingertip joint. When the slider moves upward, the gripper works in the rigid state and the fingers are actuated by the servos. When the slider moves downward, the gripper works in the flexible state that the fingertip is supported by a spring, and the fingertip joint is rotated by an embedded motor with two group cables for tuning stiffness. This novel design provides the gripper with the advantages of high precision and strong load capacity of rigid grippers and shape adaptability and safety of soft grippers. The reconfigurable mechanism allows the gripper great versatility for grasping and manipulation, which facilitates the planning and execution of the motion of objects with different shapes and stiffness. We discuss the stiffness-tunable mechanism with different states, analyze the kinematic characteristics, and test the manipulator performance to investigate the application in rigid-flexible collaborative works. Experimental results show the practicability of this gripper under different requirements and the rationality of this proposed concept.

Introduction

With the increasingly wide application of robot operation technology and the complex task scenarios, the performance requirements of grippers in the field of robot operation are constantly increasing. The development of traditional rigid grippers is relatively mature, and these grippers perform well in some tasks with positioning precision and load capacity requirements.^1–4 However, the rigid grippers are relatively bulky, and the grasping process requires complex control to ensure the stability of the object grasping. Besides, it is easy to cause damage to the grasped objects when grasping objects with different stiffness.

In recent years, soft grippers have been developing rapidly,⁵ and the main structural forms include flexible materials,^6–8 pneumatic drives,^9,10 and hydraulic drives.^11,12 Soft grippers can safely grasp objects with different shapes and stiffness and have more degrees of freedom to adapt to complex operating environments. However, the inherent low stiffness of soft grippers causes them to deform and vibrate severely during tasks that require high loading. In addition, precision and response speed also limit their wide application. Therefore, it is crucial for grippers to enhance the performance and expand the application environments if they can combine the advantages of rigid grippers and soft grippers.

To further improve the performance of grippers, some variable stiffness grippers are designed based on the soft grippers. These hands have the advantages of rigid and soft models and can withstand greater loads.^13,14 The methods for grippers to achieve variable stiffness mainly include the following two types: smart materials and structures.^15–19 The smart materials usually used for variable stiffness mainly include low melting point materials,^20–23 shape memory alloys,^24–26 and magnetic or electric field-induced fluids.^27–29

Many smart material-based variable stiffness grippers are driven by temperature changes, which offer the advantages of a wide range of stiffness changes and ease of realization. The soft-rigid hybrid actuation (SRHA) gripper is based on a polylactic acid-based variable stiffness module,³⁰ the heating circuit is divided into three regions, and each region can be activated separately for varying flexible segments to amplify the dexterity. The stiffness of the SRHA gripper can be increased up to 18 times without sacrificing flexibility. Meanwhile, a water-cooling system is used to accelerate heat dissipation, reducing the cooling time to 39 s. However, it takes a long time to tune the stiffness of smart materials by adjusting the temperature, so changing the structure of the gripper can quickly tune the stiffness, which is also a feasible method for the variable stiffness gripper.

Amend et al. designed a positive pressure universal gripper consisting of a mass of granular material encased in an elastic membrane.³¹ Using a combination of positive and negative pressure, this gripper can quickly grip and release a variety of objects with different geometric shapes. However, this gripper generates a lot of vibration when disturbed by an external force, and the posture and motion accuracy of the object cannot be guaranteed during the process of grasping the object. The fingers of the RobInLab variable-stiffness (VS) gripper combine a jammed material core with an external structure, which is made of rigid and flexible materials. The stiffness of the finger is controlled by the pressure of the internal gas, and the motion is driven by cables. This allows the finger to gently adapt itself to the shape of objects when the capsule is not active and stiffen when suction is applied. But the drawback is obvious, that it cannot be fully transformed into a purely rigid finger.³²

Zhu et al. designed a hybrid finger, which is coupled in parallel by a rigid actuator based on an underactuated skeleton and a fiber-reinforced soft actuator. The rigid actuator's large load and the soft actuator's softness can be selectively fully highlighted, but in some tasks where rigidity is required, the rigid skeleton does not sufficiently enclose the soft actuator, such as the fingertip.³³ In summary, whether the method is based on smart material or structure, both can tune the stiffness of grippers to achieve some performance benefits. However, there are also some problems, such as unable to achieve precise control and unable to ensure stability after an impact force.

In this article, we propose a new method to change the state of the gripper between rigid and flexible and tune the stiffness by utilizing the reconfigurable finger joint, and we call this gripper the Rigid-Flexible Reconfigurable Hand (RFRH). The fingertip is supported by a spring, and the fingertip joint is rotated by two group cables for variable stiffness.^34–38 The cable driven motion has been used in many soft robots and can effectively control joints motion.^39–43 A slider wraps the joint; when the slider is moving upward, the gripper works in the rigid state to gain the advantages of rigid grippers. When the slider is moving downward, the gripper works in the flexible state to gain the advantages of soft grippers. There have been corresponding studies on the use of locking mechanisms in grippers,^44,45 but the current studies mainly implement finger stiffness tuning by gears and pawls to optimize the mechanical properties of flexible joints and do not implement switching between pure rigid and flexible states.

There have been previous studies on the application of slider structures to grippers,^46,47 but in these studies the slider is inside the finger and the entire finger is made of soft materials. These grippers do not have a rigid state and cannot achieve accurate grasping. Based on this design in this article, the gripper can work precisely and grasp heavy objects without deformation in the rigid state. In addition, the gripper can also tune the stiffness of joints according to the objects with different shapes and ensure safe manipulations when working in the flexible state.

The main contributions of this article are summarized as follows: (1) A novel gripper with the advantages of rigid and flexible states has been designed, which has a compact structure and can switch between different states stably by a slider. (2) The flexible joints of the fingers are cable-driven mechanisms that can change stiffness rapidly. Based on this, the relationship between the initial angles and the angular stiffness (As) has been analyzed and it is shown to be controllably linear in a certain range. (3) Experimentally, the grasping ability of the gripper is compared in the rigid and flexible states. In addition, the effect of different states and stiffness on grasp precision is statistically analyzed. (4) Finally, we attempt to apply the novel gripper in some tasks to achieve better synergistic effects with the rigid and flexible states and verify the feasibility of the designed gripper in practical operations.

Design of the Variable Stiffness Gripper

The RFRH gripper shown in Figure 1 is designed for changing between different states and variable stiffness by the repositioning of reconfigurable fingers. Three fingers based on the gripper palm are structurally independent entities. Besides, each finger actuation requires a servo and two mini DC motors with a reduction gearbox. The design of the gripper system is discussed below.

FIG. 1.

Concept illustration of the RFRH. (A) Mechanism of the reconfigurable finger in the rigid state. (B) Mechanism of the reconfigurable finger in the flexible state. (C) Cable connection mode in 3D diagram. (D) Compositions of the tendon-based mechanism, and the yellow arrow indicates that when the slider is in the maximum positive position, the finger works in the rigid state. (E) Cables linking method in the rigid state. (F) The yellow arrow indicates that when the slider is in the reverse maximum position, the finger works in the flexible state. (G) Cables linking method in the flexible state. (H) The rigid state of the RFRH. (I) The flexible state of the RFRH. 3D, three-dimensional; RFRH, Rigid-Flexible Reconfigurable Hand.

Reconfigurable finger

To ensure the versatile manipulation of the RFRH gripper, reconfigurable fingers with unique mechanisms are crucial, as shown in Figure 1A. To maintain structural stability and gripping continuity, a four-bar linkage is constructed on the underside of the finger, while the linkage is also fixed on the gripper palm. The servo installed behind the four-bar linkage rotates from 0° to 60° in vertical direction, which drives the reciprocating movement of the fingers and provides enough grasping force for the gripper. The intermediate position of the finger is the finger limb; it is hollowed out to install a mini DC motor (motor 1) to drive the small turntable to rotate. The turntable is fixed on the top of the motor shaft, and there are four fixing holes spaced symmetrically at 90°. Another mini DC motor (motor 2) is fixed on the back of the finger, and this motor's main function is to move the slider upward and downward through the leading screw, which is composed of the motor's shaft and slider's inside nut.

On the top of this finger is the fingertip, as shown in Figure 1D. Between the finger limb and the fingertip is a tendon-based mechanism, composed of one spring and four green cables, which can support the fingertip and provide flexibility when the finger works in the flexible state. Cables are connected to the small turntable, and flexible deformation of the finger joint can be actuated by the motor 1 through the four cables. The cables linking method is shown in Figure 1C; four cables are divided into two groups, the inside of the finger and the outside of the finger. While the small turntable rotates, one group of cables shrinks and the other group expands, which makes the fingertip joint rotate to tune stiffness in the flexible state, as shown in Figure 1G. The turntable only can rotate at a small angle from 0° to 45° for structural safety.

To allow deformation of the finger joint, the slider is packaging the joint, and the slider can be actuated by the bulge's nut and motor's shaft. Both mini DC motors rotate slowly with the function of the reduction gearboxes, which provide output forces to compress the spring and counteract the friction. In the meanwhile, the finger is safer and easier to control.

Integral design of the RFRH gripper

The RFRH gripper is constructed by three reconfigurable fingers, which are symmetrically distributed at 120°. A cylindrical palm is designed to support fingers. Most components of fingers are made by three-dimensional (3D) printing with resin material, whereas the small turntable is printed out of the nylon material for increased rigidity. This is advantageous as to the requirements for dimensional accuracy and structural strength. The top and the bottom of cylindrical gripper palm are made of carbon fiber reinforced plastic plates, which have good effect on strengthening the gripper's structure. We design the palm to be the right size for the three servos contained within it, with a control panel and a battery fixed on the back of the bottom. Each finger can move independently. When the fingers are fully grabbed, the height of the RFRH gripper is 190 mm, and when the fingers are fully released, the height of the RFRH gripper is 170 mm. Besides, the diameter of the palm is 130 mm.

Change process of rigid-flexible states

The RFRH gripper can switch work states between rigid and flexible by driving the slider upward and downward. The changing process of rigid-flexible states takes 28 s, as shown in the Supplementary Video S1. The transition time could be further reduced to even <5 s, if the motor is replaced by another one with a smaller reduction ratio gearbox. However, the fingers are made by 3D printing and have processing and assembly errors, resulting in large friction forces when the mini DC motors push the slider. Therefore, a motor with a smaller reduction ratio gearbox may increase the probability of the slider getting stuck. To maintain the balance between the transition speed and stability, we have finally chosen a 50 r/min motor with comparatively large torque and comparatively high speed.

When motor 2 pushes the slider to the maximum upward position, the limiting groove at the top of the slider combines with the protruding supporting ears on both sides of the fingertips, and the fingertip is fixed under the combined action of cables and fixed slider. At this time, the gripper works in the rigid state. As the motor 2 pushes the slider to the maximum downward position, the limiting groove at the top of the slider is separated from the protruding supporting ears of the fingertips. At this time, the fingertip joint is flexible in all directions and can be rotated inward by motor 2 to tune its stiffness. Furthermore, the gripper now works in the rigid state. This design combines the advantages of rigid gripper and soft gripper and increases the application scenarios of the gripper with low cost mechanism improvement. To reflect the unique features of the RFRH gripper, we also design a simple fully articulated gripper for comparison, which will be discussed later.

Grasping configurations

Using the state switch mechanism and servos driving sequence, we can define some grasp configurations of the RFRH gripper for a variety of objects, as shown in Figure 2. In its default configuration, fingers are actuated by the servos with no fingertip joint rotation and only the fingertips contact with objects (Fig. 2A). This configuration, called the rigid grasp, can only be used in the rigid work state, and it is ideal for precise manipulations. When the RFRH gripper works in the flexible state, fingertip joints can rotate with motor 1 to tune stiffness (Fig. 2B), called the flexible grasp, and also only the fingertips contact with objects. This configuration is suitable for some soft objects with quick grasp and quick release. Based on the flexible grasp, when the objects contact with both fingertips and limbs, the grasp can be more stable, and we call this configuration the flexible packing grasp (Fig. 2C).

FIG. 2.

Three grasping configurations. (A) Rigid grasp. (B) Flexible grasp. (C) Flexible packing grasp.

Kinematic Characteristics

Forward kinematic modeling of the finger

The research of this part can be divided into the rigid and flexible states. When the finger is in the rigid state, joints can only rotate in a plane. A coordinate system is established, and the schematic of structure is shown in Figure 3A, where α₁ is defined as the rotation of the continuous joint around point B. Since the finger is in the rigid state, the slider makes the links BC and CD as collinear, which always keep perpendicular to the positive X-axis under the function of the four-bar linkage mechanism. The entire model is fixed to the ground through the base A, and link AB maintains an initial angle of 30° with the positive X axis. Rigid finger system has only one input, which makes the mechanism swing around point A. Take point A as the origin of the coordinates; the coordinates of point B and point C can be expressed as:

FIG. 3.

The coordinate system for the kinematic solution of the finger. (A) The coordinate system for the rigid state. The link AB rotates around point A, while the links BC and CD are collinear and vertical to horizontal. (B) The coordinate system for Flexible state. The link AB rotates around point A, the link CD rotates around point C, and the link BC keeps vertical to horizontal.

^{R} B = [\begin{matrix} X_{B} \\ Z_{B} \end{matrix}] = [\begin{matrix} a cos (α_{1} + 3 0^{\circ}) \\ a sin (α_{1} + 3 0^{\circ}) \end{matrix}]

(1)

The output position of D can be calculated out easily by the geometric relationship as: $^{R} D = [\begin{matrix} X_{D} \\ Z_{D} \end{matrix}] = [\begin{matrix} a cos (α_{1} + 3 0^{\circ}) \\ a sin (α_{1} + 3 0^{\circ}) + b + c \end{matrix}]$ (2)

where a denotes the length of link AB, b denotes the length of link BC, c denotes the length of link CD.

The method of studying the forward kinematics of the flexible state is similar to that of the rigid state. In the flexible state, the slider is actuated to the open position, which removes constraints between fingertip and middle limb. Due to the function of the four-bar linkage, the rod BC always remains vertical, as shown in Figure 3B. The input of flexible state study differs from rigid study in that it has two rotary actuators, and more actuators enable the finger to have more degrees of freedom and operational capabilities. Creating similar axes as the rigid state, the coordinate of point B can be expressed as: $^{F} B = [\begin{matrix} X_{B} \\ Z_{B} \end{matrix}] = [\begin{matrix} a cos (α_{1} + 3 0^{\circ}) \\ a sin (α_{1} + 3 0^{\circ}) \end{matrix}]$ (3)

Then, the coordinates of point C and output position of D can be given by the relationship of each joint angle: $^{F} C = [\begin{matrix} X_{C} \\ Z_{C} \end{matrix}] = [\begin{matrix} a cos (α_{1} + 3 0^{\circ}) \\ a sin (α_{1} + 3 0^{\circ}) + b \end{matrix}]$ (4) $^{F} D = [\begin{matrix} X_{D} \\ Z_{D} \end{matrix}] = [\begin{matrix} a cos (α_{1} + 3 0^{\circ}) - c sin α_{3} \\ a sin (α_{1} + 3 0^{\circ}) + b + c cos α_{3} \end{matrix}]$ (5)

Gripper workspace

Setting the extreme rotation angle of each joint of the finger, the workspace of the finger and gripper can be solved using the Monte Carlo and geometric methods. Within the range of motion of each joint, the value of each joint angle was randomly taken 6000 times. All joints are combined to draw the corresponding fingertip position points in a 3D coordinate system, and the area composed of all points is approximately the gripper's workspace. The workspace of the grasped object is the union of the centers of the coordinates of the three fingertips.

The results are shown in Figure 4, where the dots of different colors represent the fingers' end locations for various joint configurations solved using the geometric method and the Monte Carlo method. We considered not only the active joints but also the passive joints which are caused by springs in the flexible state. With the function of passive joints, the grabbed object could be actuated by the synergic movements of the gripper's three fingers, which permit a larger workspace than active joints' actuation alone. Comparing the results of workspace in different states, the gripper reaches more places and adapts better to the shape and size of objects in the flexible state.

FIG. 4.

Workspace of finger and gripper. (A) Workspace of a single finger in the rigid state. (B) Workspace of a single finger in the flexible state. (C) Workspace of grasped objects in the rigid state. (D) Workspace of grasped objects in the flexible state.

Performance Evaluation

Force and stiffness experiment

When the finger is grasping the object, it contacts the object through the inner side of the fingertip, and the direction of force is perpendicular to the axial of the fingertip. Therefore, when the gripper works in the flexible state, the grasping force is related to the stiffness of the flexible joint. For the convenience of analysis, we use the initial angle to represent the stiffness. Figure 5A shows the process of changing the initial angle of the fingertip from rigid to flexible. The initial angle is controlled by the cable, and the larger the initial angle is, the greater the spring deformation and stress within the flexible joint are. When subjected to the same external force, the spring with greater stress is less deformed, and therefore, the stiffness of the flexible joint is greater. So, the larger the initial joint angle is, the greater the stiffness is, and the smaller the angle changes when external forces are applied.

FIG. 5.

Force and stiffness experiment. (A) Change process of the rigid-flexible state. (B) Test system of force and stiffness experiment, and different colors represent different initial angles. (C) Relationship between force and angle variation. (D) Relationship between initial angle and angular stiffness.

In this experiment, we fixed the reconfigurable fingers horizontally on the bench clamp, gave the flexible joints different initial angles at the beginning of each experiment, and gradually added weights to the top of the fingertips to change the joint angle (Fig. 5B). Since the assembly error and open-loop control made the initial angle unable to be accurately controlled, many experiments were carried out to make the initial angle numerical distribution as uniform as possible to facilitate statistical analysis.

Figure 5C shows the relationship between force and angle variation, where different colors of lines represent different initial angles. Angle changes as the force increases until the joint angle reaches its maximum value. The result shows that the larger the initial angle, the lower the slope of the line and the greater the stiffness. That means, the larger the initial angle is in this experiment, the more weights can be mounted on the fingertips and the greater the ultimate force that can be carried. Calculated stiffness value As (Angular stiffness) corresponding to each initial angle is shown in the upper left panel of Figure 5C. Compared to smart materials that use heating or aerating to change stiffness,^31,32 the flexible joints in this article, consisting of cables and springs, have a faster rate of stiffness change and higher accuracy. In addition, some other structural improvement methods, such as adding sensors in the muscle tendon driven mechanism and using motors to actively adjust finger stiffness,^13,19 are more complex than the structure in this article and often need to install a large volume drive system outside the finger, which is also more difficult to control.

To improve the grasping accuracy of the gripper in the flexible state, we propose to calibrate the stiffness of all three fingers of the gripper before testing and record the stiffness of each finger with different initial angles. Figure 5D further analyzes the experimental results, which show the relationship between the value of F/angle and the angles and defines F/Angle as the angular stiffness. When the initial angle is <10°, the fingertip joint works in a fluctuating state, which may be caused by the influence of the assembly gap on the small angle. When the initial angle is 10°–20°, it is a linear relationship with the scaling factor of 5.3. When the initial angle is >20°, the rising speed of the line slope becomes faster and the stiffness growth rate becomes larger. The reason is that the spring is deformed in the axial direction and changes the radial linear characteristics. Therefore, we think the optimal range of the initial angle of the fingertip joint is 10°–20°.

Grasping capability

To research the grasping capability, the RFRH gripper was fixed at the end of the AUBO-i5 robot to grasp the different objects of different weights and shapes, and these objects would be raised by 20 cm (Supplementary Video S2). We choose different grasping configurations mentioned above to grasp these objects, the rigid grasp, the flexible grasp, and the flexible packing grasp. All experiments are open-loop control.

First, we compare the performance of rigid grasp and flexible grasp, as shown in Figure 6A–G. Testing these two different grasping configurations to grasp plastic balls and tapes, respectively, the result shows that both rigid grasp and flexible grasp can grasp some objects with regular shapes and lighter weight.

FIG. 6.

Demonstration of grasping various objects. (A) Grasping and picking up the light plastic balls by rigid grasp. (B) Grasping and picking up the scotch tape with smooth surface by rigid grasp. (C) Picking up a jar of grease and rotating 90° by rigid grasp. (D) Grasping and picking up the light plastic balls by flexible grasp. (E) Grasping and picking up the scotch tape with smooth surface by flexible grasp. (F) Gripper can pick up a jar of grease by flexible grasp, but the jar will fall off during rotating process. (G) The crisp was crushed by rigid grasp. (H) Gripper can pick up a crisp without crushing by flexible grasp. (I) Flexible grasp successfully grasps a chip, while the fingers move the same distance as in the rigid state. (J) Grasping and picking up the square battery by flexible grasp. (K, L) Grasping and picking up irregular objects such as the scissor and mouse by flexible grasp. (M) Grab some heavier spherical objects by flexible grasp.

However, when grasping some heavy objects like a jar of grease (Fig. 6C, F), although the jar can be picked up by both grabbing configurations, when the jar swings 90° around the arm, it will slide down due to the deformation of the fingertip joint caused by its own gravity under the flexible grasp. This shows that rigid grasp can stably grasp some heavy objects, and the objects' posture can be transformed after grasping.

Figure 6G shows the RFRH gripper grasping a crisp, but the crisp is crushed due to the inability to accurately control the servo rotation angle under open-loop control. However, the crisp can be easily grasped and picked up by flexible grasp through flexible fingertip joints with certain stiffness, as shown in Figure 6H. In Figure 6H, the motion distance of the fingers is smaller compared with the rigid state. To make the experiments more comparable, we also performed another flexible grasping experiment with the same fingers' movement distance as the rigid, and the result shows that the chip can also be successfully grasped, as shown in Figure 6I. These experiments were performed 10 times for 2 types of flexible grasping with different finger movements. The number of successful grasping in Figure 6H is 10 times, while in Figure 6I is 8 times. Therefore, we recommend the flexible grasping in Figure 6H. Comparing the results of these experiments, flexible grasp is safer than rigid grasp and more suitable for some fragile items.

The square battery is not easy to grasp in the rigid state because the three fingers are distributed in an equilateral triangle, but the battery can be picked up by the flexible grasp, as shown in Figure 6J. The scissor and the mouse, which are irregular shapes, can also be grasped by the RFRH gripper through the flexible grasp (Fig. 6K, L). The mouse wrapped around the wire is a challenge for grasping, but the RFRH gripper still completed the grasping action very well with the flexible state. These three experiments reveal that the flexible grasp also has an advantage in grasping irregularly shaped objects.

We also tested the flexible packing grasp capability with a billiard ball (Fig. 6M). The billiard ball has a smooth surface and heavy weight, so it is not easy work for the rigid grasp and flexible grasp. The process of flexible packing grasp is divided into two steps. First, wrap the billiard ball by finger movement and then lift the object. Flexible packing grasp can grab some objects with a certain weight and smooth surface, but is only suitable for some objects where the fingertips can insert into the bottom.

To demonstrate the reproducibility of the experiments and the stability of the gripper, each of the above experiments was repeated 10 times under the same conditions, and the number of successful experiments was recorded for further comparison and analysis, as shown in Table 1. The success rate of the gripper in grasping objects is very high, but the rigid state is not capable of grasping some fragile objects, such as chips. In addition, when the gripper works in the flexible state to grasp some heavy object for movement, such as the jar of grease, the object is prone to slip, and all the processes of failure occurred during the rotation of the manipulator after a successful grasp. A summary of the above experiments is made that the rigid grasp is better at grasping objects with large weight and with regular shapes. In the flexible state, the fingertip joint has a higher degree of freedom and less influence on the surface deformation of the objects, which make the flexible grasp suitable for grasping objects with small weight and irregular shapes. Besides, using the flexible packing grasp, the heavy objects can also be grasped with flexible state.

Table 1.

Number of Successful Experiments in Each Group

	RFRH: rigid grasp	RFRH: flexible grasp	RFRH: flexible packing grasp	PRH: packing grasp
Light plastic balls	10	10	—	10
Scotch tape	10	10	—	10
A jar of grease	10	0	—	9
Crisp	2	10	—	3
Square battery	—	10	—	—
Scissor	—	10	—	—
Mouse	—	10	—	—
Billiard ball	—	—	10	10

PRH, Purely Rigid Hand; RFRH, Rigid-Flexible Reconfigurable Hand.

In addition, the grasp poses of the gripper, the weight, and shape of the object do have a significant impact on grasping performance. In this article, we mainly focus on the qualitative researches, but do not pay attention to the quantitative analysis, to investigate the difference in grasping capability of the gripper in the rigid and flexible states. In future, we will study this question quantitatively, in particular, the influence of the grasp angle of the gripper, the weight, and the shape of the object on the grasp ability.

Grasping precision experiment

Operating precision of the gripper is another important characteristic. To study the operation precision in different states, we designed the experiment as shown in Figure 7A and Supplementary Video S3. Considering that the gripper is always used together with the arm, we analyze the system composed of the two when researching the precision. Because the grasping error of the gripper is small and difficult to observe, we enlarge the error proportionally by reflecting laser through a mirror. In addition, the experiment only carries out the grasping in the vertical direction, because the flexible state is affected by the gravity of the grasped objects during the horizontal grasping, and the error is obviously larger compared with the rigid state.

FIG. 7.

Grasping precision experiment of the RFRH combined with a manipulator. (A) Experimental schematic diagram to test the grasping precision. (B) Looking for the zero-error position according to the principle of optical path reversibility. (C) The positions of the spots under the repeated experiments of rigid state, initial angle of 15°, 19°, and 26°. (D) Statistical analysis of experimental results shows significant difference between the rigid state and the flexible states.

Before each experiment, we place the laser pointer vertically at the origin position through the locating block to minimize the effect of experimental errors on grasping accuracy. One locating block is fixed on the table to place the laser pointer, and the other is L-shaped to determine that the sides of the cylindrical laser pointer and the previous locating block are tangent. The RFRH gripper is fixed at the end of the AUBO-i5 robot to grasp the laser point, which is held vertical by gravity and gripper, and moves the laser pointer above the mirror. The angle between the mirror and the table is 45°, which is used to reflect the laser toward the vertical plane at d3, and we mark the laser points in the d3 plane. The plane at d3 is a transparent plexiglass. D1 is the plane where the three fingers touch the objects, and this is the plane where we are talking about grasp precision. Take the connection between the gripper and the center of the Aubo-i5 end as the reference points, measure the value of d1, d2, and d3, and the grasping precision error of d1 can be calculated by equal proportional calculation: $e_{1} = \frac{e_{3} \cdot d_{1}}{d_{1} + d_{2} + d_{3}}$ (6)

While errors are inevitable, they can be mitigated by equal proportional calculations and repeated experiments. Repeat the experiment 20 times in the rigid state and the flexible state with initial angle of 15°, 19°, and 26°. The results are shown in Figure 7C, and the statistical analysis of the results is shown in Figure 7D. The degrees at d1 are the same as d3, and the error distances at d1 are proportional to d3. Figure 7C shows the grasping precision error in d1 plane after equal proportional calculations, where the degrees truly reflect the orientation of the error points and the distances show the magnitude of the grasping error of the gripper.

The accuracy of the Aubo-i5 robot is much higher than the RFRH, so the laser irradiated from the center of the Aubo-i5 end has been set as the reference position of zero at d3. However, the laser pointer could not be directly mounted on the end of the Aubo-i5. To determine the zero-error position on the coordinate, we make the top of the laser pointer coincide with the plexiglass surface at d3, so that the laser pointer is perpendicular to the d3 plane and irradiates the laser from d3 through the plexiglass toward the mirror. According to the principle of optical path reversibility, the position of the laser pointer at d3 is the zero-error position when the laser point irradiates from the outside of the plexiglass to the mirror and finally reflected at the center of Aubo-i5 robot end, as shown in Figure 7B.

The separate points drawn from the experimental results are distributed around the center of the coordinate origin. The closer the separate points are to the origin, the more uniform the distribution of separate points is and the higher the grasp precision is. Since the manipulator has its own motion precision control algorithm, the points plotted in the experiment show circular distributions with the same initial angle conditions. This does not affect the grasping precision of the gripper in our study, as the motion precision of the manipulator is the same in each experiment, and the motion precision control algorithm does not affect the comparative analysis of the experimental results. In addition, the gripper in practical applications should also work with the manipulator.

Figure 7C shows that the blue points are the experimental results of the rigid state, and the points show a uniform distribution around the origin of the coordinate. The purple points are the experimental results with the initial angle of 15°, and these points deviate from the origin of the coordinate and spread over a larger area. The same dispersion results appear in the experimental conditions with initial angles of 19° and 26°, and the green and yellow points further deviate from the origin of coordinates. To facilitate the comparison of experimental results, we conducted statistical analysis on the experimental data, as shown in Figure 7D. The points drawn from the rigid state have the smallest distance from the origin of the coordinate and the best dispersion. As the initial angle increases, the distance between the separate points and the origin of the coordinate gradually increases. There is little difference between the results when the initial angle is 26° and 15°. The main reason is that the initial angle at 26° has exceeded the linear variation range of angular stiffness, as shown in Figure 5D.

We conjecture that when the initial angle is within the linear variation range of angular stiffness, the pretension force of the flexible joint increases with the initial angle, resulting in a smaller dispersion of grasping errors. However, the dispersion increases further when the initial angle is outside the linear variation range. Compared with the flexible state, the grasping precision in the rigid state is better and the dispersion is smaller, so the rigid state is more suitable for some works with high precision requirements. When the gripper works in the flexible state, due to the existence of the assembly error, the greater the initial angle is, the larger the pretension force of the flexible joint is, and the worse the grasping precision is.

Comparing with the purely rigid hand

To reflect the characteristics of the mechanical structure of the RFRH gripper, we have designed a simple gripper similar in shape and size to the one in the article. The fingers are fully articulated and have the same number of actuated degrees of freedom as the number of motors used in the proposed gripper. We call the new gripper the Purely Rigid Hand (PRH), as shown in Figure 8A. The joint below the fingertip is actuated by a servo, so that the angle of this joint can be precisely controlled to simulate the shape of the fingers of the RFRH with different angles.

FIG. 8.

The RFRH and PRH are compared experimentally. (A) Mechanism of the PRH. (B) Workspace of the PRH. (C) Grasping and picking up the light plastic balls. (D) Grasping and picking up the scotch tape with smooth surface. (E) Picking up a jar of grease and rotating 90°. (F) Grab the heavier spherical objects. (G) The experimental results on grasping precision of the PRH and RFRH are statistically analyzed. PRH, Purely Rigid Hand.

The PRH gripper workspace is solved using the Monte Carlo method, where dots of different colors represent the end positions of the fingers for various joint configurations, as shown in Figure 8B. Compared with the workspace discussion above, the density of discrete points is moderate, which means the rigid RFRH finger has one less joint and a smaller workspace than the PRH finger due to the fingertip joint that is fixed by the slider. The flexible RFRH finger has a larger workspace than the PRH finger due to the passive deformation of the spring joint. Thus, while the slider structure limits the working space of the RFRH in the rigid state, it can reach more places in the flexible state and better adapt to the shape of the objects to be grasped. Overall, the slider structure increases the gripper's dexterity and mobility.

The experimental results of the PRH grasping capability are shown in the last column of Table 1 and Figure 8C–F. When the PRH fingertip joint is 0°, its shape and characteristics are similar to those of the rigid RFRH, so the packing grasping configuration is used in the PRH experiment process, and it's mainly compared with the flexible RFRH. Since the previous flexible RFRH grasping objects are an open-loop control, the accuracy of the flexible joint angle could not be guaranteed, so we selected the angle of the PRH fingertip joint as 15°, which is the middle value of the optimal initial angles of 10–20° for the flexible RFRH fingertip. The results show that the PRH can successfully grab light plastic balls, scotch tape, a jar of grease, and billiard balls, but not potato chips and some irregularly shaped objects.

Compared to the rigid RFRH, the PRH is able to grasp some smooth and heavy spherical objects using the packing grasp configuration, due to the additional freedom of the fingertip joints. However, this shortcoming of the rigid RFRH can be remedied by the flexible state. The flexible joint improves the gripper's safety, allowing the RFRH to be able to grasp fragile objects such as the crisp. In addition, the passive flexible joints of the flexible RFRH allow it to successfully grasp some irregularly shaped objects, and it can also grasp heavy and smooth billiard balls by changing its configurations. In general, the RFRH with different states is better at grasping objects than the simple PRH.

Figure 8G presents a statistical comparison analysis of the experimental results of the PRH and the RFRH grasping precision experiments. During the experiments, the initial angles of the fingertip joints of PRH are set as 0°, 15°, 19°, and 26°, respectively. The experimental results are statistically analyzed and compared with the results of the RFRH (Fig. 7D). For different initial angles, the distances between the marked points and the zero-error position in the PRH experiments are smaller than in the RFRH experiments, and the dispersion of the PRH points is better. This result indicates that the PRH has better grasp accuracy. Moreover, the grasp accuracy of the PRH shows a further trend of improvement as the initial angle increases. We guess that this is because the fingertip joint rotates and the contact points between the fingertips and the laser pointer move toward the palm, making d1 smaller and grasping accuracy better.

At the same time, the changes in the initial joint also mean that as the initial fingertip angle increases, the packing grasp configuration is able to grasp the object more stably. The grasping accuracy of the rigid RFRH is also very good, and there is only a small difference with the PRH whose initial angle is 0°. We believe that this difference is mainly due to the manufacturing and assembly errors in the slide structure. To reduce friction forces and ensure smooth sliding, there is a small gap between the fingertip and the slider, which results in a partial loss of the rigid RFRH accuracy during grasping. This problem could be improved by improving the mechanical process. In general, compared to the PRH, the flexible RFRH has higher security and the rigid RFRH also has very good grasp accuracy.

Cooperative grasping in rigid-flexible state

To explore the application scenarios of cooperative work between rigid state and flexible state, we designed an experiment in which the RFRH gripper mounts a nut to a screw (Supplementary Video S4). The process of tightening the nut is divided into two steps. The first step is to take the nut and align the screw. The second step is to repeat the rotating nut. The gripper consists of three fingers that need to work together to complete the grasping motion. However, there are 3D-printing errors in the fingers, assembly errors in the flexible joints, and stiffness errors due to initial angle tuning in the flexible state. These errors accumulate and are amplified at the tips of the fingers as the servos rotate, leading to the differences in the tips' pose of the three fingers in flexible state. Therefore, the grasping precision cannot be guaranteed when the gripper is grasping an object in the flexible state, which is also a shortcoming of most flexible soft robots.

According to previous studies, the grasping precision of the rigid state gripper is better; therefore, in the first step, the rigid state should be selected to align the nut with the screw, as shown in Figure 9C. Figure 9E shows that the gripper in the flexible state cannot align the nut with the screw, due to the grasping error caused by initial stiffness. Because of the machining and assembly errors, there will be translation and rotation errors between the axis of the gripper and the axis of the robot arm. When the gripper rotates at a certain angle around the axis of the arm, the center point of three fingertips will be displaced in the horizontal plane, as shown in Figure 9D. At this time, if the gripper works in the rigid state, the gripper and the grasped object will be broken.

FIG. 9.

Cooperative operation of rigid state and flexible state. (A) Translation error of the operation system. (B) Rotation error of the operation system. (C) Gripper aligns the nut to the screw in rigid state. (D) Error in horizontal direction after 120° the gripper rotates 120° around the axis. (E) Gripper cannot align the nut to the screw in the flexible state. (F) Process of installing the nut in operating system. (F.i) Grasping and picking up the screw. (F.ii) Aligning nut with screw. (F.iii) Changing state from rigid to flexible. (F.iv) Rotating 120° forward. (F.v) Rotating 120° reversely, and in preparation for the next nut rotation.

The gripper in the flexible state can handle the center offset after the rotation well because its flexible joints are elastic, so the flexible state is selected to complete the task in the second step. The whole process of the experiment is shown in Figure 9F. The RFRH gripper grabs the nut in the rigid state, aligns the screw, turns into flexible state, rotates the nut forward by 120°, loosens and reverses by 120° to return to the original position, and repeats the rotation. There are still many application scenarios of cooperative work between rigid state and flexible state. For example, robots open doors with keys, unmanned aerial vehicles (UAVs) capture objects in the wind, and some medical applications. In future researches, we will further explore the advantages of rigid-flexible collaborative works.

Conclusion

In this study, we introduce a reconfigurable dexterous gripper, which can switch states between rigid and flexible. The gripper is composed of three fingers, and each finger can be controlled independently to select different grasping configurations for different objects. The reconfigurable robotic finger changes its rigidity and flexibility by moving the slider up and down. The mathematical models of the rigid state and the flexible state of the gripper are established, respectively, and the kinematic characteristics of the single finger and the parallel system composed of three fingers are analyzed. Finally, we experimentally demonstrated the flexible angular stiffness of the fingertip joint in the flexible state, the grasping ability of the gripper, and the cooperative work in the rigid-flexible state.

In the future research, we will focus on the closed-loop control method of the gripper and further improve its grasping ability through the method of visual feedback. Furthermore, it is expected to make use of the security advantages of the flexible state of the manipulator to make the gripper have the ability of intelligent learning.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This study is supported by the Natural Science Foundation of Liaoning Province of China (State Key Laboratory of Robotics joint funding, 2022-KF-22-01).

Supplementary Material

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Supplementary Material

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