This project presents the design of a novel variable stiffness gripper using permanent magnets as nonlinear springs. Two servo motors control the position of the magnets to simultaneously adjust the position and stiffness of each gripper finger. An experiment showed the gripper's ability to safely grasp a fragile object when an unexpected collision occurred, demonstrating the benefits of variable stiffness for safety and compliant motion. Future work will focus on dynamic manipulation with the gripper and experiments involving human-robot interaction.

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Design of A Novel Variable Stiffness Gripper Using Magnets
Hongfei Lin
Graduate Student
Mechanical and Aerospace Engineering
State University of New York at Buffalo
Amirhossein Hajiagha Memar
Ph.D. Student
Mechanical and Aerospace Engineering
State University of New York at Buffalo
Ehsan T Esfahani
Professor
Mechanical and Aerospace Engineering
State University of New York at Buffalo
INTRODUCTION OUR VSA MECHANISM EXPERIMENT AND SIMULATION
In this experiment The stiffness was set to a
low value to avoid damages to the fragile
object. with a low stiffness. The end effector
moved toward a table and one of the gripper
fingers collided with the table.
DESIGN AND MODELING
Based on the experiment strategy, we also
simulated this experiment in v-rep by
creating the model for the gripper as well as
the magnets and using Matlab to control the
robotic arm and gripper.
What is Variable Stiffness Actuator
• If the stiffness of a compliant joint is adjustable, it is called a series elastic
actuator (SEA) or a variable stiffness actuator (VSA).
• In the VSA, an elastic elements such as a spring is used in series with a stiff
actuator. The elastic element of VSA acts as a low-pass filter and absorbs the
impact energy from or to the actuator.
• VSA provides users with the intrinsic capabilities of bandwidth, impacts,
and energy storage as well as a useful range of stiffness.
Different Approach of VSA :
• The stiffness varies by changing the elastic element preload.
• The stiffness is altered by changing the transmission ratio between the load
and the spring.
• The stiffness is adjusted by changing the properties of elastic elements
•
Limitation:-
• Safety is one of the most important factor in the robot interaction with
unknown and dynamic environments and a robot needs to handle fragile or
sharp objects as well as service robots during physical interaction with
human.
• High-efficiency is another important factor in industry. Based on VSA the
gripper can handle more items with different kind of size, materials and
shapes.
Our Focus:
• We want our gripper takes advantage of the magnetic force in repulsive
configuration as the nonlinear elastic element.
• To achieve variable stiffness function in a compact design and control the
position and stiffness simultaneously by control two independent motor
WHY IT’S IMPORTANT
CONCLUSION
• This project presented the design aspects of a novel variable stiffness gripper with two
fingers. Magnetic springs in a repulsive configuration were used as the non-linear preload
springs in an antagonistic springs with antagonistic actuators setup.
• Two servo motors in position control mode were used to adjust the position and stiffness
of the gripper simultaneously.
• The proposed design provides the gripper with capability of force measurement
individually for each finger. This property can provide the grasping controller with
• higher capabilities and more stability in the case of uncertain grasping or collision with
stiff objects.
• An Experiment was conducted to show how the proposed variable stiffness gripper can
improve grasping task in the context of safety and compliant motion. In this experiment
the compliance of the gripper was investigated in a task where a robotic arm equipped
with the designed gripper grasped a fragile object and an unexpected collision happened.
• The results showed the effectiveness of the proposed mechanism for a two finger gripper..
One part of the future work is the gripper dynamic manipulate which means we would be
able to use the gripper to throwing and catching a item like what human finger can do.
The other part is have some experiment working with human-robot interaction to see how
it will work when the gripper have some physical contact with human.
FUTURE WORK
In this project, permanent magnets were chosen as
non-linear springs, since they can provide the system
with not only a compact non-linear elasticity but also
a noncontact force interaction between the actuators
and the load
Basically, in the absence of external forces, each
finger tends to stay in the static equilibrium point
which is at the middle of the two actuated magnets
by neglecting the effect of gravity.
This mechanism can be classified as antagonistic
springs with antagonistic motors’ group because
both the springs and the actuators are placed in an
antagonistic setup.
As a result, the position and stiffness of the fingers
can be adjusted simultaneously, by controlling the
positions of the actuated magnets.
In this design, timing belt was used to
transfer the rotational motion of actuators
to translational movement of the magnets.
Both sides of the belts were used to
transfer actuator forces to the magnets
because each pair of magnets need to
move simultaneously.
Each motor axis were passed through two
pulleys; an active pulley fixated on the
associated axis and one passive pulley
maintaining the belt tension.
The expression of the repulsive force between two cylindrical
magnets with radius R, and height h can be well approximated by
𝐹𝑚 𝑠 =
𝜋𝑢0 𝑀2 𝑅4
4
1
𝑠2
+
1
(𝑠 + 2ℎ)2
−
2
(𝑠 + ℎ)2
(1)
The distances between magnets can be calculated by
𝑙1 =
𝑑12 − 𝑊𝑚 − 𝑊𝑓
2
− ∆𝑥 𝑓 = 𝑥 𝑓 − 𝑥1 −
𝑊𝑚 + 𝑊𝑓
2
(2)
𝑙2 =
𝑑12 − 𝑊𝑚 − 𝑊𝑓
2
− ∆𝑥 𝑓 = 𝑥2 − 𝑥 𝑓 −
𝑊𝑚 + 𝑊𝑓
2
(3)
Then the force can be calculated by
𝐹 𝑥1, 𝑥2, 𝑥 𝑓 = 𝐹 𝑚1 − 𝐹 𝑚2 = 𝐹𝑚 𝑙1 − 𝐹𝑚 𝑙2 (4)
Mathematical expression of the stiffness for a given state can be
derived using the chain rule
𝐾 𝑥1, 𝑥2, 𝑥 𝑓 =
𝑑𝐹𝑚
𝑑𝑥 𝑓
=
𝑑𝐹 𝑚1
𝑑𝑥 𝑓
−
𝑑𝐹 𝑚2
𝑑𝑥 𝑓
=
𝑑𝐹 𝑚1
𝑑𝑙1
𝑑𝑙1
𝑑𝑥 𝑓
−
𝑑𝐹 𝑚2
𝑑𝑙2
𝑑𝑙2
𝑑𝑥 𝑓
=
𝑑𝐹𝑚
𝑑𝑠
𝑙1 +
𝑑𝐹𝑚
𝑑𝑠
𝑙2 (5)
Gripper Assembly Figure
Gripper Force Model
VSA Mechanism based on Magnet
Gripper Attached with Robotic Arm
Basic VSA Mechanism