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Design, modeling, and manipulability evaluation of a novel four-DOF parallel gripper for dexterous in-hand manipulation

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Abstract

This study presents a novel four-degrees-of-freedom parallel gripper with potential application to industrial automation. The gripper adopts a parallel grasping mode on objects and can independently complete in-plane horizontal and vertical motions and in-hand twisting motion. Kinematic and dynamic models of the gripper–object system are developed. The controllable internal force acting on the object is calculated to obtain the minimum driving force/torque. An energy-based manipulability index is developed on the basis of the derived solutions. The numerical simulation includes a comparison between the MATLAB model and the ADAMS model to verify the motion forms of the parallel gripper and the rationality of analytical modeling studies. Manipulability performance is evaluated along the transportation path of the object. Results indicate that the gripper can achieve horizontal transmission to supplement the workspace of a robotic arm, and it exhibits relatively better performance in in-hand manipulation and in-plane vertical transmission.

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Abbreviations

X F :

Coordinate of point F expressed in the coordinate system O-XY in the X-axis direction

X Ai :

Coordinate of point Ai expressed in the coordinate system O-XY in the X-axis direction

Y F :

Coordinate of point F expressed in the coordinate system O-XY in the Y-axis direction

I 1 :

Length of link AiDi

I 2 :

Length of link DiHi

I EiF :

Distance between points Ei and F in the X-axis direction

S EiGi :

Initial length in the Y-axis direction between points Ei and Gi

θ i :

Input rotation angle around axis Ai

S i :

Input length between points Di and Ei

R :

Radius of the object

θ F :

Rotation angle of the object

S arc :

Arc length of the object

F ẋ :

Velocity vector of the contact point expressed in the coordinate system O-XY

\({\dot{\boldsymbol{u}}}\) :

Output object velocity vector with respect to the coordinate system O-XY

G :

Grasp matrix

G ẋ :

Velocity vector of the contact point expressed in the coordinate system O-XY

\({\dot{\boldsymbol{q}}}\) :

Input joint velocity vector

J :

Jacobian matrix

T :

Transformation matrix

F ci :

Contact force exerted on a grasp slider

F’ci :

Reaction force of Fci

F fi :

Friction force exerted on a grasp slider

F’fi :

Reaction force of Ffi

F Ni :

Normal force exerted on a grasp slider

F’Ni :

Reaction force of FNi

F di :

Driving force exerted on a grasp slider

F’di :

Reaction force of Fdi

M i :

Driving torque of joint Ai

a FX :

Output translational acceleration of the object in the X-axis direction

a FY :

Output translational acceleration of the object in the Y-axis direction

\({\ddot \theta _F}\) :

Output angular acceleration of the object

\({\dot \theta _i}\) :

Input angular velocity of active link AiDi around axis Ai

\({\ddot \theta _i}\) :

Input angular acceleration of active link AiDi around axis Ai

a Yi4 :

Acceleration of link DiHi along the Y-axis

a Yi5 :

Acceleration of each grasp slider along the Y-axis

\({\ddot s_i}\) :

Acceleration of each grasp slider with respect to link DiHi

m F :

Mass of the object

g :

Gravitational acceleration

I F :

Inertia of the object

M :

Coefficient of the static friction force

F k :

Internal force added to each side of the contact surface of the object

m 1 :

Mass of link AiDi

m 2 :

Mass of link BiCi

m 3 :

Mass of link CiDi

m 4 :

Mass of link DiHi

m 5 :

Mass of each grasp slider

X Di :

Coordinate of point Di expressed in the coordinate system O-XY in the X-axis direction

Y Di :

Coordinate of point Di expressed in the coordinate system O-XY in the Y-axis direction

T i :

Kinetic energy

V i :

Potential energy

Φ :

Vector of the generalized forces contributed by an external force

λ :

Lagrange multiplier

I 1 :

Moment of inertia of link AiDi

I 2 :

Moment of inertia of link BiCi

V DiX :

Velocity of point Di in the X-axis direction

V DiY :

Velocity of point Di in the Y-axis direction

h i1 :

Height of the mass center of link AiDi in the coordinate system O-XY

h i2 :

Height of the mass center of link BiCi in the coordinate system O-XY

h i3 :

Height of the mass center of link CiDi in the coordinate system O-XY

h i4 :

Height of the mass center of link DiHi in the coordinate system O-XY

δX Di :

Virtual displacement of XDi

δY Di :

Virtual displacement of YDi

δθ i :

Virtual displacement of θi

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Acknowledgments

This research was funded in part by the Beijing Natural Science Foundation (grant number: 3204036), the National Natural Science Foundation of China (grant number: 61903011), the National Key R&D Program of China (grant numbers: 2018YFB1307004 and 2020YFC2004200), and the General Program of the Science and Technology Development Project of the Beijing Municipal Education Commission (grant number: KM202010005021).

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Authors and Affiliations

  1. Beijing Key Laboratory of Advanced Manufacturing Technology, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing, 100124, China

    Shiping Zuo, Jianfeng Li & Mingjie Dong

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  1. Shiping Zuo
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  2. Jianfeng Li
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  3. Mingjie Dong
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Corresponding author

Correspondence to Mingjie Dong.

Additional information

Shiping Zuo was born in Liaoning, China in 1994. He is currently a Ph.D. candidate in Mechanical Engineering at Beijing University of Technology, Beijing, China. His research interests include parallel mechanism, exoskeleton mechanism, and rehabilitation robotics.

Jianfeng Li obtained his Ph.D. in Mechanical Engineering from Beihang University, Beijing, China in 1999. After completing postdoctoral training from Tsinghua University, he is currently a Professor at Beijing University of Technology. His research interests include theory of parallel mechanism, wearable exoskeleton, external fixators, and rehabilitation robotics.

Mingjie Dong obtained his Ph.D. in Mechatronics from Beihang University, Beijing, China in 2018. He is currently a faculty member in the College of Mechanical Engineering and Applied Electronics Technology at Beijing University of Technology. His research interests include intelligent control of rehabilitation robotics.

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Zuo, S., Li, J. & Dong, M. Design, modeling, and manipulability evaluation of a novel four-DOF parallel gripper for dexterous in-hand manipulation. J Mech Sci Technol 35, 3145–3160 (2021). https://doi.org/10.1007/s12206-021-0636-7

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