Article
Kinematic Analysis and Verification of a New 5-DOF
Parallel Mechanism
Yesong Wang, Changhuai Lyu and Jiang Liu *
Citation: Wang, Y.; Lyu, C.; Liu, J.
Kinematic Analysis and Verification
of a New 5-DOF Parallel Mechanism.
Appl. Sci. 2021, 11, 8157. https://
doi.org/10.3390/app11178157
Academic Editors: Giovanni Boschetti
and Alessandro Gasparetto
Received: 15 July 2021
Accepted: 30 August 2021
Published: 2 September 2021
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School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
b20180269@xs.ustb.edu.cn (Y.W.); S20190475@xs.ustb.edu.cn (C.L.)
* Correspondence: Liuj_69@ustb.edu.cn; Tel.: +86-010-6233-2538
Abstract:
This paper first designs a new 5-DOF parallel mechanism with 5PUS-UPU, and then analy-
ses its DOF by traditional Grubler–Kutzbach and motion spiral theory. It theoretically shows that
the mechanism meets the requirement of five dimensions of freedoms including three-dimensional
movement and two-dimensional rotation. Based on this, the real mechanism is built, but unfortu-
nately it is found unstable in some positions. Grassmann line geometry method is applied to analyze
its unstable problem caused by singular posture, and then an improving method is put forward to
solve it. With the improved mechanism, closed loop vector method is employed to establish the
inverse position equation of the parallel mechanism, and kinematics analysis is carried out to get
the mapping relationships between position, speed, and acceleration of moving and fixed platform.
Monte Carlo method is used to analyze the workspace of the mechanism, to explore the influencing
factors of workspace, and then to get the better workspace. Finally, an experiment is designed to
verify the mechanism working performance.
Keywords: screw theory; singularity; inverse position solution; Monte Carlo
1. Introduction
Parallel mechanism (PM) can be defined as a closed-loop mechanism in which the
moving platform and the fixed platform are connected by at least two independent kine-
matic chains. The mechanism has two or more degrees of freedom and is driven in parallel.
Common parallel mechanisms are Delta and Stewart. Unlike traditional series structure,
parallel structure is widely used in automobile, mechanical manufacturing [
1
–
5
], avia-
tion [
6
], medical treatment [
7
], electronic manufacturing [
8
], education, and other fields
due to its small cumulative error, high precision, light weight of moving part, high speed,
fast dynamic response, compact structure, high rigidity, and large bearing capacity [
9
–
12
].
At present, scholars at home and abroad have done much research on parallel mecha-
nism with few degrees of freedom [
13
–
15
]. Xiaoqiang Du [
16
] proposed a new U-PRU-PUS
parallel mechanism solar tracking device with two degrees of freedom, analyzed its sin-
gular position, and optimized its motion range. Compared with the solar tracking device
with series mechanism, it improved its anti-interference ability, load capacity, and stability
to the environment. Ziming Chen [
17
] put forward a new 3-DOF multi-turn center 3-PUU
parallel mechanism, analyzed its motion characteristics using srew theory, obtained the
Jacobian matrix of 3-PUU parallel mechanism by establishing inverse kinematic equation,
determined the singular type of mechanism by analyzing Jacobian matrix, and obtained
its workspace by using inverse kinematic method. Matteo Russo et al. [
18
] proposed a
3-UPR parallel mechanism and solved its inverse kinematics problem and forward kine-
matics problem. The Jacobian matrix is calculated to estimate the singular position of the
mechanism. The parameters of the mechanism are optimized.
In conclusion, scholars have done more research on 3-DOF parallel robots and less
on 5-DOF parallel robots. 5-DOF parallel robot is an important class of low-degree-of-
freedom parallel mechanism. It is more flexible than 3-DOF parallel robots and has a
Appl. Sci. 2021, 11, 8157. https://doi.org/10.3390/app11178157 https://www.mdpi.com/journal/applsci
