Standing on the shoulders of giants: A brief note from the perspective of kinematics
CHINESE JOURNAL OF MECHANICAL ENGINEERING
Standing on the Shoulders of Giants: A Brief Note from the Perspective of Kinematics
0 KONG Xianwen School of Engineering and Physical Sciences Heriot-Watt University Edinburgh EH14 4AS , UK
Kinematics[1‒3] has evolved with and contributed
significantly to the human demands. For example,
slider-crank mechanisms have been widely used in engines
since the industrial revolution. Additionally,
constant-velocity couplings have been developed to meet
the needs of the automobile industry since the 1920’s. With
the development of robots, robot kinematics has been one
of the research focuses in Kinematics since the 1970’s.
Several research areas in Kinematics, such as parallel
mechanisms, compliant mechanisms, cable-driven parallel
mechanisms, reconfigurable mechanisms, origami-inspired
mechanisms, and biohybrid systems, have emerged in the
past three decades.
The development of Kinematics has been closely related
to mathematics and machine design. Recent advances in
computer algebra geometry and numerical algebra
geometry[4‒5] have enabled in-depth analysis of multi-mode
parallel mechanisms[5‒6] which requires solving polynomial
equations with positive dimensional solution sets. Now,
advances in software engineering, artificial intelligence,
biomimetics, materials, sensing, actuation, control, and
manufacturing technologies are expected to have
significant impact on Kinematics in the future. For instance,
the application of mechanical CAD software can free
people from deriving complicated mathematical equations
in solving certain kinematic problems[7‒8].
In the following, three cases will be presented to
illustrate the importance and challenges in maintaining an
awareness of the state-of-the-art in the research in
Kinematics and certain topics which may involve old
references in addition to the recent ones.
The first case pertains to the closed-form determination
of the crank position corresponding to the maximum slider
velocity in a slider-crank mechanism. This is a fundamental
problem in engine design. Although slider-crank
mechanisms have been used for centuries, the above
problem had not been solved until the publication of Refs.
[10‒12] at the end of 19th century. In these publications, a
cubic equation was derived using analytic or geometric
approaches and then solved to obtain the crank position.
However, these references were ignored for many years.
This led to the publication of an alternative closed-form
solution of the same problem in Ref.  in 1941. Refs.
[10‒13] were also not known to the authors of Ref. , in
which the slide-crank mechanism was taken as an example
in the application of their approach to the analysis of
four-bar linkages. Unware of the work of Refs. [10‒14], a
numerical solution was presented in Ref.  in 1958 when
the work of Refs. [10‒14] was pointed out in the discussion
of Ref.  by the reviewers. Without knowing the work of
Refs. [10‒13, 15] and based on the work of Ref. , a
third closed-form solution was proposed in Ref.  in
2005 to replace the approximate solutions to this problem
in textbooks. This was more than one hundred years after
the publication of Refs. [10‒12]. Should the authors of Refs.
[13‒16] have known the previous work in Refs. [10‒12],
they may have saved both time and effort in finding their
solutions. Possible causes of the unawareness of the Refs.
[10‒12] might include: (a) It was not easy to access the
information about these old references at that time; and (b)
Some terminologies used in Refs. [10‒12] were different
from those in Refs. [13‒16].
The second case is on the type synthesis of parallel
mechanisms. In the first decade of the 21st century, several
systematic approaches to the type synthesis of parallel
mechanisms were proposed using different mathematical
tools around the world[17‒27]. However, the work on the
constant-velocity coupling connecting parallel axes by
HUNT K H published in 1973 was ignored by almost all
the researchers on parallel mechanisms, although it was
closely related to the type synthesis of translational parallel
mechanisms. The ignorance of HUNT’s work might be
caused by (a) It was on a different topic from parallel
mechanisms; (b) HUNT himself did not mention his
work on the constant-velocity coupling in his paper on
the type synthesis of parallel mechanisms, which was based
on the mobility equation; and (c) Not many people
understood screw theory before 2000. Should researchers
have known the work of Ref.  earlier, they would have
saved much time in reinventing the 3-DOF translational
parallel mechanisms. Fortunately, such ignorance led to the
development of several systematic methods on the type
synthesis using different approaches[17‒27] and invention of
a large number of parallel mechanisms. In addition, the
introduction of inactive joints in parallel mechanisms
provided a solid foundation for the type synthesis of
parallel mechanisms with multiple operation modes. It is
also noted in 1960’s, HUNT and PHILLIPS J revived the
screw theory published in 1900 by BALL R S.
The last case is the successful extension of classic
single-loop overconstrained mechanisms to the design of
parallel mechanisms[21, 31, 32] and multi-mode mechanisms[31,
33], motion structure or deployable systems and
thick-plate folding. Without understanding single-loop
overconstrained mechanisms, these advances would not
have been possible.
The above cases have demonstrated the significant
impact of having awareness of the state-of-the-art in the
relevant areas on the research in Kinematics. Although
access to the literature has become more convenient than
ever before, it is even more challenging to have full
awareness of the state-of-the-art compared with decades
ago when it was not easy to get the references one needed.
This is because there are now so many emerging areas of
research and technologies combined with a large number of
new conference and journal publications. In addition to
individual effort, collaboration within the same discipline
and across different disciplines may provide a potential
solution to meet this challenge.
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