Motion analysis of a device including a disk and two slender bars with a design change for full disk revolution


Editorial decision for TJOE
Devin Berg
Dr. Fleischfresser,After a review of your revised document submitted in response to the reviewers comments, we have decided to accept your article for publication in the Journal of Open Engineering.Thank you for your contribution! Devin BergEditor, TJOE
Editorial comments for TJOE
Devin Berg and Luciano Fleischfresser
Dr. Fleischfresser, Thank you for your submission to the Journal of Open Engineering. Please consider the two reviews that have been completed. In particular, there are three main points that I'd like you to address. 1) While TJOE does not screen submissions on the basis of novelty or impact, both reviewers have noted that it is not clear what the main thrust of your manuscript is. Can you please clarify the main point that you are trying to make with this article? From your manuscript you address both numerical evaluation of the kinematic equations as well as the project-based engineering pedagogy. Perhaps the manuscript could be reframed to make it more clear what the implications are in one of these areas. 2) One of the reviewers noted that the notation presented in equations 1 through 3 made following the rest of the mathematics more difficult. Please consider eliminating this notation and instead writing out the trigonometric expressions fully in the subsequent equations. 3) In the numerical experiments portion of the manuscript you include some figures. In the spirit of the journal, it would be desirable to provide the code used to generate those figures as part of your submission. Thank you again for your submission and please consider the reviewer comments as well as my comments above in your revision.
1. The main thrust is the numerical evaluation of the kinematic equations and its reproducibility. The interest to develop this work originated from my daily routine of teaching vector mechanics to undergraduates, and a couple of years ago the pedagogical side of using computer projects was the main interest. But the focus is different here. 2. An argument for keeping the notation was made in my reply to the reviewer. 3. Direct link:
Thank your for your response. Could you perhaps address the first item in your introduction. Incorporating the argument of your response here should be sufficient.
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Review by J. Iossaqui
Juliano Iossaqui and Luciano Fleischfresser
REVIEW FOR THE JOURNAL OF OPEN ENGINEERING The manuscript presents an kinematics analysis of a mechanism denoted by two slender bars with a design revolution. This mechanism is a typical four-bar linkage analyzed in a wide variety of books and papers about mechanism and dynamics of machinery. Numerical simulations are performed to compare two different configurations. TECHNICAL SOUNDNESS Technical formulation seems to be correct. However, an approach using generalized coordinates or dimensionless variables might be more interesting. Some typos can be found in the paper: - vector notation: omega, V_A, V_B, ,rho_OA, rho_CB, rho_BA,.... - units in mathematical mode CLARITY It is not clear the main contribution of the manuscript: the kinematic analysis or numeric simulations? In spite of technically correct formulation of the kinematics equations, the notation and abbreviations used makes it difficult to read. It might be preferable to use throughout the manuscript the notation sin(alpha) instead l, cos(alpha) instead, and so on. It is not clear why the kinematic analysis was separated in original mechanism and modified mechanism. That seems the original mechanism is a particular configuration of the modified mechanism. Author does not explain why they employed the constant rotation w= 2 rad/s and the variable rotation w = 0,1+2,3alpha rad/s for the kinematics analysis. The selected simulated rotation constitute two really simple examples to evaluate the mechanism. It would be more appropriate to use more complex simulations. For instance, harmonic and exponential rotation. COMPLETENESS The state-of-the-art section is weak. Taking a look at the literature, it can check that there are many works about kinematics and kinetics analysis of four-bar mechanisms. The citations section is incomplete, no reference has date.
Regarding the typos, this is a LaTeX/Markdown rendering issue. I am still not able to fix them. The use of generalized coordinates for this problem is beyond my technical knowledge. The suggestion to use dimensionless variables would require deciding which parameters to choose as intrinsic to the system. The analysis might become more elegant, but we are only plotting positions, velocities and accelerations, and the equations are all algebraic. Also, the current code implementation would not be valid anymore. The difficulty in using the trig functions explicitly is that the numerical implementation follows the one-letter notation. Consequently, it would make the submission inconsistent with the Fortran code. Also, as an example, writing them out explicitly would make eq. (21) rather cumbersome, since the parameter "f" itself is an expression of trig functions embedded into another arrangement of parameters. The original mechanism was based on Shames (1997). Both the constant and variable rotation rates are taken from this reference. The modified version is the name found to highlight the turn reversal direction and, more importantly, the lesser distance between the fixed rotation centers. This modification is what allows the mechanism to perform a full turn. The pre-print versions (arXiv:1508.07444 [physics.ed-ph]) present only the analysis for the original constant and variable rotation cases ( The variable rate used gives an average angular velocity of about 2 rad/s for the 90-degree turn, and that is one reason for using it. It is mentioned in the paragraph between equations (9) and (10). Regarding the comments about completeness, I am updating the citations section. Provisionally, one can download the bib file from
Corrected link:
Review by Jason K. Moore
Jason Moore and Luciano Fleischfresser
REVIEW FOR THE JOURNAL OF OPEN ENGINEERING In this paper the author derives the kinematic equations governing the four bar linkage, a common dynamics benchmark problem. The author then compares different linkage lengths and two driver input angular velocities by numerically evaluating the equations. This article is something that may belong well in an introduction to kinematics course notes, but does not really belong in a modern technical journal. The four bar linkage is one of the most common and widely studied linkages there are. There are many thousands and thousands of derivations of this out in the wild. It isn't clear to me that this derivation offers anything new to this classic problem. At the end of the article the author states "This work was motivated by the desire to introduce project-based activities in the undergraduate engineering mechanics’ classroom." This article could possibly be framed in this light and offer something useful to the journal's audience. Maybe this derivation method is an exceptional way to enlighten students and that would be worth telling a story about. But as it stands this article doesn't have a story worth telling in this journal. TECHNICAL SOUNDNESS I think this article is likely technically sound. If the author compared his results with other benchmark results of the four bar linkage then we could feel fully confident of the soundness. CLARITY The writing is fine but doesn't use common nomenclature and descriptions for kinematics. For example, it is odd that the author never mentions the phrase "four bar linkage". The introduction cites a number of frivolous references that do not seem related to the article in any substantial way. COMPLETENESS This is fine. OPENNESS AND REPRODUCIBILITY This article over presents the derivation of this common problem, which is good for reproducibility but simply showing the final kinematic equations would be more than sufficient. The author evaluates the equations numerically and it isn't apparent if software was used to do this. If it was used, there is no code or data artifact cited.
One additional comment. It is not acceptable to use copyrighted figures from a textbook in this venue.
REGARDING INITIAL COMMENTS: One of the main goals is to present a design modification to the original case, and, to this author's knowledge, this modification has not been presented before. The 2D device investigated may be viewed as a four bar linkage when the stationary reference is considered the 4th link. If it is standard to consider such variations as four bar linkages, then an explicit mention to this equivalence in the paper's introduction is due. But note that various terms that imply four bar linkage are used in the abstract. The reviewer states: "The author then compares different linkage lengths and two driver input angular velocities...". The length being changed is the distance between the fixed centers of rotation, and only for the design modification case. I agree that -- when viewed as a four bar linkage -- this would be the "length of the fourth bar". But the only reason this distance was changed was to keep the same linking bar, or, in other words, it is still the same mechanism. The disk (the "link" fixed to the ground on the left in pure rotation) never changes its radius; the output bar (the "link" fixed to the ground on the right, also in pure rotation) never changes its length; and, finally, the linking bar (the only rigid body undergoing general planar motion) does not change its length either. If one had a physical model of this 2D device, the design modification could be effected by loosening some screws with a wrench for example, and then fastening them again in the new position without replacing any of the three parts of the device. As mentioned, the motivation comes from an example problem in Shames' Engineering Mechanics, which is one of many excellent textbooks used in Introductory Dynamics classes usually offered in the 2nd year of various Engineering majors in campuses worldwide. My understanding is that four bar linkages are mainly studied in the Mechanical Engineering curriculum. These classes go by names like Analysis and Synthesis of Mechanisms, and thus they belong to the specialized curriculum of Mech. Eng. Having stated this, I am not sure for which audience the reviewer thinks the pub would serve as "introduction course notes to kinematics", but, from the above, I would not assume he is referring to the kinematics of rigid bodies typically offered in Introductory Dynamics (where the focus is on instantaneous positions without regard for the time evolution of the motion). The statement regarding the PBL activities was simply a digression at the end, but it is not intended to be the main thrust. There is no pedagogical analysis presented. The detailed derivation of the equations and the subsequent numerical evaluations are. All tools to reproduce the results shown are available. As mentioned earlier, Kinematics problems for 2nd-year Engineering students aim to find solutions at particular instants of time. Such solutions provide a very limited perspective. Here we offer a simulation with graphical output where the reader is able to verify the evolution of motion variables. REGARDING COMMENTS ON TECHNICAL SOUNDNESS: The benchmark at my disposal is the full solution for the initial position of the original mechanism (mentioned at the end of the 1st paragraph of the Numerical experiments section, just before figure 3). That result was replicated and used to validate my solution. I am not aware of any other benchmarks that could be used. REGARDING COMMENTS ON CLARITY: The nomenclature used is commonly seen in writings dealing with the kinematics of rigid bodies I encountered over the years. Terms like crank-rocker, double-rocker, and slider-crank are mentioned in the abstract and they are inherently related to four bar linkages. I disagree that some references in the introduction are frivolous, since they are all generally related to the paper's main topic to illustrate important applications of rigid body kinematics. REGARDING COMMENTS ON OPENNESS AND REPRODUCIBILITY: Please see: TJOE is about openness and reproducibility. As such, simply showing the final kinematic equations is not enough. An effort was made to provide needed information to reproduce results with confidence. One can take the equations presented and corroborate them with the code available. Interested readers ought to appreciate the level of detail. Some routine calculations are in the appendix to allow the more knowledgeable specialist to skip them if desired. Regarding the Additional Comment: The figures are redraws of the original ones. In order to comply with the CC-BY license, the text stating the "permission to reproduce" can be removed from the captions to make them compliant.