Research of Kinematics and Dynamics of the Lever Lifting Mechanism Used in the Mobile Automotive Lift
, Nutpulla Jamalov 1,2, Assylbek Jomartov 1, Jacek Cieslik 3, Azizbek Abduraimov 1, Aziz Kamal 1, Madi Kaliyev 1 and Kuatbay Bissembayev 1Round 1
Reviewer 1 Report
The authors develop and analyze a lifting mechanism alternative to the scissors scheme. While the proposed mechanism is interesting and its analysis for stability is given, theoretically and experimentally, the article is written in a confusing way. Many of the figures do not correspond to their captions, and the symbols in the figures do not correspond to the ones given in the text. The language adopted in the article is very confusing as well, and should be thoroughly revised. The equations are presented without proper discussion, so the reader is unable to know the approximations adopted. The experimental details were not given at all, so it is impossible to assess the validity of the comparison between theoretical and experimental data. Still, the described mechanism is interesting by itself, which can afford publication in this journal once it is described in sufficient detail.
My recommendation is that the article must be reevaluated after major corrections.
Revise entire text. Adopt formal english for scientific soundness and clarity.
Author Response
Response to Reviewer 1
Comments: The authors develop and analyze a lifting mechanism alternative to the scissors scheme. While the proposed mechanism is interesting and its analysis for stability is given, theoretically and experimentally, the article is written in a confusing way. Many of the figures do not correspond to their captions, and the symbols in the figures do not correspond to the ones given in the text. The language adopted in the article is very confusing as well, and should be thoroughly revised. The equations are presented without proper discussion, so the reader is unable to know the approximations adopted. The experimental details were not given at all, so it is impossible to assess the validity of the comparison between theoretical and experimental data. Still, the described mechanism is interesting by itself, which can afford publication in this journal once it is described in sufficient detail.
My recommendation is that the article must be reevaluated after major corrections.
Comments on the Quality of English Language
Revise entire text. Adopt formal English for scientific soundness and clarity.
Response: Thank you for pointing this out. The article has been completely revised taking into account comments.
1) The novelty of the research lies in the new design of the lever mechanism of the lift, where the joints of the connection of the mechanism to the movable platform and the base are fixed motionless, which increases stability compared to the scissor mechanism; the development of methods for kinematic and kinetostatic analysis of the mechanism; the study of the stability of an automotive lift with a load on a moving platform and determination the boundaries of the stability area; the experimental measurement of stresses in mechanism links and comparison with the results of numerical calculations.
2) The kinematic equations of the lever mechanism were written using the vector method: first, vectors were introduced along the links of the mechanism; after that, closed vector contours (Figure 3), are considered; and finally, vector equations were written. Then the following vector equations take place:
, (1)
, (2)
. (3)
3) Reactions in cylindrical pairs of link connections can be determined based on the general equations of dynamics in the form of the d'Alembert-Lagrange equations (14). It allows us to determine the reactions of all releasing bonds, including those with any redundancy number.
, (14)
where, - active forces and reactions of connections, - inertial forces, - virtual displacement.
The equilibrium of each link was considered separately, which was influenced by: the projections of reactions in the joints, the force from the weight of the link, the projections of the force of inertia applied at the center of gravity of the link, and the moment of inertia of the link were applied. A balancing moment was also applied to the leading link 1
For example, Link 1
The equations:
(14)
Likewise for other links. Thus, we obtained a system of 21 equations with 21 unknowns.
4) The following has been added in Section 4:
Let us assume that the conditions are satisfied, then equation (32) can be written as:
|
(33) |
) |
It follows that or , since these are the equilibrium conditions of an automotive lift.
We assume that the equilibrium of the lift is stable; therefore, the stability of an automotive lift moving from a place with acceleration depends on the height and distance between the wheels of the lift. To illustrate the stability analysis of an automotive lift, consider a system with the following parameters:
|
|
(34) |
Then, based on formula (25), we obtain restrictions on the acceleration of the lift in the following form: for values and , the restrictions would be described by the inequalities and , respectively. It follows that as the distance between the wheels of the lift increases, the stability area of moving automotive lift increases, and with increasing height it decreases.
Figure 11 plots the dependence of relative accelerations on the ratio for various . The stability area of the lift decreases with increasing displacement of the load relative to the lift.
Figure 12 shows the boundaries of the lift stability area for various values of the ratio of the mass of the load to the mass of the lift . Based on the analysis of these graphs, it can be said that with an increase in the mass of the load, the stability area of the lift decreases.
Figure 11. Graph of the dependence of relative accelerations on the ratio of the distance between the wheels to the height of the lift at various .
Figure 12. Graph of dependence on at various .
The obtained dependencies of the stability area on the parameters of the lift can be used for the optimal design of an automotive lift with a load.
5) Section 5 describes the equipment used to carry out the experiments.
Foil strain gauges were used to measure stresses in the links. Strain gauges were glued to points on the links, to determine the stresses arising during the movement of the lever lifting mechanism. The strain gauges are connected to the ZET 058 strain gauge measuring system [zetlab.com], which, together with the ZETLAB TENZO software, allows collecting information from the strain gauges in real time via eight channels simultaneously.
6) Section 6 is completely revised
The article discusses the scheme of a new lever mechanism of the lift, where the joints connecting the mechanism to the movable platform and the base are fixed. This type of lifting mechanism has increased stability compared to the scissor mechanism.
To design the lever mechanism of the lift, methods for kinematic analysis of the lever mechanism, kinetostatic analysis of the lever mechanism under the influence of load, research of the stability of an automotive lift with a load, and determination of the boundaries of the stability area were developed.
An experimental sample was made according to scheme of a new lever mechanism of an automotive lift, and an experimental measurement of stress in four links were carried out, which were compared with the calculated stresses. The experiment showed that the circuit of the new lever mechanism of the lift is operational, the normal stresses in the links of the mechanism have an acceptable value. All research methods described in the article can be applied only to the design of a new lift lever mechanism.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This article introduces a novel design for a lifting apparatus that addresses the shortcomings of conventional scissor-type mechanisms. The design, crafted by the authors, comprises a single group of second-class links and two groups of fourth-class links. The lifting mechanism is affixed to a mobile platform. Within the article, you will find an examination of kinematics, kinetostatics, an assessment of lift stability, and findings from experiments conducted on a prototype of the newly developed lifting system.
Abstract should be restated by adding the importance and contribution of the work
Introduction section should be completely updated by adding motivation, organization and novelty of the work. Highlights the importance of proposed method over the several other existing methods.
Result and discussion section needs to be more generalized ways.
The detail comparison and sensitivity analysis should be added and also the limitation and advantage should be added.
English language needs to be improved significantly.
Please check and, if needed, add all the missing punctuation or missing italics.
Please revise the structure of the paper. It is recommendable to add in each section a couple of sentences that explain the purpose of the section. With this organisation, the reader can clearly understand the sequence of the paper.
I don’t see any conclusion section in the submitted file.
Comments for author File: 
Comments.pdf
Please improve the linguistic quality of the paper.
Author Response
Response to Reviewer 2
Comment 1: Abstract should be restated by adding the importance and contribution of the work.
Response 1: Thank you for pointing this out. Abstract has been completely redesigned.
Abstract:
Most of the arm lifts used in today’s industry are designed and manufactured based on the scissor mechanism. Such schemes have one drawback, when the mechanism is raised, their connection points with the base and the movable platform narrow, which leads to a letdown in its stability. This article proposes a new scheme of the lifting device, which eliminates the above disadvantage of scissor schemes. In the scheme developed by the authors, the joints connecting the mechanism to the moving platform and the base are fixed, which means that the distance between the connection points does not change, leading to its stable operation. The mechanism consists of one group of links of the second class and two groups of links of the fourth class. The article discusses the stability of the design of an automotive lift when moving with a load. The article presents the results of a kinematic, and kinetostatic analysis, a study of the stability of the lift and the results of studies of an experimental sample of the developed lift. The results of computer modeling and experiments showed that the methods described in this article allow to design of automotive lifts with new lever mechanisms.
Comment 2: Introduction section should be completely updated by adding motivation, organization and novelty of the work. Highlights the importance of proposed method over the several other existing methods.
Response 2: Thank you for pointing this out. The introduction has been completely rewritten.
- Introduction
At present, automotive lifts are widely used in many areas of industrial production. Among them are the construction industry, large-scale trade (malls), agro-industry, logistics of terminals and transport warehouses (airports, railway transport, road and sea transport), military equipment, etc. The Automotive Scissor Arm Lift is used for stacking, lifting or lowering, transporting and/or moving material [1].
The lever scissor mechanism provides economical lifting of loads [2-5]. Raising or lowering of the lever scissor mechanism is carried out by moving hydraulic drives or a linear actuator, which is acting on the scissor mechanism, that causes the vertical movement of the working platform. The automotive lift with a scissor arm mechanism has poor stability, which is due to the design of the scissor mechanism. When lifting the load, the distance between the attachment points of the scissor mechanism to the base and the movable platform decrease, therefore the base of the scissor mechanism decreases (Figure 1) and, accordingly, it becomes possible to overturn the automotive lift [6,7]. According to the Census of Fatal Occupational Injuries (CFOI), between 1992 and 2003, there were 78 accidents while using a scissor lift [8]. In [9,10], using the finite element method, a scissor mechanism was designed. In [11], the dynamics of a scissor mechanism was studied using the method of bond graphs. Articles [12,13] discuss the modeling of a scissor mechanism based on curvilinear and pneumatic drives to implement the curvilinear movement of a moving platform.
The article considers the scheme of a new lever mechanism [14,15], where the joints of the connection of the mechanism to the movable platform and the base are fixed motionless, i.e., the distance between the connection joints does not change. This scheme of the lifting mechanism has increased stability compared to the scissor mechanism. The development and research of a lifting lever mechanism with a fixed base is an urgent task. This article is devoted to the study of the proposed lift.
The novelty of the research lies in the new design of the lever mechanism of the lift, where the joints of the connection of the mechanism to the movable platform and the base are fixed motionless, which increases stability compared to the scissor mechanism; the development of methods for kinematic and kinetostatic analysis of the mechanism; the study of the stability of an automotive lift with a load on a moving platform and determination the boundaries of the stability area; the experimental measurement of stresses in mechanism links and comparison with the results of numerical calculations.
(a) (b)
Figure 1. Positions of the base of the scissor mechanism (a) in the folded state, (b) in the maximum raised state.
This article has the following structure. Section 1 provides an overview of the research methods of the scissor mechanism used in the moving platforms and disadvantages of such a mechanism. Also, the need for a new lever mechanism that has increased stability compared to the scissor mechanism and the methods required to design such lever mechanism are described.
Section 2 is devoted to the design of a new lifting lever mechanism. An analysis of the design of the new lifting lever mechanism showed that the mechanism consists of two main modules. The analysis of the kinematics of the considered spatial mechanism was carried out on the basis of a study of its flat scheme.
Section 3 describes the equations for finding reactions in cylindrical pairs of link connections, which were determined on the basis of general dynamic equations in the form of the d'Alembert-Lagrange equations.
Section 4 deals with the forces acting on the structure of an automotive lift. The condition for the stability of an automotive lift under the action of external forces, including the gravity of the load, is written. The boundaries of the lift stability area for an automotive lift have been determined.
Section 5 describes the results of experimental studies on the determination stresses in the links of the mechanism and compares them with the results of stresses calculated using the d’Alembert-Lagrange equations.
Section 6 presents the conclusions obtained as a result of the research.
Comment 3: Result and discussion section needs to be more generalized ways.
Response 3: Thank you for pointing this out. Conclusions section has been completely redesigned.
- Conclusions
The article discusses the scheme of a new lever mechanism of the lift, where the joints connecting the mechanism to the movable platform and the base are fixed. This type of lifting mechanism has increased stability compared to the scissor mechanism.
To design the lever mechanism of the lift, methods for kinematic analysis of the lever mechanism, kinetostatic analysis of the lever mechanism under the influence of load, research of the stability of an automotive lift with a load, and determination of the boundaries of the stability area were developed.
An experimental sample was made according to scheme of a new lever mechanism of an automotive lift, and an experimental measurement of stress in four links were carried out, which were compared with the calculated stresses. The experiment showed that the circuit of the new lever mechanism of the lift is operational, the normal stresses in the links of the mechanism have an acceptable value. All research methods described in the article can be applied only to the design of a new lift lever mechanism.
Comment 4: The detail comparison and sensitivity analysis should be added and also the limitation and advantage should be added.
Response 4: Thank you for pointing this out. Comparison and sensitivity analysis has been added to Section 4.
The stability conditions for an automotive lift moving from place to place and accelerating in a dimensionless form have the form:
|
(32) |
( |
where - distance between lift wheels.
Let us assume that the conditions are satisfied, then equation (32) can be written as:
|
(33) |
( |
It follows that or , since these are the equilibrium conditions of an automotive lift.
We assume that the equilibrium of the lift is stable; therefore, the stability of an automotive lift moving from a place with acceleration depends on the height and distance between the wheels of the lift. To illustrate the stability analysis of an automotive lift, consider a system with the following parameters:
|
. (34) |
( |
Then, based on formula (25), we obtain restrictions on the acceleration of the lift in the following form: for values and , the restrictions would be described by the inequalities and , respectively. It follows that as the distance between the wheels of the lift increases, the stability area of moving automotive lift increases, and with increasing height it decreases.
Figure 11 plots the dependence of relative accelerations on the ratio for various . The stability area of the lift decreases with increasing displacement of the load relative to the lift.
Figure 12 shows the boundaries of the lift stability area for various values of the ratio of the mass of the load to the mass of the lift . Based on the analysis of these graphs, it can be said that with an increase in the mass of the load, the stability area of the lift decreases.
Figure 11. Graph of the dependence of relative accelerations on the ratio of the distance between the wheels to the height of the lift at various .
Figure 12. Graph of dependence on at various .
The obtained dependencies of the stability area on the parameters of the lift can be used for the optimal design of an automotive lift with a load.
Comment 5: I don’t see any conclusion section in the submitted file.
Response 5: Thank you for pointing this out. Conclusions section added to the article.
- Conclusions
The article discusses the scheme of a new lever mechanism of the lift, where the joints connecting the mechanism to the movable platform and the base are fixed. This type of lifting mechanism has increased stability compared to the scissor mechanism.
To design the lever mechanism of the lift, methods for kinematic analysis of the lever mechanism, kinetostatic analysis of the lever mechanism under the influence of load, research of the stability of an automotive lift with a load, and determination of the boundaries of the stability area were developed.
An experimental sample was made according to scheme of a new lever mechanism of an automotive lift, and an experimental measurement of stress in four links were carried out, which were compared with the calculated stresses. The experiment showed that the circuit of the new lever mechanism of the lift is operational, the normal stresses in the links of the mechanism have an acceptable value. All research methods described in the article can be applied only to the design of a new lift lever mechanism.
Author Response File: Author Response.docx
Reviewer 3 Report
In this study, a new lift model was proposed and validated. However, for a clearer understanding of the study, the advantages of the proposed model should be clearly listed. In parallel, the novelties of the study should be emphasized.
While there are no apparent theoretical flaws, it is imperative to furnish comprehensive information regarding the tools employed in the application process.
There is no document in English in the link "[https://immash.kz]" provided on page 2. What do the authors want to share with this link? This link should also be added to references if necessary.
The reviewer could not see the REF [13] in the article. It is necessary to review both the references and their corresponding citations within the article.
In the concluding section, it is advisable to present a qualitative assessment of the advantages offered by the proposed model, complemented by relevant performance measures.
Author Response
Response to Reviewer 3
Comment 1: In this paper, the fixation points of the scissor mechanism do not slide on the movable platform. So what is the advantage of this design over the traditional scissor mechanism? Please clarify.
Response 1: Thank you for pointing this out. The introduction lists the advantages of the proposed model. The novelty of the study is also described:
The article considers the scheme of a new lever mechanism [14,15], where the joints of the connection of the mechanism to the movable platform and the base are fixed motionless, i.e., the distance between the connection joints does not change. This scheme of the lifting mechanism has increased stability compared to the scissor mechanism. The development and research of a lifting lever mechanism with a fixed base is an urgent task. This article is devoted to the study of the proposed lift.
The novelty of the research lies in the new design of the lever mechanism of the lift, where the joints of the connection of the mechanism to the movable platform and the base are fixed motionless, which increases stability compared to the scissor mechanism; the development of methods for kinematic and kinetostatic analysis of the mechanism; the study of the stability of an automotive lift with a load on a moving platform and determination the boundaries of the stability area; the experimental measurement of stresses in mechanism links and comparison with the results of numerical calculations.
Comment 2: While there are no apparent theoretical flaws, it is imperative to furnish comprehensive information regarding the tools employed in the application process.
Response 2: Thank you for pointing this out. The text describing the recording of equations was inserted in Sections 2 and 3. Text describing 2 graphs of the dependence of the stability area on the parameters of the loaded lift is inserted in Section 4.
2.2 …
The kinematic equations of the lever mechanism were written using the vector method: first, vectors were introduced along the links of the mechanism; after that, closed vector contours (Figure 3), are considered; and finally, vector equations were written. Then the following vector equations take place:
, (1)
, (2)
. (3)
- …
Reactions in cylindrical pairs of link connections can be determined based on the general equations of dynamics in the form of the d'Alembert-Lagrange equations (14). It allows us to determine the reactions of all releasing bonds, including those with any redundancy number
, (14)
where, - active forces and reactions of connections, - inertial forces, - virtual displacement.
The equilibrium of each link was considered separately, which was influenced by: the projections of reactions in the joints, the force from the weight of the link, the projections of the force of inertia applied at the center of gravity of the link, and the moment of inertia of the link were applied. A balancing moment was also applied to the leading link 1
For example,
Link 1
The equations:
(14)
Likewise for other links. Thus, we obtained a system of 21 equations with 21 unknowns.
The following has been added in Section 5:
Let us assume that the conditions , are satisfied, then equation (32) can be written as:
(33)
It follows that or , since these are the equilibrium conditions of an automotive lift.
We assume that the equilibrium of the lift is stable; therefore, the stability of an automotive lift moving from a place with acceleration depends on the height and distance between the wheels of the lift. To illustrate the stability analysis of an automotive lift, consider a system with the following parameters:
. (34)
Then, based on formula (25), we obtain restrictions on the acceleration of the lift in the following form: for values and the restrictions would be described by the inequalities and , respectively. It follows that as the distance between the wheels of the lift increases, the stability area of moving automotive lift increases, and with increasing height it decreases.
Figure 11 plots the dependence of relative accelerations on the ratio for various . The stability area of the lift decreases with increasing displacement of the load relative to the lift.
Figure 12 shows the boundaries of the lift stability area for various values of the ratio of the mass of the load to the mass of the lift . Based on the analysis of these graphs, it can be said that with an increase in the mass of the load, the stability area of the lift decreases.
Figure 11. Graph of the dependence of relative accelerations on the ratio of the distance between the wheels to the height of the lift at various .
Figure 12. Graph of dependence on at various .
The obtained dependencies of the stability area on the parameters of the lift can be used for the optimal design of an automotive lift with a load.
Comment 3: There is no document in English in the link "[https://immash.kz]" provided on page 2. What do the authors want to share with this link? This link should also be added to references if necessary.
Response 3: Thank you for pointing this out. Link «[https://immash.kz] has been removed from the article.
Comment 4: The reviewer could not see the REF [13] in the article. It is necessary to review both the references and their corresponding citations within the article.
Response 4: Thank you for pointing this out. Links and corresponding citations in the article have been completely reworked.
Comment 5: In the concluding section, it is advisable to present a qualitative assessment of the advantages offered by the proposed model, complemented by relevant performance measures.
Response 5: Thank you for pointing this out. The conclusion has been completely revised:
- Conclusions
The article discusses the scheme of a new lever mechanism of the lift, where the joints connecting the mechanism to the movable platform and the base are fixed. This type of lifting mechanism has increased stability compared to the scissor mechanism.
To design the lever mechanism of the lift, methods for kinematic analysis of the lever mechanism, kinetostatic analysis of the lever mechanism under the influence of load, research of the stability of an automotive lift with a load, and determination of the boundaries of the stability area were developed.
An experimental sample was made according to scheme of a new lever mechanism of an automotive lift, and an experimental measurement of stress in four links were carried out, which were compared with the calculated stresses. The experiment showed that the circuit of the new lever mechanism of the lift is operational, the normal stresses in the links of the mechanism have an acceptable value. All research methods described in the article can be applied only to the design of a new lift lever mechanism.
Author Response File: Author Response.docx
Reviewer 4 Report
This paper presented the kinematic and dynamic analysis of a novel scissor mechanism. Overall, the presented concept is interesting. However, several important issues should still be addressed. Below are several comments for the authors to consider:
1. In this paper, the fixation points of the scissor mechanism do not slide on the movable platform. So what is the advantage of this design over the traditional scissor mechanism? Please clarify.
2. The caption of Figure 2 is a template. Please address this issue.
3. The literature study in the introduction section is limited. Currently, there are also other studies developing novel scissor mechanisms to realize curvilinear output motions. In my opinion, the authors should also mention those work in the introduction section as important state of the art of the scissor mechanism. Below are several related work of the curvilinear-motion scissor mechanism:
"Kinematic Modeling of Scissor-Mechanism-Based Curvilinear Actuator". https://doi.org/10.1109/IECON49645.2022.9968802
"A Versatile Pneumatic Actuator Based on Scissor Mechanisms: Design, Modeling, and Experiments". https://doi.org/10.1109/LRA.2021.3057286
Author Response
Response to Reviewer 4
Comment 1: In this paper, the fixation points of the scissor mechanism do not slide on the movable platform. So what is the advantage of this design over the traditional scissor mechanism? Please clarify.
Response 1: The introduction contains revised text in response to your comment. Thank you for pointing this out. We agree with this comment. We’ve revised the text:
The article considers the scheme of a new lever mechanism [14,15], where the joints of the connection of the mechanism to the movable platform and the base are fixed motionless, i.e., the distance between the connection joints does not change. This scheme of the lifting mechanism has increased stability compared to the scissor mechanism. The development and research of a lifting lever mechanism with a fixed base is an urgent task. This article is devoted to the study of the proposed lift.
The novelty of the research lies in the new design of the lever mechanism of the lift, where the joints of the connection of the mechanism to the movable platform and the base are fixed motionless, which increases stability compared to the scissor mechanism; the development of methods for kinematic and kinetostatic analysis of the mechanism; the study of the stability of an automotive lift with a load on a moving platform and determination the boundaries of the stability area; the experimental measurement of stresses in mechanism links and comparison with the results of numerical calculations.
Comment 2: The caption of Figure 2 is a template. Please address this issue.
Response 2: Thank you for pointing this out. We have changed the caption of Figure 2.
Figure 2 - Kinematic diagram of the new lift lever mechanism
Comment 3: The literature study in the introduction section is limited. Currently, there are also other studies developing novel scissor mechanisms to realize curvilinear output motions. In my opinion, the authors should also mention those work in the introduction section as important state of the art of the scissor mechanism. Below are several related work of the curvilinear-motion scissor mechanism:
"Kinematic Modeling of Scissor-Mechanism-Based Curvilinear Actuator". https://doi.org/10.1109/IECON49645.2022.9968802
"A Versatile Pneumatic Actuator Based on Scissor Mechanisms: Design, Modeling, and Experiments". https://doi.org/10.1109/LRA.2021.3057286
Response 3: Thank you for pointing this out. We have included an overview of new scissor mechanisms for realizing curvilinear output movements in the Introduction. References contains links to 2 articles.
Articles [12,13] discuss the modeling of a scissor mechanism based on curvilinear and pneumatic drives to implement the curvilinear movement of a moving platform.
- Sun Y., Pancheri F. and Lueth T. C., "Kinematic Modeling of Scissor-Mechanism-Based Curvilinear Actuator", IECON 2022 – 48th Annual Conference of the IEEE Industrial Electronics Society, Brussels, Belgium, 2022, pp. 1-6, DOI: 10.1109/IECON49645.2022.9968802.
- Yu B., Yang J., Du R. and Zhong Y., "A Versatile Pneumatic Actuator Based on Scissor Mechanisms: Design, Modeling, and Experiments", in IEEE Robotics and Automation Letters, vol. 6, no. 2, pp. 1288-1295, April 2021, DOI: 10.1109/LRA.2021.3057286.
Reviewer 5 Report
The paper is not well written in present form. It needs major revision:
1. I suggest the authors revise the abstract using the following format: 1- What is the purpose? 2- Research question 3- methodology 4- validation 5- results 6- why are your results significant?
2. All equations should be mentioned or explained in the main text.
3. The introduction section is written well. However, the research questions should be mentioned as well.
4. Managerial implications are missing from the paper.
5. The figures should be briefly explained.
6. The limitations of the current study should be mentioned in the conclusion section clearly based on the employed methods and data.
Extensive editing of English language required
Author Response
Response to Reviewer 5
Comment 1: All equations should be mentioned or explained in the main text.
Response 1: Thank you for pointing this out. Abstract was remade in accordance with comment 1.
Abstract:
Most of the arm lifts used in today’s industry are designed and manufactured based on the scissor mechanism. Such schemes have one drawback, when the mechanism is raised, their connection points with the base and the movable platform narrow, which leads to a letdown in its stability. This article proposes a new scheme of the lifting device, which eliminates the above disadvantage of scissor schemes. In the scheme developed by the authors, the joints connecting the mechanism to the moving platform and the base are fixed, which means that the distance between the connection points does not change, leading to its stable operation. The mechanism consists of one group of links of the second class and two groups of links of the fourth class. The article discusses the stability of the design of an automotive lift when moving with a load. The article presents the results of a kinematic, and kinetostatic analysis, a study of the stability of the lift and the results of studies of an experimental sample of the developed lift. The results of computer modeling and experiments showed that the methods described in this article allow to design of automotive lifts with new lever mechanisms.
Comment 2: I suggest the authors revise the abstract using the following format: 1- What is the purpose? 2- Research question 3- methodology 4- validation 5- results 6- why are your results significant?
Response 2: Thank you for pointing this out. Text describing the recording of the equations has been inserted in Sections 2 and 3.
2.2 …
The kinematic equations of the lever mechanism were written using the vector method: first, vectors were introduced along the links of the mechanism; after that, closed vector contours (Figure 3), are considered; and finally, vector equations were written. Then the following vector equations take place:
, (1)
, (2)
. (3)
- …
Reactions in cylindrical pairs of link connections can be determined based on the general equations of dynamics in the form of the d'Alembert-Lagrange equations (14). It allows us to determine the reactions of all releasing bonds, including those with any redundancy number
, (14)
where, - active forces and reactions of connections, - inertial forces, - virtual displacement.
…
The equilibrium of each link was considered separately, which was influenced by: the projections of reactions in the joints, the force from the weight of the link, the projections of the force of inertia applied at the center of gravity of the link, and the moment of inertia of the link were applied. A balancing moment was also applied to the leading link 1
For example, Link 1
The equations:
(15)
Likewise for other links. Thus, we obtained a system of 21 equations with 21 unknowns.
Comment 3: The introduction section is written well. However, the research questions should be mentioned as well.
Response 3: Thank you for pointing this out. We have inserted text in the Introduction with our research.
…
The article considers the scheme of a new lever mechanism [14,15], where the joints of the connection of the mechanism to the movable platform and the base are fixed motionless, i.e., the distance between the connection joints does not change. This scheme of the lifting mechanism has increased stability compared to the scissor mechanism. The development and research of a lifting lever mechanism with a fixed base is an urgent task. This article is devoted to the study of the proposed lift.
The novelty of the research lies in the new design of the lever mechanism of the lift, where the joints of the connection of the mechanism to the movable platform and the base are fixed motionless, which increases stability compared to the scissor mechanism; the development of methods for kinematic and kinetostatic analysis of the mechanism; the study of the stability of an automotive lift with a load on a moving platform and determination the boundaries of the stability area; the experimental measurement of stresses in mechanism links and comparison with the results of numerical calculations.
Comment 4: The introduction section is written well. However, the research questions should be mentioned as well.
Response 4: Thank you for pointing this out. We wrote that the experimental sample of the lever mechanism of an automotive lift has a hydraulic drive in section 5.
For the considered scheme of an automotive lift, an experimental sample of a lever lifting mechanism with a hydraulic drive was made, on which stress measurements were carried out in four links, which were then compared with the calculated stress values obtained in Section 3.
Comment 5: The figures should be briefly explained.
Response 5: Thank you for pointing this out. Text describing 2 graphs of the dependence of the stability area on the parameters of the loaded lift has been inserted in Section 4. Section 5 contains text describing 2 pictures.
…
Let us assume that the conditions are satisfied, then equation (32) can be written as:
|
(33) |
It follows that or , since these are the equilibrium conditions of an automotive lift.
We assume that the equilibrium of the lift is stable; therefore, the stability of an automotive lift moving from a place with acceleration depends on the height and distance between the wheels of the lift. To illustrate the stability analysis of an automotive lift, consider a system with the following parameters:
. (34)
Then, based on formula (25), we obtain restrictions on the acceleration of the lift in the following form: for values and the restrictions would be described by the inequalities and , respectively. It follows that as the distance between the wheels of the lift increases, the stability area of moving automotive lift increases, and with increasing height it decreases.
Figure 11 plots the dependence of relative accelerations on the ratio for various . The stability area of the lift decreases with increasing displacement of the load relative to the lift.
Figure 12 shows the boundaries of the lift stability area for various values of the ratio of the mass of the load to the mass of the lift . Based on the analysis of these graphs, it can be said that with an increase in the mass of the load, the stability area of the lift decreases.
Figure 11. Graph of the dependence of relative accelerations on the ratio of the distance between the wheels to the height of the lift at various .
Figure 12. Graph of dependence on at various .
The obtained dependencies of the stability area on the parameters of the lift can be used for the optimal design of an automotive lift with a load.
…..
As can be seen from Figures 14, 15, the study using the d'Alembert-Lagrange equations gives an approximate description of the dynamics without taking into account oscillatory phenomena in the lift mechanism during its movement. The obtained values of stress in the links are sufficient for selecting the sections of the links of the lever mechanism.
Comment 6: The limitations of the current study should be mentioned in the conclusion section clearly based on the employed methods and data.
Response 6: Thank you for pointing this out. Text which indicates that all research methods described in the article are applied only to the diagram of the new lever mechanism of the lift has been added in the Conclusions section.
- Conclusions
The article discusses the scheme of a new lever mechanism of the lift, where the joints connecting the mechanism to the movable platform and the base are fixed. This type of lifting mechanism has increased stability compared to the scissor mechanism.
To design the lever mechanism of the lift, methods for kinematic analysis of the lever mechanism, kinetostatic analysis of the lever mechanism under the influence of load, research of the stability of an automotive lift with a load, and determination of the boundaries of the stability area were developed.
An experimental sample was made according to scheme of a new lever mechanism of an automotive lift, and an experimental measurement of stress in four links were carried out, which were compared with the calculated stresses. The experiment showed that the circuit of the new lever mechanism of the lift is operational, the normal stresses in the links of the mechanism have an acceptable value. All research methods described in the article can be applied only to the design of a new lift lever mechanism.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The revised version of the manuscript is clearly an enhancement when compared to the submitted version. However, I still think that the figures 2 and 3 are rather confusing. The text given in the context of such figures is also confusing, and the choice to embed some equations in the text is not helpful. For instance, the kinematic relations given in lines 99 to 103 should be presented as equations, and carefully discussed. The vector contours indicated in line 118 should be presented in color in figure 3, to aid the reader in the derivation of equations 1 to 3. From these, all of the other equations are demonstrated and the stability conditions are evaluated.
Is there any reason for equation 16 not to be left-bracketed with a large { as all the other group of equations?
Still there is no reference on how the measurements presented in figures 14 and 15 were made, and the discussion on the lack of agreement between theory and experimental data is very superficial.
The number of references cited in the article is alarmingly small, and should be reconsidered.
Considering that the present version is a significant enhancement when compared to the previous, I think that the article can be accepted for publication once these minor corrections are incorporated in the text. No further review from me should be necessary.
Author Response
The authors revised the manuscript in accordance with the reviewer's remarks.
Reviewer 2 Report
I). The main findings of the research should be written in the conclusion section.
II). Why the first para of conclusion is written in present indefinite tense?
III). There are many grammatical and language issues in the article.
IV). Please include some lines directly after the titles of each part to help readers understand the goal of each section.
Please improve the language quality of the paper.
Author Response
The authors revised the manuscript in accordance with the reviewer's remarks.
A detailed response is provided in the attached file.
Author Response File: Author Response.pdf
Reviewer 4 Report
The authors have revised the manuscript according to my comments. Therefore, I recommend to publish this paper in this journal.
Author Response
The authors revised the manuscript in accordance with the reviewer's comments.
Reviewer 5 Report
The authors made the revision very carefully. So, strongly recommended for publications.
Extensive editing of English language required
Author Response
The authors revised the manuscript in accordance with the reviewer's comments.
Round 3
Reviewer 2 Report
The article may be accepted in its present form.
