Mathematical Complexity Research Articles

Introduction: Poetry and extremity

In thinking about the relationship between poetry and the extreme, we wanted to examine how poetry functions in a number of ways: how it creates the space – and new forms of language – to articulate events which seem inexpressible; how poets innovate to enact resistance; how poetry helps to break silences and taboos; and how poetry, and the role of the poets, is so often linked to the transgression of boundaries. The submissions we received embraced the notion of extremity in a variety of ways, considering the mathematical complexities of the work of Louis Zukofsky, for instance, and the desire for liberation in the poetry of Alejandra Pizarnik, whose life, Caio Yurgel writes, might be understood as “a long preparation for suicide”. We received work on provocative ideas about nationalism and resistance, politics and disaster, about collaboration through the extremities of climate change and COVID, and how women poets might “disrupt and disturb” patriarchal systems to construct new visions of autobiographical memory, as Paul Hetherington and Cassandra Atherton examine. The poetic responses also echo these themes, often eerily, focussing on abject bodies and the taboo, on autobiographical memories, on places overwhelmed by the devastations of extreme weather events, and on the “phenomena of perception” as a reaction to the alienating nature of pandemic ‘normal’. Importantly, the responses, both scholarly and creative, demonstrate the centrality of poetry to the difficult, wrestling with questions about selfhood and belonging, for example, as well as with language itself, its contortions and transformations in seeking to find new shapes for the ineffable.

A novel multi-stable sinusoidal chaotic map with spectacular behaviors

Chaotic behavior can be observed in continuous and discrete-time systems. This behavior can appear in one-dimensional nonlinear maps; however, having at least three state variables in flows is necessary. Due to the lower mathematical complexity and computational cost of maps, lots of research has been conducted based on them. This paper aims to present a novel one-dimensional trigonometric chaotic map that is multi-stable and can act attractively. The proposed chaotic map is first analyzed using a single sinusoidal function; then, its abilities are expanded to a map with a combination of two sinusoidal functions. The stability conditions of both maps are investigated, and their different behaviors are validated through time series, state space, and cobweb diagrams. Eventually, the influence of parameter variations on the maps’ outputs is examined by one-dimensional and two-dimensional bifurcation diagrams and Lyapunov exponent spectra. Besides, the diversity of outputs with varying initial conditions reveals this map’s multi-stability. The newly designed chaotic map can be employed in encryption applications.

WAM 3D Discrete Chaotic Map for Secure Communication Applications

Chaotic systems have become widely adopted as an effective way for secure data communications, because of its simple mathematical complexity and good security. The relationship between encryption algorithms and chaos systems has gained a lot of attention in the past few years, since it avoids the data spreading as well as lower the transmission delay and costs. In this paper a novel 3D discrete chaotic map is proposed for data encryption and secure communication and named as WAM. For secure communication, the Pecora and Carroll (P-C) method was utilized to achieve synchronization between the master system and the slave system. The simulation results of WAM 3D discrete chaotic map showed that the system has a chaotic behavior and a characteristic randomness and can pass 0-1, Lyapunov exponent (LE) and NIST tests which are usually used to check chaotic behavior. The statistical outcomes of the LE test were 0.0193, the frequency test (FT) was 0.4237, and the run test (RT) yielded a value of 0.0607. As a result, it enrich the theoretical basis of the equations and implementation of chaos, and it is superior for encryption algorithms and communication security applications.

Electromagnetic Performance Analysis of a Field-Modulated Permanent Magnet Motor Using Improved Hybrid Subdomain Method

The hybrid subdomain method (HSDM) combining conventional SDM with equivalent magnetic network has been proved to be a qualified approach to field prediction. However, this method still suffers two issues: first, the saturation effect of stator core is considered but that of rotor core is ignored, thus causing no-accuracy calculation; second, the mathematical complexity is inevitable due to adoption of virtual line-current density as extra interface conditions. This work is to develop an improved HSDM (IHSDM) for accurately and efficiently predicting the electromagnetic performance of a field-modulated permanent-magnet motor. The key of the proposed IHSDM is to fully consider magnetic saturation inside both stator and rotor cores. More importantly, the replacement of virtual-line current density by virtual-surface magnetization and current density makes interface conditions as simple as the SDM. The quantitative comparisons with conventional HSDM and FEA are conducted and the prototyping tests are also performed. It shows that the proposed IHSDM has lower time consumption and occupied memory, and electromagnetic quantities have about two times more accuracy than conventional HSDM. Additionally, a dynamic calculation is achieved by the IHSDM and verified by FEA.

CHAT SIMULATOR USING AES ENCRYPTION

Smartphones have become an integral part the lives of individuals and their priorities The present moment. The most visible uses are to chat and chat programs Most of these apps do does not provide the necessary protection and privacy information exchanged between users. Chat apps have become one of the most important and popular smartphone apps. It has the ability to exchange text messages, images and files that can freely communicate with each other. All messages must be protected and in this paper the encryption to used for secure all messages is by using AES encryption. AES (Advanced Encryption Standard) is a symmetric encryption algorithm widely used to keep data confidential in Internet networks. AES uses a block cipher with a block length of 128 bits and can encrypt data with keys consisting of 128, 192, or 256 bits. AES is one of the strongest encryption algorithms available today. It has been adopted by many organizations, including governments, banks, and technology companies. AES security is based on mathematical complexity and is difficult to crack even on ultra-fast computers. The AES encryption process involves multiple steps such as replace, move, and merge. The original data is split into smaller blocks and encrypted with the provided key. The blocks then change periodically, complicating the data patterns an attacker might find

Parameter Estimation Techniques for Photovoltaic System Modeling

In improving PV system performance, the parameters associated with electrical photovoltaic equivalent models play a pivotal role. However, due to the increased mathematical complexities and non-linear traits of PV cells, the precise prediction of these parameters is a challenging task. To estimate the parameters associated with PV models, a reliable, robust, and accurate optimization technique is needed. This paper introduces a new algorithm, Rat Swarm Optimizer (RSO), for obtaining the optimum PV cell and module parameters. The proposed method maintains an adequate balance between the exploration and exploitation phases to overcome premature particle issues. The results obtained using RSO are compared with those of other algorithms, i.e., Particle Swarm Optimization (PSO), Ant Lion Optimizer (ALO), Salp Swarm Algorithm (SSA), Harris Hawks Optimization (HHO), and Grasshopper Optimization (GOA), in this work. The modified one-diode model (MODM) and modified two-diode model (MTDM) are used to analyze the parameters of the mono-crystalline PV cell using the suggested RSO. The obtained findings imply that the parameters estimated by the suggested RSO are more accurate than those calculated by the other algorithms taken into consideration in the paper. The statistical results are compared, and it is clear that RSO is a very accurate, fast, and dependable approach for the parameter estimation of PV cells.

Impedance Analysis of Semiconductor Electrodes Biased in the Accumulation Regime for Fuels Evolution

This work explores the theory and experimental use of impedance analyses of semiconductor electrodes in the accumulation regime of semiconductor electrodes under bias. It contrasts with the established practice of measuring capacitance of the semiconductor-electrolyte biased in the depletion region to obtain semiconductor doping densities and flatband potentials (Ufb). The goal is to establish Ufb and the solution Helmholtz capacitance for an electrode in the working bias region where research is done on semiconductor electrodes for CO2 reduction and H2 evolution.The technique of measuring the capacitance of semiconductor electrodes when polarized in the depletion region was introduced by DeWald1 and is based upon the work of Garrett and Brattain2 where mathematical expressions were derived for the electric field of a semiconductor space charge region. A significant assumption in that work was that a Boltzmann expression could be used to determine the population of the majority charge carriers in the bands created through ionization of dopant. Research in this area is extensive and has been summarized.3 However, for degenerate semiconductors or for bias potentials of the semiconductor where the fermi level at the electrode surface equals the energy of the band edges, a full fermi function must be employed to describe population statistics in the solid. This is the condition commonly found in systems for fuels production at semiconductor electrodes. The solid state physics theory for this situation is known4 and describes the electric field in a semiconductor space charge region. However, it was put aside during the development of impedance evaluations in semiconductor electrochemistry because its mathematical complexity was too tedious to evaluate at that time. Only limits and simplifications were explored.5 With modern computational software, this theory has become straightforward to calculate and it becomes possible to apply it to experimental systems in a description of behavior over the entire range of doping and polarization. The nature of this full theoretical description will be discussed and illustrated through experimental measurements of Si and InP semiconductor electrodes.

Oscillations in SIR behavioural epidemic models: The interplay between behaviour and overexposure to infection

Oscillations in epidemic models including human behaviour indicate that the human factor might play a key role in the occurrence of periodically high levels of incidence and prevalence of the disease. Such phenomena can be captured even with minimal models, i.e. basic SIR or SEIR models with a reduced mathematical complexity. In such models, the effects of information-dependent changes in contact patterns are strongly affected by the function used to describe the memory of the population. In particular, the endemic equilibrium cannot be destabilized in case of exponentially fading memory but sustained oscillations are possible when the memory of the population is described by certain unimodal functions. In this work, we introduce a behavioural SIR-like model with information-dependent social distancing to investigate the interplay between individuals’ behaviour and overexposure to infection due to unconscious exposure to contagion. We use spectral analysis to show that sustained oscillations may take place even with exponentially fading memory. We show that this result holds both in case of prevalence-based and incidence-based social distancing. Furthermore, we show that the individual’s behavioural response to information may stabilize the oscillations induced by overexposure.

Allocating operating room capacity to non-elective neurosurgical patients improves access and safety for elective patients at Aarhus University Hospital

Introduction This study addresses surgical scheduling within the Department of Neurosurgery at Aarhus University Hospital (AUH). The department provides neurosurgical care to a population of 1.3 million in central Denmark, and has treatment obligations for specific neurosurgical diseases for the entire country, which has a population of 5.8 million. Efficient utilisation of the department’s four operating suites is crucial to ensure that patients have timely access to both non-elective and elective neurosurgical procedures. Historically, the elective operating room (OR) schedule was made without consideration of the possible arrival of non-elective patients; consequently, elective surgeries were often cancelled to accommodate those with more urgent indications. The challenge was thus to introduce a structured way of planning for these non-elective surgical procedures that would minimise the need for cancelling elective surgeries without decreasing overall productivity. Methods Using a mathematical model developed in a previous study at Leiden University Medical Center, the effect of allocating OR time during regular working hours for non-elective neurosurgical procedures at AUH was analysed, so that a weighted trade-off could be made between cancellations of elective patients due to an overflow of non-elective patients and unused OR time due to excessive reservation of time for non-elective patients. This allocation was tested in a six-week pilot study during weeks 24 & 25 and weeks 34–37 of 2020 before being implemented in 2021. Results In the 35 weeks following the implementation, the new allocation strategy resulted in a significant 77% decrease in the cancellation of elective neurosurgical procedures when compared with the same time period in 2019, with a significant 16% increase in surgical productivity. Conclusions This study shows that with mathematical modelling complex problems in the distribution of neurosurgical OR capacity can be solved, improving both patient safety and the working environment of neurosurgeons and OR staff.

An innovative mathematical approach to the evaluation of susceptibility in liver disorder based on fuzzy parameterized complex fuzzy hypersoft set

Several liver diseases are collectively termed as liver disorder. Usually the diagnosis of a particular disease is accomplished by considering symptoms as parameters but this is not the case for liver disorder due to the involvement of large number of symptoms relating to several diseases. The most suitable approach is to assess the susceptibility of patients for liver disorder by considering the features of relevant laboratory tests as parameters. In this study the characterization and aggregations of novel mathematical model fuzzy parameterized complex fuzzy hypersoft set (FpcFHSS) are utilized to evaluate the susceptibility of patients for liver disorder. This model is capable to cope with uncertain nature of parameters, the classification of parameters into their respective sub-parametric values and the periodicity of data collectively. The five appropriate laboratory test features relevant to liver disorder are considered as parameters and their standard ranges are opted as sub-parametric values. The uncertain nature of sub-parametric tuples is managed by assigning them a fuzzy parameterized degree which is determined with the suitable criteria. Using the matrix aggregations of FpcFHSS, an algorithm is proposed for the assessment of the susceptibility of patients for liver disorder and then validated with the help of real-world multi-attribute decision-making application. The reliability and flexibility of proposed model are discussed by its structural comparison with some pre-developed relevant models.

Compensation of the Current Imbalance of an Interleaved DC–DC Buck Converter, Sensorless Online Solution Based on Offline Fuzzy Identification and Post-Linearization

This paper presents a new approach to compensate for the current imbalance of an interleaved DC–DC buck converter (IBC), in which the current sensors are not involved in the operation of the converter when it is connected to an invariable load. The current sensors are only used during the offline identification process that builds the universal fuzzy model of the converter’s steady states. Model building involves an upstream identification phase, followed by further dimensionality reduction of the model and error minimization. The method presented here discusses the mathematical complexity of the analytical modelling of hybrid systems and opposes it with a complexity-reduced identification by learning from data. An offline rendered model of the stable and steady states of the IBC is used as a mapping of the required inverter output current to n-fold asymmetric duty cycles, which are distributed among the IBC phases to allow arbitrarily accurate load sharing. The mapping is carried out in the mathematically normalized space of variables or in the physical sense RMS values, achieving the desired robustness in a noisy environment and stability. The final and canonical feedback control is built from the standard and optimized PI controller, which is compensated by the identified IBC model correction. The only measured feedback of the whole controller is the output voltage. Even when applied to the simulation model (physical MATLAB platform) of a two-phase IBC with the built-in system asymmetry, the presented methodology is also applicable to the n-phase IBC without loss of generality.

Echocardiogram Image Quality Enhancement using Upsampling and Histogram Matching Methods

The prevalence of heart disease has been increasing in the last ten years. One of the cardiac diagnostic tools is echocardiography. Echocardiogram medical images provide essential information, including shape, size, pumping capacity, heart function abnormalities, and location of heart damage, but echocardiogram images have high noise content and poor contrast, as well as limitations due to differences in anatomy or body mass. This will affect the reading results of patient diagnosis. Therefore, image quality improvement is needed by removing noise and increasing image contrast. This research has improved image quality using a method with low mathematical complexity and a fast computational process. The method used is the Upsampling method to generate a reference image. The quality of the image produced was the Nearest Neighbor upsampling method: 2.8 dB, Bi-linear Interpolation: 2.78 dB, and Bi-cubic Interpolation: 2.73 dB. Furthermore, the image with the highest SNR value is processed with Histogram Matching to accelerate improving image quality. The Histogram Matching image increases quality by more than 50% with a SSIM value of 0.54. The required computational process to apply this method to each medical image has an average duration of 0.4 s. This result provides a higher value than several methods using linear scaling and speckle reducing.

Structure of polymeric nanoparticles encapsulating a drug – pamoic acid ion pair by scanning transmission electron microscopy

Drug-delivery systems based on polymeric nanoparticles are useful for improving drug bioavailability and/or delivery of the active ingredient for example directly to the cancerous tumour. The physical and chemical characterization of a functionalized nanoparticle system is required to measure drug loading and dispersion but also to understand and model the rate and extent of drug release to help predict performance. Many techniques can be used, however, difficulties related to structure determination and identifying the precise location of the drug fraction make mathematical prediction complex and in many published examples the final conclusions are based on assumptions regarding an expected structure. Cryogenic scanning transmission electron microscopy imaging in combination with electron energy loss spectroscopy techniques are used here to address this issue and provide a multi-modal approach to the characterisation of a self-assembled polymeric nanoparticle system based upon a polylactic acid - polyethylene glycol (PLA-PEG) block copolymer containing a hydrophobic ion-pair between pamoic acid and an active pharmaceutical ingredient (API). Results indicate a regular dispersion of spherical nanoparticles of 88 ± 9 nm diameter. The particles are shown to have a multi-layer structure consisting of a 25 nm radius hydrophobic core of PLA and pamoic acid-API material with additional enrichment of the pamoic acid-API material within the inner core (that can be off-centre), surrounded by a 9 nm dense PLA-PEG layer all with a low-density PEG surface coating of around 10 nm thickness. This structure suggests that release of the API can only occur by diffusion through or degradation of the dense, 9 nm thick PLA-PEG layer either of which is a process consistent with the previously reported steady release kinetics of the API and counter ion from these nanoparticle formulations. Establishing accurate measures of product structure enables a link to performance by providing appropriate physical parameters for future mathematical modelling of barriers controlling API release in these nanoparticle formulations.

Abstraction, mimesis and the evolution of deep learning

Deep learning developers typically rely on deep learning software frameworks (DLSFs)—simply described as pre-packaged libraries of programming components that provide high-level access to deep learning functionality. New DLSFs progressively encapsulate mathematical, statistical and computational complexity. Such higher levels of abstraction subsequently make it easier for deep learning methodology to spread through mimesis (i.e., imitation of models perceived as successful). In this study, we quantify this increase in abstraction and discuss its implications. Analyzing publicly available code from Github, we found that the introduction of DLSFs correlates both with significant increases in the number of deep learning projects and substantial reductions in the number of lines of code used. We subsequently discuss and argue the importance of abstraction in deep learning with respect to ephemeralization, technological advancement, democratization, adopting timely levels of abstraction, the emergence of mimetic deadlocks, issues related to the use of black box methods including privacy and fairness, and the concentration of technological power. Finally, we also discuss abstraction as a symptom of an ongoing technological metatransition.

Engineering and navigating calculation the flight of unmanned aircrafts of tactical class

The regulatory documents of the Ministry of Defense of Ukraine provide for navigational training of the crews of unmanned aircraft complexes and establish the necessity of having a navigational plan and an engineering-navigator flight calculation at the workplace of an external UAV pilot. The article notes that today there are no normative documents that would establish the content and scope of engineering and navigational calculations and methods of their implementation for unmanned aircraft complexes of tactical classes. The article as a whole is devoted to the consideration of issues of methodical support of navigator training of crews of unmanned aerial systems of the tactical class with an electric power plant. It is indicated that, based on the tactical and technical capabilities of UAVs of tactical classes, the nature of the tasks performed by them and the typical educational level of their external pilots, the creation of the most simplified methodology for performing basic engineering and navigational calculations of UAV flights is required. The mathematical complexity of such a method should not go beyond general secondary education. When performing navigational calculations of aircraft flights, the main difficulty is created by the problem of taking into account the influence of the wind. Simple algorithms for calculating the correction to the wind drift course, road speed and flight duration on straight sections of the route and sections of U-turns in the presence of wind are proposed. Algorithms for calculating the total need for energy resources for a flight along a given route and for separate sections of the route, including additional energy resource needs for sections of altitude gain, are proposed. Recommendations for evaluating the energy capacity of the battery available for flight performance are given. An algorithm for calculating the critical reserve of energy resources, which is necessary for the possibility of returning the UAV from the farthest point of the route under meteorological conditions for the scheduled flight time, is proposed. Options for full and abbreviated engineering and navigational calculations are offered.

Parameter Estimation of a Thermoelectric Generator by Using Salps Search Algorithm

Thermoelectric generators (TEGs) have the potential to convert waste heat into electrical energy, making them attractive for energy harvesting applications. However, accurately estimating TEG parameters from industrial systems is a complex problem due to the mathematical complex non-linearities and numerous variables involved in the TEG modeling. This paper addresses this research gap by presenting a comparative evaluation of three optimization methods, Particle Swarm Optimization (PSO), Salps Search Algorithm (SSA), and Vortex Search Algorithm (VSA), for TEG parameter estimation. The proposed integrated approach is significant as it overcomes the limitations of existing methods and provides a more accurate and rapid estimation of TEG parameters. The performance of each optimization method is evaluated in terms of root mean square error (RMSE), standard deviation, and processing time. The results indicate that all three methods perform similarly, with average RMSE errors ranging from 0.0019 W to 0.0021 W, and minimum RMSE errors ranging from 0.0017 W to 0.0018 W. However, PSO has a higher standard deviation of the RMSE errors compared to the other two methods. In addition, we present the optimized parameters achieved through the proposed optimization methods, which serve as a reference for future research and enable the comparison of various optimization strategies. The disparities observed in the optimized outcomes underscore the intricacy of the issue and underscore the importance of the integrated approach suggested for precise TEG parameter estimation.

Implementation and propagation of prestress forces in pin-jointed and tensegrity structures

The implementation of targeted prestress forces in pin-jointed structures, such as tensegrity structures, is often elusive since the activation of a prestressing device in a single cable or strut propagates forces into all other structural elements. Simultaneously controlling the internal forces and the shape of the structure through an appropriate set of length variations imposed by the devices, referred to as prestress scenario herein, has been a focus of research for over three decades. Overall, this article proposes a pedagogical state-of-the-art on the topic of prestressing and presents an alternative to the force sensitivity matrix, a commonly used method to anticipate the forces in all elements due to the unit length variation imposed on each element. Contrary to this element-to-element approach, a modal paradigm is presented here to simplify the mathematical complexity of a prestressing problem and provide a more intuitive understanding of the propagation phenomenon. Key concepts introduced in the article include the modal scenario, stiffness matrix of the self-stress modes, and propagation matrix. The propagation matrix quantifies the propagation of self-stress levels from one mode to another and offers a valuable design tool to plan the prestressing stages at each construction step or to correct errors observed in the self-stress levels. The article also introduces the self-stress scenario, which anticipates the elastic deformations caused by prestressing to achieve exact targeted forces and geometry while avoiding the propagation of prestress forces. Two examples of the application of the proposed concepts are given.

Managing Tenders in the Procurement of Advanced Medical Devices: An Original Model Based on the Net Monetary Benefit Combined With Three Clinical Endpoints.

In medical devices, recent studies have proposed original approaches for standardizing competitive tenders with the aim of promoting reproducibility, avoiding discretional decisions, and applying value-based principles. In the framework of tenders' standardization, the net monetary benefit (NMB) method has attracted much interest, but its mathematical complexity has prevented a wide application. In the present work, we developed a procurement model that simplifies clinical information management for high-technology devices purchased for our public hospitals. Our objective was to promote the application of NMB in competitive tenders, particularly at the final stage of the procurement process, where the tender scores are determined. Software to facilitate this task in everyday practice has been developed. This software is made available through the present technical report. We surveyed the most relevant literature about NMB to select the main models commonly used in the studies published thus far. Standard equations of cost-effectiveness were identified. A simplified computation model based on three clinical endpoints was developed to estimate the NMB with less mathematical complexity. This model is proposed as an alternative to the standard approach based on a full economic analysis. The model developed herein has been implemented in a web-based software freely available on the Internet. This software is accompanied by a detailed description of the equations by which the NMB is estimated. A detailed application example is reported; a real tender carried out in 2021 has been re-examined for this purpose. In this re-analysis, the new software has been used to calculate the NMB of three devices. To our knowledge, this is the first experience in which an institution of the Italian healthcare system has evaluated the NMB as a tool for determining tender scores. The model is designed to offer performance similar to a full economic analysis. Our preliminary results are encouraging and suggest a wider application of this method. This approach has important implications regarding cost-effectiveness and cost containment because a value-based procurement is known to maximize effectiveness without determining an increase in costs.

Performance comparison of IHACRES, random forest and copula-based models in rainfall-runoff simulation

In this study, two models of Random Forest and copula-based simulation were used to evaluate the accuracy and efficiency of the IHACRES rainfall-runoff model in simulating the daily discharge of the Siminehroud River in the south of Lake Urmia basin, Iran. A trivariate copula-based model was created using discharge, rainfall and temperature data on a daily scale in the period 1992–2018. Vine family models and their conditional densities were used to implement the copula-based model. By calibrating the IHACRES model and also selecting the tree sequence in accordance with the data, rainfall-runoff simulations were performed in the study area. The accuracy and efficiency of the studied models were evaluated using RMSE and NSE criteria, and also violin plot and Taylor diagram. The results of comparing the error rate of rainfall-runoff simulation in the study area showed that the vine-based model reduces the RMSE statistics by about 14.5 and 16.5%, respectively, compared to the IHACRES and Random Forest models. According to the presented diagrams, the efficiency and certainty of IHACRES and copula-based simulation models are acceptable. While the Random Forest model does not have acceptable accuracy and efficiency in the study area. The copula-based simulation model has a good performance due to the unique tree sequence as well as involving the marginal distributions fitted to the data. Although the copula-based simulation model has increased the efficiency of the model in simulating the daily discharge by about 5% compared to the IHACRES model, it is not significant compared to the mathematical complexity of the copula-based model.

Dynamic Model of a Novel Planar Cable Driven Parallel Robot with a Single Cable Loop

Cable-Driven Parallel Robots (CDPRs) are a special kind of parallel manipulator that uses cables to control the position and orientation of the mobile platform or end effector. The use of cables instead of rigid links offers some advantages over their conventional rigid counterparts. As cables can only pull but not push, the number of cables (n) required to command the end-effector is always n+1. This configuration is known as fully-constrained, and it is the most extended configuration for CDPRs. Although CDPRs have many advantages, such as their ability to cover large working areas, one of their main problems is that their working area (workspace) is limited in comparison to its frame area (planar case) or frame volume (spatial case), due to the minimum and maximum allowed tensions. Depending on these tension values, the workspace can notoriously decrease. In order to tackle this problem, lots of works focus on solving kinematics or dynamics problems for cable sagging, i.e., they take into account sagging when modelling the robot kinematic and include these poses inside the usable robot workspace. Taking into account phenomena such as this increases the mathematical complexity of the problem, and much more complex techniques are required. On the other hand, the lack of workspace problem can be tackled by adding active or passive elements to the robot design. In this sense, this paper proposes two mechanical modifications: to add passive carriages to the robot frame and to use a single cable loop to command the end-effector position and orientation. This work presents the kinematic, static, and dynamic models of the novel design and shows the gain of workspace for a planar case while taking into account different parameters of the robot.