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Two Decades of Multidimensional Systems Research and Future Trends
Published in Krzysztof Gałkowski, Jeff David Wood, Multidimensional Signals, Circuits and Systems, 2001
• Implementation of decision algebra by cylindrical algebraic decomposition has been inspired by the development of computer algebra for symbolic and algebraic manipulations. Recent research on multivariate polynomial positivity tests when the coefficients arc symbolic (literal) and not numeric will be summarized for applications in robust system design.
Computer integrated work-space quality improvement of the C4 parallel robot CMM based on kinematic error model for using in intelligent measuring
Published in International Journal of Computer Integrated Manufacturing, 2021
Mohammad Aliakbari, Mehran Mahboubkhah, Mohammadali Sadaghian, Ahmad Barari, Sina Akhbari
Work-space is the other important factor for assessing the capabilities of a robot because it shows the operational capacity of the robot. The work-space for PKMs is smaller than that of serial robots; therefore, work-space investigation of the PKMs is important. It is impossible to graphically display the work-space of robots with a DOF greater than 3. Instead, the spatial shape of the work-space has been usually studied in different conditions, such as reachable work-space, dexterous work-space, fixed-orientation work-space and many others (Li and Angeles 2017, Merlet 2006a). The techniques of obtaining work-space are categorized into three methods, namely geometrical methods (Laribi, Romdhane, and Zeghloul 2007; Mahmoodi, Tabrizi, and Alipour 2015; Gutiérrez-Preciado, González-Palacios, and Aguilera-Cortés 2015; Li, Zhao, and Zhao 2019; Li and Angeles 2017; Gosselin and Angeles 1990; Bonev and Gosselin 2002; Rugbani and Schreve 2012; Hamdoun, El Bakkali, and Baghli 2017), discretizing methods (Staicu et al. 2018; Anvari, Ataei, and Masouleh 2019; Li and Xu 2007; Masory and Wang 1994; Monsarrat and Gosselin 2003; Dash et al. 2005; Cui et al. 2015; Zheng, Cong, and Liu 2016; Wu and Dong 2018) and numerical methods (Gharahsofloo and Rahmani 2015; Haug et al. 1996; Gosselin and Schreiber 2016). Each of these methods has advantages and limitations (Li and Angeles 2017, Merlet 2006b). Dragos et al. (2012) used a method that digitized the positioning parameters of the angles related to the kinematic couplings of the joints to obtain the Delta robot work-space. Jha et al. (2016) and Chablat, Baron, and Jha (2017) used the cylindrical algebraic decomposition algorithm to obtain the work-space of a Delta-like robot within the same family of PKMs. Aboulissane, Haiek, and El Bakkali (2018) investigated the work-space of a 3UPU PKM using a quaternion-based method that considered the rotations as a sphere. Mahboubkhah and Barari (2019) obtained the work-space of the new C4 robot using both a geometric and a discrete method. They identified all the kinematic and geometric constraints, as well as the possible collisions between the links.