Cable-driven robots (CDRs) are a special class of parallel mechanisms in which the end-effector is actuated by cables, instead of rigid-linked actuators (see Fig. 1). Alternatively known as “tendon-driven” or “wire-driven,” these CDRs are characterized by lightweight structures with low moving inertia and large workspace. These are attributed to the location of the cable winching actuators at the fixed base of the structure (instead of being located at the moving joints, as typically found in rigid-linked mechanisms). In addition, cables are spooled onto winches which makes the workspace virtually unlimited. The cable winching system generally consists of a rotary actuation unit that is coupled to a spooling drum which winds/unwinds the cable (see Fig. 2a). Other forms of cable winching systems include actuators coupled to leadscrews that directly change the cable lengths without the use of a spooling drum (see Fig. 2b). These advantages make the CDRs promising candidates for applications requiring high speed, high acceleration, and high payload. However, the flexibility of the cables limits CDRs to have lower stiffness and accuracy. On the plus side, this flexibility of the cables allows CDRs to have an intrinsically safe feature in the event of any collisions and allows them to be ideal candidates in providing safe manipulation within the human environment. As such, CDRs have received significant interest in the past two decades, with applications ranging from the factory floor to offices and homes with close proximity to their human counterparts.

One of the earliest applications of CDRs was in the form of cable-driven articulated fingers (Salisbury and Craig 1982). This cable-driven concept was then extended to numerous applications such as load lifting and positioning (Albus et al. 1993; Dallej et al. 2011), coordinate measurement (Jeong et al. 1998; Thomas et al. 2005), aircraft testing (Lafourcade and Llibre 2002), paint stripping of aircrafts (Nist robocrane cuts aircraft maintenance costs), video capturing over large areas (http://www.skycam.tv), slim dexterous manipulators for confined space applications (Buckingham et al. 2007), humanoid arms (Yang et al. 2011; Chen et al. 2013), haptics (Morizono et al. 1997; Williams 1998), and neurorehabilitation (Homma et al. 2003; Mustafa et al. 2006; Rosati et al. 2009; Mao and Agrawal 2012) (see Fig. 3). Typically, CDRs can be generally classified into two main categories: (i) under-constrained and (ii) fully constrained. For an n-DOF CDR driven by m cables, it is classified as under-constrained if m ≤ n and classified as fully constrained if m > n. Under-constrained CDRs rely on additional constraining wrenches, such as gravity (Dallej et al. 2011; Pusey et al. 2004) or springs (Behzadipour 2009; Liu and Gosselin 2011; Mustafa and Agrawal 2012a), to control the specified end-effector’s degrees-of-freedom (DOF). However, a fully constrained CDR can control all its end-effector’s DOFs using the cables only.

Unlike rigid links, cables exhibit a unilateral driving property, i.e., it can only exert a tensile force. Hence, analysis approaches obtained for rigid-linked robots cannot be directly applied, and such cable-driven robots require additional force considerations. As such, one of the earliest work to address this was by Ming and Higuchi (1994). They had mathematically proven that a single-bodied 6-DOF CDR required a minimum of seven cables in positive tension for it to be fully constrained. This paved the way for extensive efforts in force-closure analysis (i.e., achieving equilibrium with a set of positive cable tension under the influence of external wrenches) of planar and spatial CDRs with both under-constrained and fully constrained configurations (Pham et al. 2006a; Gouttefarde et al. 2006; Stump and Kumar 2006; Ferraresi et al. 2007; Diao and Ma 2008; Gouttefarde 2008; Hassan and Khajepour 2011). In addition to single-bodied CDRs, Mustafa and Agrawal (2012b) had also mathematically proved that an n-DOF multi-bodied open chain CDR requires a minimum of n + 1 cables for the entire chain to be fully constrained. Force-closure analysis is aimed at evaluating the workspace, optimizing it and minimizing the number of cables. As one would realize, too many cables will result in control complexity, increase in system setup costs, and possible cable interference. As such, due to the unilateral driving property of cables, two classical theorems in convex analysis (i.e., Carathe´odory and Steinitz Theorems) can be employed as guidelines to determine the lower and upper bounds of the minimal number of cables in order to effectively drive the CDRs (Murray et al. 1994). For an n-DOF CDR, Carathe´odory’s theorem implies that a minimum of n + 1 cables in positive tension is required, while Steinitz’s theorem implies that at most 2n cables in positive tension are required. In short, the most effective number of the driving cables ranges from n + 1 to 2n. If the number of cables is lower than n + 1, positive cable tension cannot be achieved, unless with the aid of external constraining wrenches, like gravity or springs (in the case of under-constrained CDRs). If the number of cables is greater than 2n, too many redundant cables will make the driving scheme complicated and inefficient.
This chapter will focus on the performance analysis tools for the design of CDRs and is organized as follows: Section “Mathematical Preliminaries” presents the mathematical preliminaries required in the kinetostatic analysis of CDRs. Section “Force-Closure Analysis” presents an overview of the research endeavors in force-closure algorithms, as well as generic force-closure algorithms for both single-bodied and multi-bodied CDRs. Section “Stiffness Analysis” presents a literature survey on the stiffness evaluation for CDRs, including stiffness modeling algorithms which are vital for CDRs as they suffer from rigidity issues due to the flexibilities of the cables. Section “Workspace Analysis” presents a literature survey on the workspace analysis for CDRs, as well as workspace representations and volume determination for CDRs with orientation capabilities. Several performance measures are also presented to evaluate the workspace of CDRs, which can then be utilized to optimize the design. Section “Cable Tension Planning” presents the literature survey and an algorithm to optimally generate the cable tensions during a trajectory. Finally, section “Summary” concludes with the salient points of this chapter.