【文章內(nèi)容簡(jiǎn)介】 paper expands the singularity analysis to a considerably broader class of robots that have three legs with a spherical joints somewhere along the the reduced determinant and grassmann–cayley operators we obtain one single generic condition for which these robots are singular and provide in a simple manner the geometric meaning of this structure of this paper is as n ii describes in detail the kinematic architecture of the class of parallel robots under n iii contains a brief background on screws and outlines the nature of the actuator screws, which are zeropitch screws acting on the centers of the spherical n iv contains an introduction to grassmann–cayley algebra which is the basic tool used for finding the singularity section also includes the rigidity matrix(or jacobian)deposition into coordinatefree section v a general example of this approach is y, section vi pares the results obtained using the present method with results obtained by other tic architecture this paper deals with 6dof parallel robots that have connectivity six between the base and the moving and roth [54] provided a survey of the possible structures that yield 6dof based on the mobility formula of gr252。bler and searched for all the possibilities that satisfy this formula with respect to the number of joints connected to any of the gsp and threelegged robots are a subset of the structures with 6dof listed by shoham and similar enumeration was provided also by podhorodeski and pittens [55], who found a class of threelegged symmetric parallel robots that have spherical joints at the platform and revolute joints in each leg to be potentially advantageous over other discussed above, most of the reports in the literature limit their analysis to structures with spherical joints located on the moving platform and revolute or prismatic joints as actuated or passive additional ions are the family of 14 robots proposed by simaan and shoham [28] which contain sphericalrevolute dyads connected to the platform, and some structures mentioned below which have revolute or prismatic joints on the this classification, we include five types of joints and more optional positions for the spherical deal with robots that have three chains connected to the moving platform, each actuated by two 1dof joints or one 2dof chains are not necessarily equal, but all have mobility and connectivity six between the base and the s the spherical joint(s), the joints taken into consideration are prismatic(p), revolute(r), helical(h), cylindrical(c), and universal(u), the first three being 1dof joints and the last two being 2dof the possibilities are shown in tables i and list contains only the robots that have equal chains, totaling 144 different structures, but robots with any possible bination of chains can also be considered as membersof this total number of binations, , is larger than 500 000, calculated as follows:ing lines this section deals with the screws that determine the platform the robots under consideration have three serial chains, the direction of each actuator screw can be determined by its reciprocity to the other joint screws in the passive spherical joint in each chain forces the actuator screws to have zeropitch(lines)and to pass through its ore, three flat pencils are created having their centers located at the spherical ing a brief introduction to the screw theory that is extensively treated in [7], [73]–[75]。we address the reciprocal screw systems of all the joints listed in section geometric result for the singularity of the aforementioned class of robots is now pared with the results obtained by other approaches in the , we pare the singularity condition described above for the 63 gsp platform with the results reported for the line geometry line geometry method distinguishes among several types of singularities, according to the relative geometric condition of he lines along the prismatic actuators [81].we show that all these singularities are particular cases of the condition provided by(17c), which is valid for the threelegged robots under consideration as well as for the 63 gsp singular configurations of this structure according to line geometry analysis include five types: 3c, 4b, 4d, 5a, and 5b [17], [36].arity analysis this section determines the singularity condition for the class of robots defined in section first part consists of finding the direction of the actuator lines of action, based on the explanation introduced in section lines pass through the spherical joint center while their directions depend on the distribution and position of the second part includes application of the approach using grassmann–cayley algebra presented in section iv for defining singularity when considering six lines attaching two every pair of lines meet at one point(the spherical joint), the solution for all the cases is symbolically equal, regardless of the points’ location in the leg or the symmetry of the exemplify the solution using three robots from the ion of the actuator screws the first example is the 3prps robot as proposed by behi [61] [see (a)].for each leg the actuated screws lie on theplane defined by the spherical joint center and the revolute joint particular,the actuator screw is perpendicular to the axis of , and the actuator screw is perpendicular to the axis of , these directions being depicted in (b).the second example is the3usr robot as proposed by simaan et al.[66][see (a)].every leg has the actuator screws lying on the plane passing through the spherical joint center and containing the revolute joint actuator screw passes through the spherical joint center and intersects the revolute joint axis rly, the actuator screw passes through the spherical joint center and intersects the revolute joint axis and , these directions being depicted in (b).the third example is the 3ppsp robot built by byun and cho [65] [see (a)].for every leg the actuated screws lie on the plane passing through the spherical joi