On the Kinematics of Three-Link Spatial Cam Mechanisms

Abstract. In this paper, using only the linear algebra, compact expressions for the description of the relative instantaneous screw motion of two rigid bodies observed from a fixed reference frame is derived. These expressions are then used for the study of the generation of contact surfaces of three-link spatial, spherical and planar cam mechanisms. The surfaces of the cam and the follower are generated by the sweeping action of the relative instantaneous screw axis between the two bodies.Sommario. In questo lavoro, usando soltanto metodi algebrici, si ricavano espressioni compatte per la descrizione dell'atto di moto relativo elicoidale di due corpi rigidi usati in un sistema di riferimento fisso. Queste espressioni sono poi usate per la generazione di superfici coniugate di meccanismi a camma, generici, sferici e piani, a 3 membri. Le superfici della camma e del cedente sono generati dall'inviluppo dell'asse del moto istantaneo elicoidale visto dai due corpi.

[1]  L. B.,et al.  Elementary Matrices , 1939, Nature.

[2]  L. Brand,et al.  Vector and tensor analysis , 1947 .

[3]  T. B. Putsyata,et al.  Analytical dynamics , 1973 .

[4]  Sanjay G. Dhande,et al.  A Unified Approach to the Analytical Design of Three-Dimensional Cam Mechanisms , 1975 .

[5]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[6]  R. Paul Robot manipulators : mathematics, programming, and control : the computer control of robot manipulators , 1981 .

[7]  J. Argyris An excursion into large rotations , 1982 .

[8]  Jorge Angeles,et al.  Spatial kinematic chains , 1982 .

[9]  J. M. McCarthy,et al.  Dual Orthogonal Matrices in Manipulator Kinematics , 1986 .

[10]  Da Zhun Xiao,et al.  Kinematics of three dimensional gearing , 1989 .

[11]  John H. Argyris,et al.  Computer Methods in Applied Mechanics and Engineering , 1990 .

[12]  Y. Tokad,et al.  A network model for rigid-body motion , 1992 .

[13]  Y. Tokad,et al.  Network model approach to the analysis of multirigid-body systems , 1993 .

[14]  Jorge Angeles,et al.  Synthesis of contact surfaces of spherical cam-oscillating roller-follower mechanisms: a general approach , 1994 .

[15]  Jorge Angeles,et al.  The Generation of Contact Surfaces of Indexing Cam Mechanisms—A Unified Approach , 1994 .

[16]  G. Legnani,et al.  A homogeneous matrix approach to 3D kinematics and dynamics — I. Theory , 1996 .

[17]  Y. Tokad,et al.  On the fourth order finite screw system: general displacement of a point in a rigid body , 1998 .