Assoc. Prof. František Palčák, PhD., ÚAMM 02010
2-5520 Theory of Mechanisms
for bachelors study in 3rd year-classis, summer semester

Syllabus of course
TM_syllabus.pdf

1. Theory of mechanisms and structural parameters of MBS
• Goals in the analysis and synthesis of multibody systems
• Properties of structural parameters of multibody systems, local and global position coordinates of links, local mobility of body in geometrical constraint
• Mobility of correct multibody system, actual mobility of incorrect multibody system with slipping and rolling geometrical constraint

lecture_tm_1.pdf



2. Control curves (centrodes)
• Instantaneous slew centre (OSO) of a body
• Replacement of general motion of a body by rolling of movable centrode against fixed centrode
• Application of principle of mutually rolling centrodes in mechanisms

lecture_tm_2.pdf



3. Triad TNB and rotational motion
• Unit vectors of local position frame of body, when its origin moves along prescribed curve
• Instantaneous velocity, tangential and normal accelerations of body point. Euler’s equation for velocity of the point of rotating body
• Kinematic quantities for translational and rotational motion of a body

lecture_tm_3.pdf



4. Poissont's decomposition of general planar motion of a part in the multibody system
• Poissont‘s decomposition of general planar motion of the body to the fictive translation represented by reference point and to the fictive rotation about reference point
• Development of general formula for time derivation of the vector expressed in different spaces

lecture_tm_4.pdf



5. Velocities during simultaneous motions
• Decomposition of the body general planar motion to the simultaneous fictive carying motion and fictive local relative motion
• Resulting angular velocity of the body in the multibody system during simultaneous motions
• Resal’s angular acceleration andresulting angular acceleration of the body in the multibody system during simultaneous motions

lecture_tm_5.pdf



6. Resulting velocity and resulting acceleration
• Resulting velocity of the body in the multibody system during simultaneous motions
• Coriolis’es acceleration and resulting acceleration of the body in the multibody system during simultaneous motions

lecture_tm_6.pdf



7. Graphical methods of Poissont‘s decomposition and the simultaneous motions
• Graphical methods of Poissont‘s decomposition of general planar motion of the body and decomposition of the body general planar motion to the simultaneous fictive carying motion and fictive local relative motion application in the mechanisms

lecture_tm_7.pdf



8. Newton-Raphson numeric method for position kinematic analysis of planar mechanism
• Development of vectorial and scalar loop constraint equations for position kinematic analysis of planar mechanism
• Jacobi matrix of constraint equations
• Newton-Raphson numeric method for computing of unknown dependent global position coordinates of output links in mechanism

lecture_tm_8.pdf



9. Spherical motion of the body
• Turning and centering acceleration of the point during spherical motion of the body
• Euler’s angles for precession, nutation and local rotation
• Euler’s kinematics equations, applications of the spherical motion in mechanisms

lecture_tm_9.pdf



10. General spatial motion of a body
• Poissont‘s decomposition of general spatial motion of a body to the fictive translation of a body represented by reference point and to the fictive spherical motion of a body about reference point
• Description of general spatial motion of a body by instantaneous tangential screw motion of a body wrt axis of viration.
• Applications of general spatial motion of a body in mechanisms

lecture_tm_10.pdf



11. Kinematic position analysis of mechanisms in matrix notation
• Kinematic position analysis of spatial, open, closed and mixed mechanisms via transformation matrices
• The fictive cut across frame and arbitrary link in the basic loop of links

lecture_tm_11.pdf



12. Synthesis of planar mechanisms
• Synthesis of planar mechanisms
• Task categories of mechanisms. Mobility of mechanisms from statics, kinematics a dynamics point of view
• Continuity of statics, kinematics a dynamics according to the theory of line vectors couples
• Showtimes of computer aided analysis and synthesis of mechanisms

lecture_tm_12.pdf